Abstract

Applied quantum optics stands to revolutionise many aspects of information technology, provided performance can be maintained when scaled up. Silicon quantum photonics satisfies the scaling requirements of miniaturisation and manufacturability, but at 1.55 µm it suffers from problematic linear and nonlinear loss. Here we show that, by translating silicon quantum photonics to the mid-infrared, a new quantum optics platform is created which can simultaneously maximise manufacturability and miniaturisation, while reducing loss. We demonstrate the necessary platform components: photon-pair generation, single-photon detection, and high-visibility quantum interference, all at wavelengths beyond 2 µm. Across various regimes, we observe a maximum net coincidence rate of 448 ± 12 Hz, a coincidence-to-accidental ratio of 25.7 ± 1.1, and, a net two-photon quantum interference visibility of 0.993 ± 0.017. Mid-infrared silicon quantum photonics will bring new quantum applications within reach.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

1. Introduction

The mid-infrared (MIR) is the energy band of vibrations. The molecular ‘fingerprint’ region, 2–20 µm, is characterised by sharp molecular transitions, which lab-on-chip sensors can use to spectrally target molecular species in liquid and gaseous analytes [1]. Lidar systems can exploit atmospheric transparency and reduced scintillation in the MIR [2], as well as the high-power handling and reduced phase error of MIR optical phased arrays for improved reliability [3]. Much work has been done to bring integrated optics to the MIR, and silicon-on-insulator photonics dominates in the short-wavelength part of the band (the short-wave infrared), up to about 4 µm [48]. Here, silicon benefits from reduced two-photon absorption and an enhanced Kerr effect, facilitating nonlinear optical applications [9]: optical parametric oscillators and amplifiers [10], supercontinuum sources [11,12], and frequency combs [13,14] have all been developed.

Full quantum photonic technology has exquisite performance sensitivity, but stands to revolutionise how we measure, communicate, and ultimately process information [19]. It requires a huge scaling up for either integration or real-world deployment. As classical optics ventures into the MIR, quantum optics is close behind. Bulk-crystal photon-pair sources have been designed [20]; experiments with one [21], and two [22] MIR photons have been shown, with detection provided by avalanche photodiodes and up-conversion.

Silicon photonics, operating mainly around the 1.5-µm telecommunications band, has exploded in scale and functionality [23], and quantum silicon photonics has grown in tandem [24]. In silicon, quantum-correlated photon pairs are scattered from a bright pump laser via the refractive nonlinearity, by spontaneous four-wave mixing [25,26] (SFWM). Increasingly large interferometers have used these photons to power proof-of-concept quantum protocols [2730], but to go beyond a handful of photons, very low optical loss is needed.

Propagation and device losses have steadily fallen [3135], but two-photon absorption (TPA) is intrinsic. It allows two photons to excite a crystal electron, behaving like a stimulated absorption which grows with optical intensity. TPA limits the heralding efficiency of SFWM single photon sources [36], and so is a fundamental limit to the large-scale viability of silicon quantum photonics [24]. One common approach to avoiding TPA is to replace the guiding material with one with a wider band gap (to e.g. silicon nitride [37,38]). This approach loses the benefit of silicon’s globalised, large-scale manufacturing base, and also typically loses the reliability, low toxicity, and large linear and nonlinear refractive index of silicon-on-insulator waveguides. Beyond silicon’s two-photon band edge, though, around 2.1 µm, two photons carry insufficient energy to excite a crystal electron, and TPA rolls off. A resonant peak in the refractive nonlinearity here makes photon-pair sources more efficient, requiring less pump power and so stimulating even less absorption. Conventional silica cladding remains transparent, though environmental black-body noise is intensified. Compared to the telecommunication or visible bands, instrumentation and infrastructure is often less good or simply not available in the MIR. Linear loss from Rayleigh scattering off etched waveguide side-walls [39,40] is reduced at long wavelengths, and subwavelength features are more readily manufactured [35,41]. We plot the TPA coefficient βTPA, nonlinear refractive index $n_2$, and Rayleigh scattering cross-section, relative to their 1.55 µm values, in Fig. 1. Here we show that silicon photonics in the 2.1-µm band could be a good route to large-scale and low-loss quantum optics on a chip.

 

Fig. 1. Dispersion of key optical phenomena, relative to 1.55 µm values. Silicon intensity-dependent refractive index ($n_2$), and two-photon absorption coefficient ($\beta _{\textrm {TPA}}$) are shown, as well as simple Rayleigh scattering efficiency. Error bars represent one standard deviation of the mean of a Monte-Carlo-modelled distribution of system uncertainties. Values from Bristow et al. [15] and Wang et al. [16], both measured using the bulk Z-scan technique, are plotted in diamonds and squares. Waveguided measurements from Sinclair et al. [17] and our work are plotted as six- and five-pointed stars. Lines are: for $n_2$, a guide for the eye; for βTPA, a model for two-photon absorption [18].

Download Full Size | PPT Slide | PDF

Any new quantum photonic platform needs: a source of quantum light, a way to detect that light, and quantum interference. We report on all three ingredients here. We design and characterise a silicon waveguide able to generate entangled photon pairs, centred on 2.07 µm, and use classical nonlinear optics to verify its design (in §2). We deploy a new detector system, optimised for the 2-µm band, and verify its performance (§3). We then drive SFWM in the designed waveguide and observe quantum-correlated photon pairs (§4). Finally, we embed two such photon-pair sources in a reconfigurable on-chip interferometer and observe quantum interference (§5).

2. Waveguide design for MIR SFWM

Spontaneous four-wave mixing, where two pump photons are scattered by a nonlinear medium to higher and lower frequencies, conserves energy and momentum. For efficient SFWM, the phase-matching condition must be satisfied. The total wave-vector mismatch, $\Delta k = \Delta k_{\textrm {lin}} - 2\gamma P,$ must be zero. Here, $P$ is the peak pump power in the waveguide, and

$$\gamma = \frac{k_0 n_2}{A_\mathrm{eff}}$$
is the waveguide nonlinear parameter, with $n_2$ and $A_{\mathrm {eff}}$ the nonlinear refractive index and effective modal area [42], respectively. For frequencies near the pump, $\Delta k_{\mathrm {lin}} = -\beta _{2}\,\Delta \omega ^{2},$ where $\beta _2 = \mathrm {d}^{2}k/\mathrm {d}\omega ^{2}$ is the waveguide group-velocity dispersion (GVD), and $\Delta \omega$ is the pump-photon angular frequency detuning. For efficient four-wave mixing, $\beta _{2}\leq 0$, i.e. the GVD must be anomalous or zero.

We designed the waveguide shown in Fig. 2(a) ($510\times 340~{\textrm {nm}}^{2}$ cross-section, $15^{\circ }$ side-wall angle) based on the variations of $\beta _2$ and $A_{\mathrm {eff}}$ with waveguide width shown in Fig. 2(c), at $\lambda =2.071$ µm. The highly confined fundamental mode is shown in Fig. 2(b). To confirm the phase matching of our source, and estimate its bandwidth, we measure classical stimulated four-wave mixing [10,43]. We pump the waveguide source with a filtered, passively mode-locked, picosecond-pulsed, Ho-doped fibre laser (AdValue Photonics) centred at $\lambda = 2.0715$ µm and a tuneable continuous-wave laser (CW, Sacher Lasertechnik Lion) as the stimulating field. The two lasers are combined on a 1:1 fibre beam splitter and launched into the chip, via vertical grating couplers (VGC). Tuning the frequency of the CW laser, the stimulated FWM from a 7.2-mm spiral is measured on an optical spectrum analyser (OSA). Figure 2(f) shows a spectral map of the pump and stimulated emission, for various seed laser wavelengths. We observe phase-matched four-wave mixing over at least $60~{\textrm {nm}}$, limited by the grating coupler transmission bandwidth (Fig. 2(e)), implying a very wide SFWM spectrum.

 

Fig. 2. Waveguide design, simulation and experimental verification of phase-matching. a, Scanning electron micrograph of the waveguide cross section. Scale bar $100~\textrm {nm}$. b, Simulation of the fundamental transverse electric mode electric field intensity at $\lambda = 2.071$ µm. c, Simulations of the group velocity dispersion $\beta _2$ and effective modal area $A_{\textrm {eff}}$ varying the width of the source waveguide with a fixed height of $340~\textrm {nm}$ and side-wall angle of $15^{\circ }$. d, Nonlinear refraction and absorption. The maximum self-phase $\phi _{NL}$ and the normalised device transmission $\eta$ (decreasing due to residual two-photon absorption) are shown versus peak pump power. e, Single grating coupler transmission spectrum. f, Measured normalised power spectral density (PSD) of broadband stimulated four-wave mixing. A stimulating seed laser (continuous wave, tuneable, $\lambda \leq 2.071$ µm) is swept on one side of the pulsed pump at $2.071$ µm, while spectra are collected from an OSA, showing the stimulated output on the other ($\lambda \geq 2.071$ µm).

Download Full Size | PPT Slide | PDF

All previous measurements of silicon’s 2.1-µm optical nonlinearity have been in bulk samples: we confirm that the high nonlinear figure of merit measured in bulk is also present in nanoscale silicon waveguides. We use self-phase modulation and the Gerchberg-Saxton optical phase-retrieval method to estimate the waveguide nonlinearity [17,44]. Firstly, we filter the pump input pulses with a single-pass monochromator, centred at $\lambda = 2.0715$ µm. In the time domain, we use intensity autocorrelation (Femtochrome FR-103PD) with a hyperbolic secant-squared ansatz to estimate an input pulse duration of $\tau = 4.82~\textrm {ps}$ (see Supplement 1 Section S2). Monitoring the input power, we control it with a free-space knife-edge variable optical attenuator, and launch it into a 17.5-mm spiral, via VGC. For each launched power, a frequency spectrum is recorded by an OSA (Yokogawa AQ6375) at the chip output.

To retrieve the nonlinear phase, we iteratively apply Fourier and inverse-Fourier transforms between the time- and frequency-domain pictures of the output pulse [44]. By retaining the phase information in each iteration, but replacing the amplitude with our measured pulse envelope (time domain) or power spectrum (frequency domain), the algorithm converges on a self-consistent phase-amplitude model of the output pulse and a nonlinear phase for each input power. Separately, the free-carrier absorption (FCA), and TPA coefficients are extracted from the inverse transmission [45] against the input power. Finally, the phase profiles are fit with a hyperbolic secant-squared phase model and combined with a model for free-carrier effects, using the FCA coefficient estimated previously, and the free-carrier dispersion (FCD) parameter from Ref. [46]. From this, we extract the the nonlinear phase for each propagating power through the length of the waveguide, and hence the waveguide nonlinear parameter, $\gamma$. We invert Eq. (1) with an $A_{\mathrm {eff}}$ [42] mode-solved from the measured waveguide cross-section (shown in Fig. 2(a)) to determine $n_2$. Our results are summarised in Fig. 2(d) with further methods detailed in Supplement 1 Section S2. We find an effective waveguide nonlinearity of $\gamma = 203\pm 26~\textrm {W}^{-1}\textrm {m}^{-1}$ ($n_2 = 15.3\pm 1.9\times 10^{-18}~\textrm {m}^{2}\,\textrm {W}^{-1}$ in bulk) and waveguide nonlinear absorption coefficient $ {\alpha _{\mathrm {TPA}}} = 24.4\pm 3.3~\textrm {W}^{-1}\textrm {m}^{-1}$ ($ {\beta _{\mathrm {TPA}}} =0.557\pm 0.07~\textrm {cm}\cdot \textrm {GW}^{-1}$ in bulk). Here, $\alpha _{\mathrm {TPA}} = \partial \alpha /\partial P$ and $\beta _{\mathrm {TPA}} = \partial \alpha /\partial I$, where $\alpha$ is the waveguide loss coefficient, and the intensity $I=P/A_{\mathrm {eff}}$ for a waveguided power $P$ with calculated $A_{\mathrm {eff}} = 0.228$ µm2. Our measurements on waveguides are in agreement with those in bulk [15,16] (see Fig. 1). With the resonant $n_2$ enhancement, less pump is required for the same SFWM rate, and so less TPA ultimately results (see Supplementary Fig. S2). This is in addition to the modest reduction in βTPA which we observe.

3. MIR single-photon detection

To detect single photons from SFWM, sensitive detectors are required. Superconducting nanowire single-photon detectors (SNSPD) [47] have unrivalled timing jitter, dark count rates (DCR), and system detection efficiencies (SDE), and their sensitivity has been proven to at least $5$ µm [48]. We construct two SNSPD devices, which we refer to as $A$ and $B$, which incorporate superconducting nanowires into a dielectric stack optimised for absorption into the nanowire cavity at $\lambda =2.1$ µm. In each device, a 4-nm-thick niobium nitride film, deposited using magnetron sputtering, was patterned using electron-beam lithography into a 100-nm-wide meander, which becomes superconducting at our 780 mK operating point. Each is fibre coupled with anti-reflection-coated SM2000 fibre.

System detection efficiency is a key performance metric for many quantum applications. To measure it, we first estimate the photon flux at the cryostat fibre input, then optimise the detector bias current and discriminator voltage, and finally compare the input flux to the rate of electrical output pulses. We characterise how the SDE at the detector input varies with bias and excitation wavelength, using a spectrally tuneable source with calibrated variable photon flux. Light from a tuneable CW laser (1.98–2.09 µm) is attenuated to the single-photon level by a motorised knife-edge attenuator and four neutral-density filters (NENIR30A, ca. $25\,\mathrm {dB}$ attenuation). A span of SM2000 fibre connects this source to our detectors (ca. $30~\mathrm {m}$; 1.49 dB and 1.63 dB loss per channel, for detectors $A$ and $B$ respectively), at which point the output photon flux is estimated by a calibrated InGaAs photodiode (Thorlabs S148C). Finally, we connected this source to the superconducting detectors. This setup is shown in Supplementary Figure S3e. We recorded electrical output pulses from the SNSPDs for several bias settings. The peak pulse voltage is proportional to the bias current, with slopes $7.46 \,\mathrm {mV}/$ µA and $10.84 \,\mathrm {mV} /$ µA for detectors $A$ and $B$, respectively (Supplementary Fig. S3c,d). We used these fits to adapt the discrimination voltage of our time interval analyser (TIA, Picoquant PicoHarp 300), setting the discriminator $15 \,\mathrm {mV}$ and $20 \,\mathrm {mV}$ below the peak, for channels $A$ and $B$ for each bias step.

Varying the bias current, we find that the SDE of both detectors plateaus around $8$ µA, with peak SDE values of $44\pm 10\%$ and $48\pm 10\%$ for detectors $A$ and $B$, respectively. We choose to operate the two detectors at $7.9$ µA and $8.1$ µA, respectively, and we observe a timing jitter of $216~\textrm {ps}$ (full-width at half maximum, from cross-correlation), and a DCR around $5\,\mathrm {kHz}$. The dark count rate and efficiency as a function of bias at $\lambda =2.071$ µm is shown in Figs. 3(c) and 3(d). We sweep the source to measure the SDE spectrum, and plot this in Fig. 3(e). We find a sensitivity peak around 2.08 µm.

4. Observation of correlated photon pairs

For a bright source of quantum-correlated photon pairs, we use SFWM. We start with a picosecond-pulsed pump laser, centred at $2.0715$ µm, which we filter to a width of $1.0~ {\textrm {nm}}$ ($\tau = 5.78$ ps) using a double-pass grating monochromator. Controlling polarisation, we inject this pump into the fundamental TE mode of the waveguide with a vertical grating coupler (VGC; $-7.3$ dB transmission). The waveguide designed in Section 2, is laid out as shown in Fig. 3(a), wrapped into a 7.2-mm square spiral (3.2 dB/cm propagation loss) with 10-µm minimum radius Euler bends [49]. Signal and idler photons are emitted in the same spatial mode, coupled off-chip, and separated probabilistically by a 1:1 fibre beam splitter. Both channels are tightly filtered with back-to-back free-space grating monochromators ($\sim$4.5 dB insertion loss per monochromator) to achieve the required $>100~\textrm {dB}$ pump rejection [50,51]. The signal and idler filters are 1.0-nm wide, and separated from the pump by $\pm ~1.46$ THz (20.8 nm). The experimental scheme is shown in Fig. 3(b).

 

Fig. 3. Measurement of correlated photons and characterisation of superconducting detectors: a, Dark field optical micrograph of the waveguide (WG) source with vertical grating couplers (VGC); scale bar $50$ µm. b, Experimental configuration for correlated photon measurement. Polarisation controller (PC), input optical tap (9:1), photodiode (PD), beam splitter (1:1), output optical tap (99:1), superconducting nanowire single photon detector (SNSPD), time interval analyser (TIA). c, System detection efficiency (SDE) and dark count rate (DCR) with change in bias current measured at $\lambda = 2.07$ µm wavelength on detector $A$. Error bars are dominated by uncertainty in the number of launched photons. d, SDE and DCR for detector $B$. e, Spectral response of detector efficiencies at a fixed bias current of $8.4$ and $7.9$ µA for detectors $A$ and $B$, respectively. A moving average window of five points has been applied to data and the error bars are the standard deviation of the points in the sampled moving average window. f, Sample coincidence histogram integrated for 540 seconds at $0.67$-W peak pump power. The peak at zero delay corresponds to photon pairs generated in the same spontaneous four-wave mixing event. g, Measured coincidence-to-accidental ratio (CAR), net and raw coincidence rate with varying launched pump power. Error bars are one standard deviation of the random error in the measurement. The sample histogram in part f is indicated by a star.

Download Full Size | PPT Slide | PDF

Photon pairs are detected in coincidence. We observe a characteristic peak at zero relative delay from photons produced in the same SFWM event: Fig. 3(f) shows a representative histogram. We varied the launched optical power, fit each time correlation histogram with a Gaussian function, and integrated over 3 standard deviations (389 ps). These data are plotted in Fig. 3(g). At low pump power, we estimate an on-chip per-pulse generation efficiency of $11~\mathrm {MHz}/\mathrm {W}^{2}$, for watts of peak power, which at the repetition rate of our laser gives a generation probability of $0.28/\mathrm {W}^{2}$ (peak). These estimated on-chip rates naturally exclude loss (see Suppementary Section S4). We measure a maximum net coincidence rate of $112\pm 3~\textrm {Hz}$, with peak coincidence to accidental ratio (CAR) of $25.7\pm 1.1$, at a coincidence rate of $1.1~\textrm {Hz}$. We define $\mathrm {CAR}=(X_{\mathrm {raw}}-X_{\mathrm {acc}})/X_{\mathrm {acc}}$, where $X_{\mathrm {raw}}$ is the integrated coincidence count in the histogram central peak, and $X_{\mathrm {acc}}$ is the average integrated coincidence count in the side (accidental) peaks (see Supplement 1, Section S4 and Fig. S4 for singles rates).

Dark counts limit the maximum CAR $\propto \eta /\mathrm {DCR}$, so higher system transmission ($\eta$) and lower DCR will offer further CAR improvements. We discuss these in Section 6. On a longer 17.5-mm waveguide, we measured a peak net coincidence rate of $224~\textrm {Hz}$ (Supplementary Fig. S2c). Due to the simple separation of the signal and idler with a beam splitter, the actual pair-production rates are $4\times$ the measured net rates. Thus, we observe true rates of $448~\textrm {Hz}$ and $896~\textrm {Hz}$ for the two waveguides, respectively (see Supplement 1, Section S4).

5. On-chip quantum interference

The indistinguishability of generated photons, confirmed by high-visibility quantum interference between them, is an essential platform resource. The Hong-Ou-Mandel (HOM) effect causes two indistinguishable single photons to strictly bunch at the outputs of a balanced beam splitter [52]. Here, we demonstrate on-chip quantum interference using a time-reversed HOM experiment [53], with experimental setup and waveguide circuit shown in Figs. 4(a) and 4(b).

 

Fig. 4. Experimental measurement of on-chip quantum interference: a, Dark-field optical micrograph of the time-reversed Hong-Ou-Mandel experiment. Multimode interference coupler (MMI), waveguides (7.4-mm, WGs), thermo-optic phase modulator (TOPM), directional coupler (DC), asymmetric Mach-Zehnder interferometer (AMZI), wirebond (WB). Scale bar 50 µm. b, Experimental scheme. A pump laser is polarisation controlled (PC), filtered with a double-pass monochromator, and coupled into the waveguide circuit, with a monitor photodiode (PD) at the input tap (9:1). A controller provides DC-voltage control of the on-chip quantum state. The signal and idler photons are demultiplexed, filtered and then detected with superconducting nanowire detectors (SNSPD) and a time interval analyser (TIA). c, Quantum and classical interference fringes with varying on-chip phase $\phi$, with fitted accidental-subtracted (net) visibility $V = 0.993\pm 0.017$.

Download Full Size | PPT Slide | PDF

After filtering the pump as before, we couple it onto the chip through a VGC. We set the on-chip peak pump power to $0.32~\textrm {W}$, corresponding to a CAR of $19.3$ and $\sim 0.03$ pairs per pulse. The pump field is equally split between the two photon-pair sources, with a balanced $1\times 2$ multimode interference (MMI) coupler. Both 7.39-mm sources are coherently pumped and the relative phase $\phi$ between the two arms is varied with a thermo-optic phase modulator (see Supplement 1, Section S1 for details of integrated optics). The biphoton state then interferes on a balanced directional coupler ($R = 0.49 \pm 0.02$). Coherent pumping of both sources produces SFWM photon pairs in superposition, and the quantum state at the directional coupler output is

$$\begin{aligned} \vert {\psi}\rangle &= \frac{\sin\phi}{\sqrt{2}}\big(\vert {0_s0_i}\rangle_A\vert {1_s1_i}\rangle_B - \vert {1_s1_i}\rangle_A\vert {0_s0_i}\rangle_B\big) \\ &+ \frac{\cos\phi}{\sqrt{2}}\big(\vert {1_s0_i}\rangle_A\vert {0_s1_i}\rangle_B + \vert {0_s1_i}\rangle_A\vert {1_s0_i}\rangle_B\big), \end{aligned}$$
with signal and idler frequency ($s,i$) and spatial modes ($A,B$) in subscript (see Supplement 1, Section S5 for more details). SFWM photons are then frequency demultiplexed on-chip with asymmetric Mach-Zehnder interferometers. Off chip, we reject the pump laser, and use coincidence detection to estimate $|\langle {1_s0_i}|_A\langle {0_s1_i}|_B\vert {\psi }\rangle|^{2}$.

We observe characteristic half-period interference fringes in the coincidences [53,54], as the on-chip phase $\phi$ is varied, consistent with Eq. (2) (see Fig. 4(c)). This quantum interference has a net visibility of $V = 0.993 \pm 0.017$ (with $0.862\pm 0.014$ raw). We calculate the visibility as $V = (X_{\mathrm {max}} - X_{\mathrm {min}})/(X_{\mathrm {max}} + X_{\mathrm {min}})$, where $X_{\mathrm {max}}$ and $X_{\mathrm {min}}$ are the maximum and minimum coincidence count rates of the sinusoidal fit. This compares favourably to performance at 1.55 µm on chip [53,5557], and at 2.1 µm in bulk [58]. We observe coincidence rates of up to $5.5\pm 0.2~\textrm {Hz}$ at the interference peak. Simultaneously measuring all four chip outputs would double the observed rate. For perfect interference, the raw visibility is limited to $V \leq \mathrm {CAR}/(2 + \mathrm {CAR}) = 0.91$.

6. Discussion and conclusions

Despite operating in the 2-µm band, we see from Fig. 2(d) that two-photon absorption remains, albeit reduced from its strength at $1.55$ µm. This is to be expected at room temperature and at $\lambda =2.07$ µm, as silicon’s indirect band gap gives a TPA cut-off around $2.21$ µm (Fig. 1). Our waveguided estimates of both nonlinear absorption and refraction are in broad agreement with literature values for bulk silicon [15,16]. At low temperatures, a blue-shift in the band edge causes a blue-shift in the TPA cut-off [59], to 2.15 µm. Future room-temperature experiments will benefit from 2.2-µm laser development (e.g. semiconductor disk lasers [60]), while experiments integrating SNSPDs on-chip or in-package will benefit from this low-temperature shift of the TPA cut off.

Black-body radiation from our room-temperature apparatus was a source of noise in our measurements, reducing the CAR in conjunction with our low system efficiency. As seen in Figs. 3(c) and 3(d), the ‘dark’ count rate (DCR), collected with the lights and laser turned off, plateaus, rather than growing exponentially with bias, because environmental black-body photons nonetheless illuminate the detectors (see Supplementary Figs. S3a,b). Black-body noise will be suppressed by a cold filter. On the other hand, system efficiency will benefit from the latest advances in silicon photonic technology in the MIR [4]. Lower DCR and higher system efficiency will both improve the peak CAR and the raw interference visibility as a consequence.

In demonstrating a bright source of photon pairs, efficient single-photon detectors, and high-visibility quantum interference, we have provided all the necessary ingredients for a dense, manufacturable, and high-performance platform for applied quantum optics.

Funding

Leverhulme Trust (ECF-2018-276); Engineering and Physical Sciences Research Council (EP/L015730/1, EP/L024020/1, EP/M024458/1, EP/N015126/1); European Research Council (ERC-2014-STG 640079).

Acknowledgements

We thank D. Bonneau, A. McMillan, B.D.J. Sayers, B. Kuyken, M. Nedeljkovic, K. Erotokritou, G. Taylor, and R.H. Hadfield for their valuable inputs throughout the long gestation of this work, and are grateful to L. Kling, and G.D. Marshall for their advice and support. The chip reported here was fabricated as part of the CORNERSTONE project (EPSRC EP/L021129/1), and we are especially grateful to C. Littlejohns for his efforts therein.

Disclosures

The authors declare no conflicts of interest.

Data Availability

Data and computer code that support the findings of this study are available at the University of Bristol’s data repository, data.bris (Digital object identifier: 10.5523/bris.1ckssqmdmilj023w7f0gr36o06). Other information is available from the authors upon reasonable request.

See Supplement 1 for supporting content.

References

1. M. Sieger and B. Mizaikoff, “Toward on-chip mid-infrared sensors,” Anal. Chem. 88(11), 5562–5573 (2016). [CrossRef]  

2. P. Corrigan, R. Martini, E. A. Whittaker, and C. Bethea, “Quantum cascade lasers and the kruse model in free space optical communication,” Opt. Express 17(6), 4355–4359 (2009). [CrossRef]  

3. M. Prost, Y.-C. Ling, S. Cakmakyapan, Y. Zhang, K. Zhang, J. Hu, Y. Zhang, and S. B. Yoo, “MWIR solid-state optical phased array beam steering using germanium-silicon photonic platform,” in Optical Fiber Communication Conference, (Optical Society of America, 2019), pp. M4E–3.

4. Y. Zou, S. Chakravarty, C.-J. Chung, X. Xu, and R. T. Chen, “Mid-infrared silicon photonic waveguides and devices [Invited],” Photonics Res. 6(4), 254–276 (2018). [CrossRef]  

5. M. M. Milošević, M. Nedeljkovic, T. M. Ben Masaud, E. Jaberansary, H. M. Chong, N. G. Emerson, G. T. Reed, and G. Z. Mashanovich, “Silicon waveguides and devices for the mid-infrared,” Appl. Phys. Lett. 101(12), 121105 (2012). [CrossRef]  

6. M. Nedeljkovic, A. Khokhar, Y. Hu, X. Chen, J. S. Penades, S. Stankovic, H. Chong, D. Thomson, F. Gardes, G. Reed, and G. Mashanovich, “Silicon photonic devices and platforms for the mid-infrared,” Opt. Mater. Express 3(9), 1205–1214 (2013). [CrossRef]  

7. S. A. Miller, M. Yu, X. Ji, A. G. Griffith, J. Cardenas, A. L. Gaeta, and M. Lipson, “Low-loss silicon platform for broadband mid-infrared photonics,” Optica 4(7), 707–712 (2017). [CrossRef]  

8. N. Hattasan, B. Kuyken, F. Leo, E. M. Ryckeboer, D. Vermeulen, and G. Roelkens, “High-efficiency SOI fiber-to-chip grating couplers and low-loss waveguides for the short-wave infrared,” IEEE Photonics Technol. Lett. 24(17), 1536–1538 (2012). [CrossRef]  

9. B. Jalali, “Silicon photonics: Nonlinear optics in the mid-infrared,” Nat. Photonics 4(8), 506–508 (2010). [CrossRef]  

10. X. Liu, R. M. Osgood Jr, Y. A. Vlasov, and W. M. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics 4(8), 557–560 (2010). [CrossRef]  

11. B. Kuyken, X. Liu, R. M. Osgood, R. Baets, G. Roelkens, and W. M. Green, “Mid-infrared to telecom-band supercontinuum generation in highly nonlinear silicon-on-insulator wire waveguides,” Opt. Express 19(21), 20172–20181 (2011). [CrossRef]  

12. R. Kou, T. Hatakeyama, J. Horng, J.-H. Kang, Y. Wang, X. Zhang, and F. Wang, “Mid-IR broadband supercontinuum generation from a suspended silicon waveguide,” Opt. Lett. 43(6), 1387–1390 (2018). [CrossRef]  

13. A. G. Griffith, R. K. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6(1), 6299 (2015). [CrossRef]  

14. M. Yu, Y. Okawachi, A. G. Griffith, N. Picqué, M. Lipson, and A. L. Gaeta, “Silicon-chip-based mid-infrared dual-comb spectroscopy,” Nat. Commun. 9(1), 1869 (2018). [CrossRef]  

15. A. D. Bristow, N. Rotenberg, and H. M. Van Driel, “Two-photon absorption and kerr coefficients of silicon for 850–2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007). [CrossRef]  

16. T. Wang, N. Venkatram, J. Gosciniak, Y. Cui, G. Qian, W. Ji, and D. T. Tan, “Multi-photon absorption and third-order nonlinearity in silicon at mid-infrared wavelengths,” Opt. Express 21(26), 32192–32198 (2013). [CrossRef]  

17. G. F. Sinclair, N. A. Tyler, D. Sahin, J. Barreto, and M. G. Thompson, “Temperature dependence of the kerr nonlinearity and two-photon absorption in a silicon waveguide at 1.55 µm,” Phys. Rev. Appl. 11(4), 044084 (2019). [CrossRef]  

18. H. Garcia and R. Kalyanaraman, “Phonon-assisted two-photon absorption in the presence of a DC-field: the nonlinear Franz–Keldysh effect in indirect gap semiconductors,” J. Phys. B: At., Mol. Opt. Phys. 39(12), 2737–2746 (2006). [CrossRef]  

19. J. L. O’Brien, A. Furusawa, and J. Vučković, “Photonic quantum technologies,” Nat. Photonics 3(12), 687–695 (2009). [CrossRef]  

20. R. A. McCracken, F. Graffitti, and A. Fedrizzi, “Numerical investigation of mid-infrared single-photon generation,” J. Opt. Soc. Am. B 35(12), C38–C48 (2018). [CrossRef]  

21. Y. M. Sua, H. Fan, A. Shahverdi, J.-Y. Chen, and Y.-P. Huang, “Direct generation and detection of quantum correlated photons with 3.2 um wavelength spacing,” Sci. Rep. 7(1), 17494 (2017). [CrossRef]  

22. M. Mancinelli, A. Trenti, S. Piccione, G. Fontana, J. S. Dam, P. Tidemand-Lichtenberg, C. Pedersen, and L. Pavesi, “Mid-infrared coincidence measurements on twin photons at room temperature,” Nat. Commun. 8(1), 15184 (2017). [CrossRef]  

23. L. Pavesi and D. J. Lockwood, Silicon photonics III: Systems and applications, vol. 122 (Springer Science & Business Media, 2016).

24. J. W. Silverstone, D. Bonneau, J. L. O’Brien, and M. G. Thompson, “Silicon quantum photonics,” IEEE J. Sel. Top. Quantum Electron. 22(6), 390–402 (2016). [CrossRef]  

25. J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14(25), 12388–12393 (2006). [CrossRef]  

26. S. Clemmen, K. P. Huy, W. Bogaerts, R. G. Baets, P. Emplit, and S. Massar, “Continuous wave photon pair generation in silicon-on-insulator waveguides and ring resonators,” Opt. Express 17(19), 16558–16570 (2009). [CrossRef]  

27. N. C. Harris, J. Carolan, D. Bunandar, M. Prabhu, M. Hochberg, T. Baehr-Jones, M. L. Fanto, A. M. Smith, C. C. Tison, P. M. Alsing, and D. Englund, “Linear programmable nanophotonic processors,” Optica 5(12), 1623 (2018). [CrossRef]  

28. J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360(6386), 285–291 (2018). [CrossRef]  

29. J. C. Adcock, C. Vigliar, R. Santagati, J. W. Silverstone, and M. G. Thompson, “Programmable four-photon graph states on a silicon chip,” Nat. Commun. 10(1), 3528 (2019). [CrossRef]  

30. S. Paesani, Y. Ding, R. Santagati, L. Chakhmakhchyan, C. Vigliar, K. Rottwitt, L. K. Oxenløwe, J. Wang, M. G. Thompson, and A. Laing, “Generation and sampling of quantum states of light in a silicon chip,” Nat. Phys. 15(9), 925–929 (2019). [CrossRef]  

31. J. Cardenas, C. B. Poitras, J. T. Robinson, K. Preston, L. Chen, and M. Lipson, “Low loss etchless silicon photonic waveguides,” Opt. Express 17(6), 4752–4757 (2009). [CrossRef]  

32. D. H. Lee, S. J. Choo, U. Jung, K. W. Lee, K. W. Kim, and J. H. Park, “Low-loss silicon waveguides with sidewall roughness reduction using a SiO2 hard mask and fluorine-based dry etching,” J. Micromech. Microeng. 25(1), 015003 (2015). [CrossRef]  

33. D. Benedikovic, P. Cheben, J. H. Schmid, D.-X. Xu, B. Lamontagne, S. Wang, J. Lapointe, R. Halir, A. Ortega-Moñux, S. Janz, and M. Dado, “Subwavelength index engineered surface grating coupler with sub-decibel efficiency for 220-nm silicon-on-insulator waveguides,” Opt. Express 23(17), 22628–22635 (2015). [CrossRef]  

34. Z. Sheng, Z. Wang, C. Qiu, L. Li, A. Pang, A. Wu, X. Wang, S. Zou, and F. Gan, “A compact and low-loss MMI coupler fabricated with CMOS technology,” IEEE Photonics J. 4(6), 2272–2277 (2012). [CrossRef]  

35. M.-S. Rouifed, C. G. Littlejohns, G. X. Tina, Q. Haodong, T. Hu, Z. Zhang, C. Liu, G. T. Reed, and H. Wang, “Low loss SOI waveguides and MMIs at the MIR wavelength of 2 µm,” IEEE Photonics Technol. Lett. 28(24), 2827–2829 (2016). [CrossRef]  

36. C. A. Husko, A. S. Clark, M. J. Collins, A. De Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, “Multi-photon absorption limits to heralded single photon sources,” Sci. Rep. 3(1), 3087 (2013). [CrossRef]  

37. X. Ji, F. A. Barbosa, S. P. Roberts, A. Dutt, J. Cardenas, Y. Okawachi, A. Bryant, A. L. Gaeta, and M. Lipson, “Ultra-low-loss on-chip resonators with sub-milliwatt parametric oscillation threshold,” Optica 4(6), 619–624 (2017). [CrossRef]  

38. S. Ramelow, A. Farsi, S. Clemmen, D. Orquiza, K. Luke, M. Lipson, and A. L. Gaeta, “Silicon-nitride platform for narrowband entangled photon generation,” arXiv preprint arXiv:1508.04358 (2015).

39. D. E. Hagan and A. P. Knights, “Mechanisms for optical loss in SOI waveguides for mid-infrared wavelengths around 2 µm,” J. Opt. 19(2), 025801 (2017). [CrossRef]  

40. F. Grillot, L. Vivien, S. Laval, D. Pascal, and E. Cassan, “Size influence on the propagation loss induced by sidewall roughness in ultrasmall soi waveguides,” IEEE Photonics Technol. Lett. 16(7), 1661–1663 (2004). [CrossRef]  

41. P. Cheben, R. Halir, J. H. Schmid, H. A. Atwater, and D. R. Smith, “Subwavelength integrated photonics,” Nature 560(7720), 565–572 (2018). [CrossRef]  

42. I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Effective mode area and its optimization in silicon-nanocrystal waveguides,” Opt. Lett. 37(12), 2295–2297 (2012). [CrossRef]  

43. M. Liscidini and J. Sipe, “Stimulated emission tomography,” Phys. Rev. Lett. 111(19), 193602 (2013). [CrossRef]  

44. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21(15), 2758–2769 (1982). [CrossRef]  

45. J. F. Reintjes and J. C. McGroddy, “Indirect two-photon transitions in si at 1.06 µm,” Phys. Rev. Lett. 30(19), 901–903 (1973). [CrossRef]  

46. L. Yin and G. P. Agrawal, “Impact of two-photon absorption on self-phase modulation in silicon waveguides,” Opt. Lett. 32(14), 2031–2033 (2007). [CrossRef]  

47. C. M. Natarajan, M. G. Tanner, and R. H. Hadfield, “Superconducting nanowire single-photon detectors: physics and applications,” Supercond. Sci. Technol. 25(6), 063001 (2012). [CrossRef]  

48. F. Marsili, F. Bellei, F. Najafi, A. E. Dane, E. A. Dauler, R. J. Molnar, and K. K. Berggren, “Efficient single photon detection from 500 nm to 5 µm wavelength,” Nano Lett. 12(9), 4799–4804 (2012). [CrossRef]  

49. M. Cherchi, S. Ylinen, M. Harjanne, M. Kapulainen, and T. Aalto, “Dramatic size reduction of waveguide bends on a micron-scale silicon photonic platform,” Opt. Express 21(15), 17814–17823 (2013). [CrossRef]  

50. M. Piekarek, D. Bonneau, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “High-extinction ratio integrated photonic filters for silicon quantum photonics,” Opt. Lett. 42(4), 815–818 (2017). [CrossRef]  

51. M. Savanier, R. Kumar, and S. Mookherjea, “Photon pair generation from compact silicon microring resonators using microwatt-level pump powers,” Opt. Express 24(4), 3313–3328 (2016). [CrossRef]  

52. C.-K. Hong, Z.-Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59(18), 2044–2046 (1987). [CrossRef]  

53. J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, “On-chip quantum interference between silicon photon-pair sources,” Nat. Photonics 8(2), 104–108 (2014). [CrossRef]  

54. J. C. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3(6), 346–350 (2009). [CrossRef]  

55. J. He, B. A. Bell, A. Casas-Bedoya, Y. Zhang, A. S. Clark, C. Xiong, and B. J. Eggleton, “Ultracompact quantum splitter of degenerate photon pairs,” Optica 2(9), 779–782 (2015). [CrossRef]  

56. S. F. Preble, M. L. Fanto, J. A. Steidle, C. C. Tison, G. A. Howland, Z. Wang, and P. M. Alsing, “On-chip quantum interference from a single silicon ring-resonator source,” Phys. Rev. Appl. 4(2), 021001 (2015). [CrossRef]  

57. H. Jin, F. Liu, P. Xu, J. Xia, M. Zhong, Y. Yuan, J. Zhou, Y. Gong, W. Wang, and S. Zhu, “On-chip generation and manipulation of entangled photons based on reconfigurable lithium-niobate waveguide circuits,” Phys. Rev. Lett. 113(10), 103601 (2014). [CrossRef]  

58. S. Prabhakar, T. Shields, A. C. Dada, M. Ebrahim, G. G. Taylor, D. Morozov, K. Erotokritou, S. Miki, M. Yabuno, H. Terai, C. Gawith, M. Kues, L. Caspani, R. H. Hadfield, and M. Clerici, “Two-photon quantum interference and entanglement at 2.1 µm,” Sci. Adv. 6(13), eaay5195 (2020). [CrossRef]  

59. M. Cardona, T. A. Meyer, and M. L. W. Thewalt, “Temperature Dependence of the Energy Gap of Semiconductors in the Low-Temperature Limit,” Phys. Rev. Lett. 92(19), 196403 (2004). [CrossRef]  

60. S. Kaspar, M. Rattunde, T. Topper, R. Moser, S. Adler, C. Manz, K. Kohler, and J. Wagner, “Recent Advances in 2-µm GaSb-Based Semiconductor Disk Laser—Power Scaling, Narrow-Linewidth and Short-Pulse Operation,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1501908 (2013). [CrossRef]  

References

  • View by:
  • |
  • |
  • |

  1. M. Sieger and B. Mizaikoff, “Toward on-chip mid-infrared sensors,” Anal. Chem. 88(11), 5562–5573 (2016).
    [Crossref]
  2. P. Corrigan, R. Martini, E. A. Whittaker, and C. Bethea, “Quantum cascade lasers and the kruse model in free space optical communication,” Opt. Express 17(6), 4355–4359 (2009).
    [Crossref]
  3. M. Prost, Y.-C. Ling, S. Cakmakyapan, Y. Zhang, K. Zhang, J. Hu, Y. Zhang, and S. B. Yoo, “MWIR solid-state optical phased array beam steering using germanium-silicon photonic platform,” in Optical Fiber Communication Conference, (Optical Society of America, 2019), pp. M4E–3.
  4. Y. Zou, S. Chakravarty, C.-J. Chung, X. Xu, and R. T. Chen, “Mid-infrared silicon photonic waveguides and devices [Invited],” Photonics Res. 6(4), 254–276 (2018).
    [Crossref]
  5. M. M. Milošević, M. Nedeljkovic, T. M. Ben Masaud, E. Jaberansary, H. M. Chong, N. G. Emerson, G. T. Reed, and G. Z. Mashanovich, “Silicon waveguides and devices for the mid-infrared,” Appl. Phys. Lett. 101(12), 121105 (2012).
    [Crossref]
  6. M. Nedeljkovic, A. Khokhar, Y. Hu, X. Chen, J. S. Penades, S. Stankovic, H. Chong, D. Thomson, F. Gardes, G. Reed, and G. Mashanovich, “Silicon photonic devices and platforms for the mid-infrared,” Opt. Mater. Express 3(9), 1205–1214 (2013).
    [Crossref]
  7. S. A. Miller, M. Yu, X. Ji, A. G. Griffith, J. Cardenas, A. L. Gaeta, and M. Lipson, “Low-loss silicon platform for broadband mid-infrared photonics,” Optica 4(7), 707–712 (2017).
    [Crossref]
  8. N. Hattasan, B. Kuyken, F. Leo, E. M. Ryckeboer, D. Vermeulen, and G. Roelkens, “High-efficiency SOI fiber-to-chip grating couplers and low-loss waveguides for the short-wave infrared,” IEEE Photonics Technol. Lett. 24(17), 1536–1538 (2012).
    [Crossref]
  9. B. Jalali, “Silicon photonics: Nonlinear optics in the mid-infrared,” Nat. Photonics 4(8), 506–508 (2010).
    [Crossref]
  10. X. Liu, R. M. Osgood Jr, Y. A. Vlasov, and W. M. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics 4(8), 557–560 (2010).
    [Crossref]
  11. B. Kuyken, X. Liu, R. M. Osgood, R. Baets, G. Roelkens, and W. M. Green, “Mid-infrared to telecom-band supercontinuum generation in highly nonlinear silicon-on-insulator wire waveguides,” Opt. Express 19(21), 20172–20181 (2011).
    [Crossref]
  12. R. Kou, T. Hatakeyama, J. Horng, J.-H. Kang, Y. Wang, X. Zhang, and F. Wang, “Mid-IR broadband supercontinuum generation from a suspended silicon waveguide,” Opt. Lett. 43(6), 1387–1390 (2018).
    [Crossref]
  13. A. G. Griffith, R. K. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6(1), 6299 (2015).
    [Crossref]
  14. M. Yu, Y. Okawachi, A. G. Griffith, N. Picqué, M. Lipson, and A. L. Gaeta, “Silicon-chip-based mid-infrared dual-comb spectroscopy,” Nat. Commun. 9(1), 1869 (2018).
    [Crossref]
  15. A. D. Bristow, N. Rotenberg, and H. M. Van Driel, “Two-photon absorption and kerr coefficients of silicon for 850–2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
    [Crossref]
  16. T. Wang, N. Venkatram, J. Gosciniak, Y. Cui, G. Qian, W. Ji, and D. T. Tan, “Multi-photon absorption and third-order nonlinearity in silicon at mid-infrared wavelengths,” Opt. Express 21(26), 32192–32198 (2013).
    [Crossref]
  17. G. F. Sinclair, N. A. Tyler, D. Sahin, J. Barreto, and M. G. Thompson, “Temperature dependence of the kerr nonlinearity and two-photon absorption in a silicon waveguide at 1.55 µm,” Phys. Rev. Appl. 11(4), 044084 (2019).
    [Crossref]
  18. H. Garcia and R. Kalyanaraman, “Phonon-assisted two-photon absorption in the presence of a DC-field: the nonlinear Franz–Keldysh effect in indirect gap semiconductors,” J. Phys. B: At., Mol. Opt. Phys. 39(12), 2737–2746 (2006).
    [Crossref]
  19. J. L. O’Brien, A. Furusawa, and J. Vučković, “Photonic quantum technologies,” Nat. Photonics 3(12), 687–695 (2009).
    [Crossref]
  20. R. A. McCracken, F. Graffitti, and A. Fedrizzi, “Numerical investigation of mid-infrared single-photon generation,” J. Opt. Soc. Am. B 35(12), C38–C48 (2018).
    [Crossref]
  21. Y. M. Sua, H. Fan, A. Shahverdi, J.-Y. Chen, and Y.-P. Huang, “Direct generation and detection of quantum correlated photons with 3.2 um wavelength spacing,” Sci. Rep. 7(1), 17494 (2017).
    [Crossref]
  22. M. Mancinelli, A. Trenti, S. Piccione, G. Fontana, J. S. Dam, P. Tidemand-Lichtenberg, C. Pedersen, and L. Pavesi, “Mid-infrared coincidence measurements on twin photons at room temperature,” Nat. Commun. 8(1), 15184 (2017).
    [Crossref]
  23. L. Pavesi and D. J. Lockwood, Silicon photonics III: Systems and applications, vol. 122 (Springer Science & Business Media, 2016).
  24. J. W. Silverstone, D. Bonneau, J. L. O’Brien, and M. G. Thompson, “Silicon quantum photonics,” IEEE J. Sel. Top. Quantum Electron. 22(6), 390–402 (2016).
    [Crossref]
  25. J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14(25), 12388–12393 (2006).
    [Crossref]
  26. S. Clemmen, K. P. Huy, W. Bogaerts, R. G. Baets, P. Emplit, and S. Massar, “Continuous wave photon pair generation in silicon-on-insulator waveguides and ring resonators,” Opt. Express 17(19), 16558–16570 (2009).
    [Crossref]
  27. N. C. Harris, J. Carolan, D. Bunandar, M. Prabhu, M. Hochberg, T. Baehr-Jones, M. L. Fanto, A. M. Smith, C. C. Tison, P. M. Alsing, and D. Englund, “Linear programmable nanophotonic processors,” Optica 5(12), 1623 (2018).
    [Crossref]
  28. J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360(6386), 285–291 (2018).
    [Crossref]
  29. J. C. Adcock, C. Vigliar, R. Santagati, J. W. Silverstone, and M. G. Thompson, “Programmable four-photon graph states on a silicon chip,” Nat. Commun. 10(1), 3528 (2019).
    [Crossref]
  30. S. Paesani, Y. Ding, R. Santagati, L. Chakhmakhchyan, C. Vigliar, K. Rottwitt, L. K. Oxenløwe, J. Wang, M. G. Thompson, and A. Laing, “Generation and sampling of quantum states of light in a silicon chip,” Nat. Phys. 15(9), 925–929 (2019).
    [Crossref]
  31. J. Cardenas, C. B. Poitras, J. T. Robinson, K. Preston, L. Chen, and M. Lipson, “Low loss etchless silicon photonic waveguides,” Opt. Express 17(6), 4752–4757 (2009).
    [Crossref]
  32. D. H. Lee, S. J. Choo, U. Jung, K. W. Lee, K. W. Kim, and J. H. Park, “Low-loss silicon waveguides with sidewall roughness reduction using a SiO2 hard mask and fluorine-based dry etching,” J. Micromech. Microeng. 25(1), 015003 (2015).
    [Crossref]
  33. D. Benedikovic, P. Cheben, J. H. Schmid, D.-X. Xu, B. Lamontagne, S. Wang, J. Lapointe, R. Halir, A. Ortega-Moñux, S. Janz, and M. Dado, “Subwavelength index engineered surface grating coupler with sub-decibel efficiency for 220-nm silicon-on-insulator waveguides,” Opt. Express 23(17), 22628–22635 (2015).
    [Crossref]
  34. Z. Sheng, Z. Wang, C. Qiu, L. Li, A. Pang, A. Wu, X. Wang, S. Zou, and F. Gan, “A compact and low-loss MMI coupler fabricated with CMOS technology,” IEEE Photonics J. 4(6), 2272–2277 (2012).
    [Crossref]
  35. M.-S. Rouifed, C. G. Littlejohns, G. X. Tina, Q. Haodong, T. Hu, Z. Zhang, C. Liu, G. T. Reed, and H. Wang, “Low loss SOI waveguides and MMIs at the MIR wavelength of 2 µm,” IEEE Photonics Technol. Lett. 28(24), 2827–2829 (2016).
    [Crossref]
  36. C. A. Husko, A. S. Clark, M. J. Collins, A. De Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, “Multi-photon absorption limits to heralded single photon sources,” Sci. Rep. 3(1), 3087 (2013).
    [Crossref]
  37. X. Ji, F. A. Barbosa, S. P. Roberts, A. Dutt, J. Cardenas, Y. Okawachi, A. Bryant, A. L. Gaeta, and M. Lipson, “Ultra-low-loss on-chip resonators with sub-milliwatt parametric oscillation threshold,” Optica 4(6), 619–624 (2017).
    [Crossref]
  38. S. Ramelow, A. Farsi, S. Clemmen, D. Orquiza, K. Luke, M. Lipson, and A. L. Gaeta, “Silicon-nitride platform for narrowband entangled photon generation,” arXiv preprint arXiv:1508.04358 (2015).
  39. D. E. Hagan and A. P. Knights, “Mechanisms for optical loss in SOI waveguides for mid-infrared wavelengths around 2 µm,” J. Opt. 19(2), 025801 (2017).
    [Crossref]
  40. F. Grillot, L. Vivien, S. Laval, D. Pascal, and E. Cassan, “Size influence on the propagation loss induced by sidewall roughness in ultrasmall soi waveguides,” IEEE Photonics Technol. Lett. 16(7), 1661–1663 (2004).
    [Crossref]
  41. P. Cheben, R. Halir, J. H. Schmid, H. A. Atwater, and D. R. Smith, “Subwavelength integrated photonics,” Nature 560(7720), 565–572 (2018).
    [Crossref]
  42. I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Effective mode area and its optimization in silicon-nanocrystal waveguides,” Opt. Lett. 37(12), 2295–2297 (2012).
    [Crossref]
  43. M. Liscidini and J. Sipe, “Stimulated emission tomography,” Phys. Rev. Lett. 111(19), 193602 (2013).
    [Crossref]
  44. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21(15), 2758–2769 (1982).
    [Crossref]
  45. J. F. Reintjes and J. C. McGroddy, “Indirect two-photon transitions in si at 1.06 µm,” Phys. Rev. Lett. 30(19), 901–903 (1973).
    [Crossref]
  46. L. Yin and G. P. Agrawal, “Impact of two-photon absorption on self-phase modulation in silicon waveguides,” Opt. Lett. 32(14), 2031–2033 (2007).
    [Crossref]
  47. C. M. Natarajan, M. G. Tanner, and R. H. Hadfield, “Superconducting nanowire single-photon detectors: physics and applications,” Supercond. Sci. Technol. 25(6), 063001 (2012).
    [Crossref]
  48. F. Marsili, F. Bellei, F. Najafi, A. E. Dane, E. A. Dauler, R. J. Molnar, and K. K. Berggren, “Efficient single photon detection from 500 nm to 5 µm wavelength,” Nano Lett. 12(9), 4799–4804 (2012).
    [Crossref]
  49. M. Cherchi, S. Ylinen, M. Harjanne, M. Kapulainen, and T. Aalto, “Dramatic size reduction of waveguide bends on a micron-scale silicon photonic platform,” Opt. Express 21(15), 17814–17823 (2013).
    [Crossref]
  50. M. Piekarek, D. Bonneau, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “High-extinction ratio integrated photonic filters for silicon quantum photonics,” Opt. Lett. 42(4), 815–818 (2017).
    [Crossref]
  51. M. Savanier, R. Kumar, and S. Mookherjea, “Photon pair generation from compact silicon microring resonators using microwatt-level pump powers,” Opt. Express 24(4), 3313–3328 (2016).
    [Crossref]
  52. C.-K. Hong, Z.-Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59(18), 2044–2046 (1987).
    [Crossref]
  53. J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, “On-chip quantum interference between silicon photon-pair sources,” Nat. Photonics 8(2), 104–108 (2014).
    [Crossref]
  54. J. C. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3(6), 346–350 (2009).
    [Crossref]
  55. J. He, B. A. Bell, A. Casas-Bedoya, Y. Zhang, A. S. Clark, C. Xiong, and B. J. Eggleton, “Ultracompact quantum splitter of degenerate photon pairs,” Optica 2(9), 779–782 (2015).
    [Crossref]
  56. S. F. Preble, M. L. Fanto, J. A. Steidle, C. C. Tison, G. A. Howland, Z. Wang, and P. M. Alsing, “On-chip quantum interference from a single silicon ring-resonator source,” Phys. Rev. Appl. 4(2), 021001 (2015).
    [Crossref]
  57. H. Jin, F. Liu, P. Xu, J. Xia, M. Zhong, Y. Yuan, J. Zhou, Y. Gong, W. Wang, and S. Zhu, “On-chip generation and manipulation of entangled photons based on reconfigurable lithium-niobate waveguide circuits,” Phys. Rev. Lett. 113(10), 103601 (2014).
    [Crossref]
  58. S. Prabhakar, T. Shields, A. C. Dada, M. Ebrahim, G. G. Taylor, D. Morozov, K. Erotokritou, S. Miki, M. Yabuno, H. Terai, C. Gawith, M. Kues, L. Caspani, R. H. Hadfield, and M. Clerici, “Two-photon quantum interference and entanglement at 2.1 µm,” Sci. Adv. 6(13), eaay5195 (2020).
    [Crossref]
  59. M. Cardona, T. A. Meyer, and M. L. W. Thewalt, “Temperature Dependence of the Energy Gap of Semiconductors in the Low-Temperature Limit,” Phys. Rev. Lett. 92(19), 196403 (2004).
    [Crossref]
  60. S. Kaspar, M. Rattunde, T. Topper, R. Moser, S. Adler, C. Manz, K. Kohler, and J. Wagner, “Recent Advances in 2-µm GaSb-Based Semiconductor Disk Laser—Power Scaling, Narrow-Linewidth and Short-Pulse Operation,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1501908 (2013).
    [Crossref]

2020 (1)

S. Prabhakar, T. Shields, A. C. Dada, M. Ebrahim, G. G. Taylor, D. Morozov, K. Erotokritou, S. Miki, M. Yabuno, H. Terai, C. Gawith, M. Kues, L. Caspani, R. H. Hadfield, and M. Clerici, “Two-photon quantum interference and entanglement at 2.1 µm,” Sci. Adv. 6(13), eaay5195 (2020).
[Crossref]

2019 (3)

G. F. Sinclair, N. A. Tyler, D. Sahin, J. Barreto, and M. G. Thompson, “Temperature dependence of the kerr nonlinearity and two-photon absorption in a silicon waveguide at 1.55 µm,” Phys. Rev. Appl. 11(4), 044084 (2019).
[Crossref]

J. C. Adcock, C. Vigliar, R. Santagati, J. W. Silverstone, and M. G. Thompson, “Programmable four-photon graph states on a silicon chip,” Nat. Commun. 10(1), 3528 (2019).
[Crossref]

S. Paesani, Y. Ding, R. Santagati, L. Chakhmakhchyan, C. Vigliar, K. Rottwitt, L. K. Oxenløwe, J. Wang, M. G. Thompson, and A. Laing, “Generation and sampling of quantum states of light in a silicon chip,” Nat. Phys. 15(9), 925–929 (2019).
[Crossref]

2018 (7)

R. A. McCracken, F. Graffitti, and A. Fedrizzi, “Numerical investigation of mid-infrared single-photon generation,” J. Opt. Soc. Am. B 35(12), C38–C48 (2018).
[Crossref]

N. C. Harris, J. Carolan, D. Bunandar, M. Prabhu, M. Hochberg, T. Baehr-Jones, M. L. Fanto, A. M. Smith, C. C. Tison, P. M. Alsing, and D. Englund, “Linear programmable nanophotonic processors,” Optica 5(12), 1623 (2018).
[Crossref]

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360(6386), 285–291 (2018).
[Crossref]

M. Yu, Y. Okawachi, A. G. Griffith, N. Picqué, M. Lipson, and A. L. Gaeta, “Silicon-chip-based mid-infrared dual-comb spectroscopy,” Nat. Commun. 9(1), 1869 (2018).
[Crossref]

R. Kou, T. Hatakeyama, J. Horng, J.-H. Kang, Y. Wang, X. Zhang, and F. Wang, “Mid-IR broadband supercontinuum generation from a suspended silicon waveguide,” Opt. Lett. 43(6), 1387–1390 (2018).
[Crossref]

Y. Zou, S. Chakravarty, C.-J. Chung, X. Xu, and R. T. Chen, “Mid-infrared silicon photonic waveguides and devices [Invited],” Photonics Res. 6(4), 254–276 (2018).
[Crossref]

P. Cheben, R. Halir, J. H. Schmid, H. A. Atwater, and D. R. Smith, “Subwavelength integrated photonics,” Nature 560(7720), 565–572 (2018).
[Crossref]

2017 (6)

M. Piekarek, D. Bonneau, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “High-extinction ratio integrated photonic filters for silicon quantum photonics,” Opt. Lett. 42(4), 815–818 (2017).
[Crossref]

S. A. Miller, M. Yu, X. Ji, A. G. Griffith, J. Cardenas, A. L. Gaeta, and M. Lipson, “Low-loss silicon platform for broadband mid-infrared photonics,” Optica 4(7), 707–712 (2017).
[Crossref]

Y. M. Sua, H. Fan, A. Shahverdi, J.-Y. Chen, and Y.-P. Huang, “Direct generation and detection of quantum correlated photons with 3.2 um wavelength spacing,” Sci. Rep. 7(1), 17494 (2017).
[Crossref]

M. Mancinelli, A. Trenti, S. Piccione, G. Fontana, J. S. Dam, P. Tidemand-Lichtenberg, C. Pedersen, and L. Pavesi, “Mid-infrared coincidence measurements on twin photons at room temperature,” Nat. Commun. 8(1), 15184 (2017).
[Crossref]

X. Ji, F. A. Barbosa, S. P. Roberts, A. Dutt, J. Cardenas, Y. Okawachi, A. Bryant, A. L. Gaeta, and M. Lipson, “Ultra-low-loss on-chip resonators with sub-milliwatt parametric oscillation threshold,” Optica 4(6), 619–624 (2017).
[Crossref]

D. E. Hagan and A. P. Knights, “Mechanisms for optical loss in SOI waveguides for mid-infrared wavelengths around 2 µm,” J. Opt. 19(2), 025801 (2017).
[Crossref]

2016 (4)

M.-S. Rouifed, C. G. Littlejohns, G. X. Tina, Q. Haodong, T. Hu, Z. Zhang, C. Liu, G. T. Reed, and H. Wang, “Low loss SOI waveguides and MMIs at the MIR wavelength of 2 µm,” IEEE Photonics Technol. Lett. 28(24), 2827–2829 (2016).
[Crossref]

J. W. Silverstone, D. Bonneau, J. L. O’Brien, and M. G. Thompson, “Silicon quantum photonics,” IEEE J. Sel. Top. Quantum Electron. 22(6), 390–402 (2016).
[Crossref]

M. Sieger and B. Mizaikoff, “Toward on-chip mid-infrared sensors,” Anal. Chem. 88(11), 5562–5573 (2016).
[Crossref]

M. Savanier, R. Kumar, and S. Mookherjea, “Photon pair generation from compact silicon microring resonators using microwatt-level pump powers,” Opt. Express 24(4), 3313–3328 (2016).
[Crossref]

2015 (5)

J. He, B. A. Bell, A. Casas-Bedoya, Y. Zhang, A. S. Clark, C. Xiong, and B. J. Eggleton, “Ultracompact quantum splitter of degenerate photon pairs,” Optica 2(9), 779–782 (2015).
[Crossref]

S. F. Preble, M. L. Fanto, J. A. Steidle, C. C. Tison, G. A. Howland, Z. Wang, and P. M. Alsing, “On-chip quantum interference from a single silicon ring-resonator source,” Phys. Rev. Appl. 4(2), 021001 (2015).
[Crossref]

A. G. Griffith, R. K. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6(1), 6299 (2015).
[Crossref]

D. H. Lee, S. J. Choo, U. Jung, K. W. Lee, K. W. Kim, and J. H. Park, “Low-loss silicon waveguides with sidewall roughness reduction using a SiO2 hard mask and fluorine-based dry etching,” J. Micromech. Microeng. 25(1), 015003 (2015).
[Crossref]

D. Benedikovic, P. Cheben, J. H. Schmid, D.-X. Xu, B. Lamontagne, S. Wang, J. Lapointe, R. Halir, A. Ortega-Moñux, S. Janz, and M. Dado, “Subwavelength index engineered surface grating coupler with sub-decibel efficiency for 220-nm silicon-on-insulator waveguides,” Opt. Express 23(17), 22628–22635 (2015).
[Crossref]

2014 (2)

H. Jin, F. Liu, P. Xu, J. Xia, M. Zhong, Y. Yuan, J. Zhou, Y. Gong, W. Wang, and S. Zhu, “On-chip generation and manipulation of entangled photons based on reconfigurable lithium-niobate waveguide circuits,” Phys. Rev. Lett. 113(10), 103601 (2014).
[Crossref]

J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, “On-chip quantum interference between silicon photon-pair sources,” Nat. Photonics 8(2), 104–108 (2014).
[Crossref]

2013 (6)

M. Liscidini and J. Sipe, “Stimulated emission tomography,” Phys. Rev. Lett. 111(19), 193602 (2013).
[Crossref]

M. Cherchi, S. Ylinen, M. Harjanne, M. Kapulainen, and T. Aalto, “Dramatic size reduction of waveguide bends on a micron-scale silicon photonic platform,” Opt. Express 21(15), 17814–17823 (2013).
[Crossref]

S. Kaspar, M. Rattunde, T. Topper, R. Moser, S. Adler, C. Manz, K. Kohler, and J. Wagner, “Recent Advances in 2-µm GaSb-Based Semiconductor Disk Laser—Power Scaling, Narrow-Linewidth and Short-Pulse Operation,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1501908 (2013).
[Crossref]

C. A. Husko, A. S. Clark, M. J. Collins, A. De Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, “Multi-photon absorption limits to heralded single photon sources,” Sci. Rep. 3(1), 3087 (2013).
[Crossref]

T. Wang, N. Venkatram, J. Gosciniak, Y. Cui, G. Qian, W. Ji, and D. T. Tan, “Multi-photon absorption and third-order nonlinearity in silicon at mid-infrared wavelengths,” Opt. Express 21(26), 32192–32198 (2013).
[Crossref]

M. Nedeljkovic, A. Khokhar, Y. Hu, X. Chen, J. S. Penades, S. Stankovic, H. Chong, D. Thomson, F. Gardes, G. Reed, and G. Mashanovich, “Silicon photonic devices and platforms for the mid-infrared,” Opt. Mater. Express 3(9), 1205–1214 (2013).
[Crossref]

2012 (6)

M. M. Milošević, M. Nedeljkovic, T. M. Ben Masaud, E. Jaberansary, H. M. Chong, N. G. Emerson, G. T. Reed, and G. Z. Mashanovich, “Silicon waveguides and devices for the mid-infrared,” Appl. Phys. Lett. 101(12), 121105 (2012).
[Crossref]

N. Hattasan, B. Kuyken, F. Leo, E. M. Ryckeboer, D. Vermeulen, and G. Roelkens, “High-efficiency SOI fiber-to-chip grating couplers and low-loss waveguides for the short-wave infrared,” IEEE Photonics Technol. Lett. 24(17), 1536–1538 (2012).
[Crossref]

Z. Sheng, Z. Wang, C. Qiu, L. Li, A. Pang, A. Wu, X. Wang, S. Zou, and F. Gan, “A compact and low-loss MMI coupler fabricated with CMOS technology,” IEEE Photonics J. 4(6), 2272–2277 (2012).
[Crossref]

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Effective mode area and its optimization in silicon-nanocrystal waveguides,” Opt. Lett. 37(12), 2295–2297 (2012).
[Crossref]

C. M. Natarajan, M. G. Tanner, and R. H. Hadfield, “Superconducting nanowire single-photon detectors: physics and applications,” Supercond. Sci. Technol. 25(6), 063001 (2012).
[Crossref]

F. Marsili, F. Bellei, F. Najafi, A. E. Dane, E. A. Dauler, R. J. Molnar, and K. K. Berggren, “Efficient single photon detection from 500 nm to 5 µm wavelength,” Nano Lett. 12(9), 4799–4804 (2012).
[Crossref]

2011 (1)

2010 (2)

B. Jalali, “Silicon photonics: Nonlinear optics in the mid-infrared,” Nat. Photonics 4(8), 506–508 (2010).
[Crossref]

X. Liu, R. M. Osgood Jr, Y. A. Vlasov, and W. M. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics 4(8), 557–560 (2010).
[Crossref]

2009 (5)

2007 (2)

L. Yin and G. P. Agrawal, “Impact of two-photon absorption on self-phase modulation in silicon waveguides,” Opt. Lett. 32(14), 2031–2033 (2007).
[Crossref]

A. D. Bristow, N. Rotenberg, and H. M. Van Driel, “Two-photon absorption and kerr coefficients of silicon for 850–2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
[Crossref]

2006 (2)

H. Garcia and R. Kalyanaraman, “Phonon-assisted two-photon absorption in the presence of a DC-field: the nonlinear Franz–Keldysh effect in indirect gap semiconductors,” J. Phys. B: At., Mol. Opt. Phys. 39(12), 2737–2746 (2006).
[Crossref]

J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14(25), 12388–12393 (2006).
[Crossref]

2004 (2)

F. Grillot, L. Vivien, S. Laval, D. Pascal, and E. Cassan, “Size influence on the propagation loss induced by sidewall roughness in ultrasmall soi waveguides,” IEEE Photonics Technol. Lett. 16(7), 1661–1663 (2004).
[Crossref]

M. Cardona, T. A. Meyer, and M. L. W. Thewalt, “Temperature Dependence of the Energy Gap of Semiconductors in the Low-Temperature Limit,” Phys. Rev. Lett. 92(19), 196403 (2004).
[Crossref]

1987 (1)

C.-K. Hong, Z.-Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59(18), 2044–2046 (1987).
[Crossref]

1982 (1)

1973 (1)

J. F. Reintjes and J. C. McGroddy, “Indirect two-photon transitions in si at 1.06 µm,” Phys. Rev. Lett. 30(19), 901–903 (1973).
[Crossref]

Aalto, T.

Acin, A.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360(6386), 285–291 (2018).
[Crossref]

Adcock, J. C.

J. C. Adcock, C. Vigliar, R. Santagati, J. W. Silverstone, and M. G. Thompson, “Programmable four-photon graph states on a silicon chip,” Nat. Commun. 10(1), 3528 (2019).
[Crossref]

Adler, S.

S. Kaspar, M. Rattunde, T. Topper, R. Moser, S. Adler, C. Manz, K. Kohler, and J. Wagner, “Recent Advances in 2-µm GaSb-Based Semiconductor Disk Laser—Power Scaling, Narrow-Linewidth and Short-Pulse Operation,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1501908 (2013).
[Crossref]

Agrawal, G. P.

Alsing, P. M.

N. C. Harris, J. Carolan, D. Bunandar, M. Prabhu, M. Hochberg, T. Baehr-Jones, M. L. Fanto, A. M. Smith, C. C. Tison, P. M. Alsing, and D. Englund, “Linear programmable nanophotonic processors,” Optica 5(12), 1623 (2018).
[Crossref]

S. F. Preble, M. L. Fanto, J. A. Steidle, C. C. Tison, G. A. Howland, Z. Wang, and P. M. Alsing, “On-chip quantum interference from a single silicon ring-resonator source,” Phys. Rev. Appl. 4(2), 021001 (2015).
[Crossref]

Atwater, H. A.

P. Cheben, R. Halir, J. H. Schmid, H. A. Atwater, and D. R. Smith, “Subwavelength integrated photonics,” Nature 560(7720), 565–572 (2018).
[Crossref]

Augusiak, R.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360(6386), 285–291 (2018).
[Crossref]

Bacco, D.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360(6386), 285–291 (2018).
[Crossref]

Baehr-Jones, T.

Baets, R.

Baets, R. G.

Barbosa, F. A.

Barreto, J.

G. F. Sinclair, N. A. Tyler, D. Sahin, J. Barreto, and M. G. Thompson, “Temperature dependence of the kerr nonlinearity and two-photon absorption in a silicon waveguide at 1.55 µm,” Phys. Rev. Appl. 11(4), 044084 (2019).
[Crossref]

Bell, B. A.

Bellei, F.

F. Marsili, F. Bellei, F. Najafi, A. E. Dane, E. A. Dauler, R. J. Molnar, and K. K. Berggren, “Efficient single photon detection from 500 nm to 5 µm wavelength,” Nano Lett. 12(9), 4799–4804 (2012).
[Crossref]

Ben Masaud, T. M.

M. M. Milošević, M. Nedeljkovic, T. M. Ben Masaud, E. Jaberansary, H. M. Chong, N. G. Emerson, G. T. Reed, and G. Z. Mashanovich, “Silicon waveguides and devices for the mid-infrared,” Appl. Phys. Lett. 101(12), 121105 (2012).
[Crossref]

Benedikovic, D.

Berggren, K. K.

F. Marsili, F. Bellei, F. Najafi, A. E. Dane, E. A. Dauler, R. J. Molnar, and K. K. Berggren, “Efficient single photon detection from 500 nm to 5 µm wavelength,” Nano Lett. 12(9), 4799–4804 (2012).
[Crossref]

Bethea, C.

Bogaerts, W.

Bonneau, D.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360(6386), 285–291 (2018).
[Crossref]

M. Piekarek, D. Bonneau, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “High-extinction ratio integrated photonic filters for silicon quantum photonics,” Opt. Lett. 42(4), 815–818 (2017).
[Crossref]

J. W. Silverstone, D. Bonneau, J. L. O’Brien, and M. G. Thompson, “Silicon quantum photonics,” IEEE J. Sel. Top. Quantum Electron. 22(6), 390–402 (2016).
[Crossref]

J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, “On-chip quantum interference between silicon photon-pair sources,” Nat. Photonics 8(2), 104–108 (2014).
[Crossref]

Bristow, A. D.

A. D. Bristow, N. Rotenberg, and H. M. Van Driel, “Two-photon absorption and kerr coefficients of silicon for 850–2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
[Crossref]

Bryant, A.

Bunandar, D.

Cakmakyapan, S.

M. Prost, Y.-C. Ling, S. Cakmakyapan, Y. Zhang, K. Zhang, J. Hu, Y. Zhang, and S. B. Yoo, “MWIR solid-state optical phased array beam steering using germanium-silicon photonic platform,” in Optical Fiber Communication Conference, (Optical Society of America, 2019), pp. M4E–3.

Cardenas, J.

Cardona, M.

M. Cardona, T. A. Meyer, and M. L. W. Thewalt, “Temperature Dependence of the Energy Gap of Semiconductors in the Low-Temperature Limit,” Phys. Rev. Lett. 92(19), 196403 (2004).
[Crossref]

Carolan, J.

Casas-Bedoya, A.

Caspani, L.

S. Prabhakar, T. Shields, A. C. Dada, M. Ebrahim, G. G. Taylor, D. Morozov, K. Erotokritou, S. Miki, M. Yabuno, H. Terai, C. Gawith, M. Kues, L. Caspani, R. H. Hadfield, and M. Clerici, “Two-photon quantum interference and entanglement at 2.1 µm,” Sci. Adv. 6(13), eaay5195 (2020).
[Crossref]

Cassan, E.

F. Grillot, L. Vivien, S. Laval, D. Pascal, and E. Cassan, “Size influence on the propagation loss induced by sidewall roughness in ultrasmall soi waveguides,” IEEE Photonics Technol. Lett. 16(7), 1661–1663 (2004).
[Crossref]

Chakhmakhchyan, L.

S. Paesani, Y. Ding, R. Santagati, L. Chakhmakhchyan, C. Vigliar, K. Rottwitt, L. K. Oxenløwe, J. Wang, M. G. Thompson, and A. Laing, “Generation and sampling of quantum states of light in a silicon chip,” Nat. Phys. 15(9), 925–929 (2019).
[Crossref]

Chakravarty, S.

Y. Zou, S. Chakravarty, C.-J. Chung, X. Xu, and R. T. Chen, “Mid-infrared silicon photonic waveguides and devices [Invited],” Photonics Res. 6(4), 254–276 (2018).
[Crossref]

Cheben, P.

Chen, J.-Y.

Y. M. Sua, H. Fan, A. Shahverdi, J.-Y. Chen, and Y.-P. Huang, “Direct generation and detection of quantum correlated photons with 3.2 um wavelength spacing,” Sci. Rep. 7(1), 17494 (2017).
[Crossref]

Chen, L.

Chen, R. T.

Y. Zou, S. Chakravarty, C.-J. Chung, X. Xu, and R. T. Chen, “Mid-infrared silicon photonic waveguides and devices [Invited],” Photonics Res. 6(4), 254–276 (2018).
[Crossref]

Chen, X.

Cherchi, M.

Chong, H.

Chong, H. M.

M. M. Milošević, M. Nedeljkovic, T. M. Ben Masaud, E. Jaberansary, H. M. Chong, N. G. Emerson, G. T. Reed, and G. Z. Mashanovich, “Silicon waveguides and devices for the mid-infrared,” Appl. Phys. Lett. 101(12), 121105 (2012).
[Crossref]

Choo, S. J.

D. H. Lee, S. J. Choo, U. Jung, K. W. Lee, K. W. Kim, and J. H. Park, “Low-loss silicon waveguides with sidewall roughness reduction using a SiO2 hard mask and fluorine-based dry etching,” J. Micromech. Microeng. 25(1), 015003 (2015).
[Crossref]

Chung, C.-J.

Y. Zou, S. Chakravarty, C.-J. Chung, X. Xu, and R. T. Chen, “Mid-infrared silicon photonic waveguides and devices [Invited],” Photonics Res. 6(4), 254–276 (2018).
[Crossref]

Clark, A. S.

J. He, B. A. Bell, A. Casas-Bedoya, Y. Zhang, A. S. Clark, C. Xiong, and B. J. Eggleton, “Ultracompact quantum splitter of degenerate photon pairs,” Optica 2(9), 779–782 (2015).
[Crossref]

C. A. Husko, A. S. Clark, M. J. Collins, A. De Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, “Multi-photon absorption limits to heralded single photon sources,” Sci. Rep. 3(1), 3087 (2013).
[Crossref]

Clemmen, S.

S. Clemmen, K. P. Huy, W. Bogaerts, R. G. Baets, P. Emplit, and S. Massar, “Continuous wave photon pair generation in silicon-on-insulator waveguides and ring resonators,” Opt. Express 17(19), 16558–16570 (2009).
[Crossref]

S. Ramelow, A. Farsi, S. Clemmen, D. Orquiza, K. Luke, M. Lipson, and A. L. Gaeta, “Silicon-nitride platform for narrowband entangled photon generation,” arXiv preprint arXiv:1508.04358 (2015).

Clerici, M.

S. Prabhakar, T. Shields, A. C. Dada, M. Ebrahim, G. G. Taylor, D. Morozov, K. Erotokritou, S. Miki, M. Yabuno, H. Terai, C. Gawith, M. Kues, L. Caspani, R. H. Hadfield, and M. Clerici, “Two-photon quantum interference and entanglement at 2.1 µm,” Sci. Adv. 6(13), eaay5195 (2020).
[Crossref]

Collins, M. J.

C. A. Husko, A. S. Clark, M. J. Collins, A. De Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, “Multi-photon absorption limits to heralded single photon sources,” Sci. Rep. 3(1), 3087 (2013).
[Crossref]

Combrié, S.

C. A. Husko, A. S. Clark, M. J. Collins, A. De Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, “Multi-photon absorption limits to heralded single photon sources,” Sci. Rep. 3(1), 3087 (2013).
[Crossref]

Corrigan, P.

Cui, Y.

Dada, A. C.

S. Prabhakar, T. Shields, A. C. Dada, M. Ebrahim, G. G. Taylor, D. Morozov, K. Erotokritou, S. Miki, M. Yabuno, H. Terai, C. Gawith, M. Kues, L. Caspani, R. H. Hadfield, and M. Clerici, “Two-photon quantum interference and entanglement at 2.1 µm,” Sci. Adv. 6(13), eaay5195 (2020).
[Crossref]

Dado, M.

Dam, J. S.

M. Mancinelli, A. Trenti, S. Piccione, G. Fontana, J. S. Dam, P. Tidemand-Lichtenberg, C. Pedersen, and L. Pavesi, “Mid-infrared coincidence measurements on twin photons at room temperature,” Nat. Commun. 8(1), 15184 (2017).
[Crossref]

Dane, A. E.

F. Marsili, F. Bellei, F. Najafi, A. E. Dane, E. A. Dauler, R. J. Molnar, and K. K. Berggren, “Efficient single photon detection from 500 nm to 5 µm wavelength,” Nano Lett. 12(9), 4799–4804 (2012).
[Crossref]

Dauler, E. A.

F. Marsili, F. Bellei, F. Najafi, A. E. Dane, E. A. Dauler, R. J. Molnar, and K. K. Berggren, “Efficient single photon detection from 500 nm to 5 µm wavelength,” Nano Lett. 12(9), 4799–4804 (2012).
[Crossref]

De Rossi, A.

C. A. Husko, A. S. Clark, M. J. Collins, A. De Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, “Multi-photon absorption limits to heralded single photon sources,” Sci. Rep. 3(1), 3087 (2013).
[Crossref]

Ding, Y.

S. Paesani, Y. Ding, R. Santagati, L. Chakhmakhchyan, C. Vigliar, K. Rottwitt, L. K. Oxenløwe, J. Wang, M. G. Thompson, and A. Laing, “Generation and sampling of quantum states of light in a silicon chip,” Nat. Phys. 15(9), 925–929 (2019).
[Crossref]

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360(6386), 285–291 (2018).
[Crossref]

Dutt, A.

Ebrahim, M.

S. Prabhakar, T. Shields, A. C. Dada, M. Ebrahim, G. G. Taylor, D. Morozov, K. Erotokritou, S. Miki, M. Yabuno, H. Terai, C. Gawith, M. Kues, L. Caspani, R. H. Hadfield, and M. Clerici, “Two-photon quantum interference and entanglement at 2.1 µm,” Sci. Adv. 6(13), eaay5195 (2020).
[Crossref]

Eggleton, B. J.

J. He, B. A. Bell, A. Casas-Bedoya, Y. Zhang, A. S. Clark, C. Xiong, and B. J. Eggleton, “Ultracompact quantum splitter of degenerate photon pairs,” Optica 2(9), 779–782 (2015).
[Crossref]

C. A. Husko, A. S. Clark, M. J. Collins, A. De Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, “Multi-photon absorption limits to heralded single photon sources,” Sci. Rep. 3(1), 3087 (2013).
[Crossref]

Emerson, N. G.

M. M. Milošević, M. Nedeljkovic, T. M. Ben Masaud, E. Jaberansary, H. M. Chong, N. G. Emerson, G. T. Reed, and G. Z. Mashanovich, “Silicon waveguides and devices for the mid-infrared,” Appl. Phys. Lett. 101(12), 121105 (2012).
[Crossref]

Emplit, P.

Englund, D.

Erotokritou, K.

S. Prabhakar, T. Shields, A. C. Dada, M. Ebrahim, G. G. Taylor, D. Morozov, K. Erotokritou, S. Miki, M. Yabuno, H. Terai, C. Gawith, M. Kues, L. Caspani, R. H. Hadfield, and M. Clerici, “Two-photon quantum interference and entanglement at 2.1 µm,” Sci. Adv. 6(13), eaay5195 (2020).
[Crossref]

Ezaki, M.

J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, “On-chip quantum interference between silicon photon-pair sources,” Nat. Photonics 8(2), 104–108 (2014).
[Crossref]

Fain, R.

A. G. Griffith, R. K. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6(1), 6299 (2015).
[Crossref]

Fan, H.

Y. M. Sua, H. Fan, A. Shahverdi, J.-Y. Chen, and Y.-P. Huang, “Direct generation and detection of quantum correlated photons with 3.2 um wavelength spacing,” Sci. Rep. 7(1), 17494 (2017).
[Crossref]

Fanto, M. L.

N. C. Harris, J. Carolan, D. Bunandar, M. Prabhu, M. Hochberg, T. Baehr-Jones, M. L. Fanto, A. M. Smith, C. C. Tison, P. M. Alsing, and D. Englund, “Linear programmable nanophotonic processors,” Optica 5(12), 1623 (2018).
[Crossref]

S. F. Preble, M. L. Fanto, J. A. Steidle, C. C. Tison, G. A. Howland, Z. Wang, and P. M. Alsing, “On-chip quantum interference from a single silicon ring-resonator source,” Phys. Rev. Appl. 4(2), 021001 (2015).
[Crossref]

Farsi, A.

S. Ramelow, A. Farsi, S. Clemmen, D. Orquiza, K. Luke, M. Lipson, and A. L. Gaeta, “Silicon-nitride platform for narrowband entangled photon generation,” arXiv preprint arXiv:1508.04358 (2015).

Fedrizzi, A.

Fienup, J. R.

Fontana, G.

M. Mancinelli, A. Trenti, S. Piccione, G. Fontana, J. S. Dam, P. Tidemand-Lichtenberg, C. Pedersen, and L. Pavesi, “Mid-infrared coincidence measurements on twin photons at room temperature,” Nat. Commun. 8(1), 15184 (2017).
[Crossref]

Foster, M. A.

Fujiwara, M.

Furusawa, A.

J. L. O’Brien, A. Furusawa, and J. Vučković, “Photonic quantum technologies,” Nat. Photonics 3(12), 687–695 (2009).
[Crossref]

Gaeta, A. L.

M. Yu, Y. Okawachi, A. G. Griffith, N. Picqué, M. Lipson, and A. L. Gaeta, “Silicon-chip-based mid-infrared dual-comb spectroscopy,” Nat. Commun. 9(1), 1869 (2018).
[Crossref]

S. A. Miller, M. Yu, X. Ji, A. G. Griffith, J. Cardenas, A. L. Gaeta, and M. Lipson, “Low-loss silicon platform for broadband mid-infrared photonics,” Optica 4(7), 707–712 (2017).
[Crossref]

X. Ji, F. A. Barbosa, S. P. Roberts, A. Dutt, J. Cardenas, Y. Okawachi, A. Bryant, A. L. Gaeta, and M. Lipson, “Ultra-low-loss on-chip resonators with sub-milliwatt parametric oscillation threshold,” Optica 4(6), 619–624 (2017).
[Crossref]

A. G. Griffith, R. K. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6(1), 6299 (2015).
[Crossref]

J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14(25), 12388–12393 (2006).
[Crossref]

S. Ramelow, A. Farsi, S. Clemmen, D. Orquiza, K. Luke, M. Lipson, and A. L. Gaeta, “Silicon-nitride platform for narrowband entangled photon generation,” arXiv preprint arXiv:1508.04358 (2015).

Gan, F.

Z. Sheng, Z. Wang, C. Qiu, L. Li, A. Pang, A. Wu, X. Wang, S. Zou, and F. Gan, “A compact and low-loss MMI coupler fabricated with CMOS technology,” IEEE Photonics J. 4(6), 2272–2277 (2012).
[Crossref]

Garcia, H.

H. Garcia and R. Kalyanaraman, “Phonon-assisted two-photon absorption in the presence of a DC-field: the nonlinear Franz–Keldysh effect in indirect gap semiconductors,” J. Phys. B: At., Mol. Opt. Phys. 39(12), 2737–2746 (2006).
[Crossref]

Gardes, F.

Gawith, C.

S. Prabhakar, T. Shields, A. C. Dada, M. Ebrahim, G. G. Taylor, D. Morozov, K. Erotokritou, S. Miki, M. Yabuno, H. Terai, C. Gawith, M. Kues, L. Caspani, R. H. Hadfield, and M. Clerici, “Two-photon quantum interference and entanglement at 2.1 µm,” Sci. Adv. 6(13), eaay5195 (2020).
[Crossref]

Gong, Q.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360(6386), 285–291 (2018).
[Crossref]

Gong, Y.

H. Jin, F. Liu, P. Xu, J. Xia, M. Zhong, Y. Yuan, J. Zhou, Y. Gong, W. Wang, and S. Zhu, “On-chip generation and manipulation of entangled photons based on reconfigurable lithium-niobate waveguide circuits,” Phys. Rev. Lett. 113(10), 103601 (2014).
[Crossref]

Gosciniak, J.

Graffitti, F.

Green, W. M.

B. Kuyken, X. Liu, R. M. Osgood, R. Baets, G. Roelkens, and W. M. Green, “Mid-infrared to telecom-band supercontinuum generation in highly nonlinear silicon-on-insulator wire waveguides,” Opt. Express 19(21), 20172–20181 (2011).
[Crossref]

X. Liu, R. M. Osgood Jr, Y. A. Vlasov, and W. M. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics 4(8), 557–560 (2010).
[Crossref]

Griffith, A. G.

M. Yu, Y. Okawachi, A. G. Griffith, N. Picqué, M. Lipson, and A. L. Gaeta, “Silicon-chip-based mid-infrared dual-comb spectroscopy,” Nat. Commun. 9(1), 1869 (2018).
[Crossref]

S. A. Miller, M. Yu, X. Ji, A. G. Griffith, J. Cardenas, A. L. Gaeta, and M. Lipson, “Low-loss silicon platform for broadband mid-infrared photonics,” Optica 4(7), 707–712 (2017).
[Crossref]

A. G. Griffith, R. K. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6(1), 6299 (2015).
[Crossref]

Grillot, F.

F. Grillot, L. Vivien, S. Laval, D. Pascal, and E. Cassan, “Size influence on the propagation loss induced by sidewall roughness in ultrasmall soi waveguides,” IEEE Photonics Technol. Lett. 16(7), 1661–1663 (2004).
[Crossref]

Hadfield, R. H.

S. Prabhakar, T. Shields, A. C. Dada, M. Ebrahim, G. G. Taylor, D. Morozov, K. Erotokritou, S. Miki, M. Yabuno, H. Terai, C. Gawith, M. Kues, L. Caspani, R. H. Hadfield, and M. Clerici, “Two-photon quantum interference and entanglement at 2.1 µm,” Sci. Adv. 6(13), eaay5195 (2020).
[Crossref]

M. Piekarek, D. Bonneau, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “High-extinction ratio integrated photonic filters for silicon quantum photonics,” Opt. Lett. 42(4), 815–818 (2017).
[Crossref]

J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, “On-chip quantum interference between silicon photon-pair sources,” Nat. Photonics 8(2), 104–108 (2014).
[Crossref]

C. M. Natarajan, M. G. Tanner, and R. H. Hadfield, “Superconducting nanowire single-photon detectors: physics and applications,” Supercond. Sci. Technol. 25(6), 063001 (2012).
[Crossref]

Hagan, D. E.

D. E. Hagan and A. P. Knights, “Mechanisms for optical loss in SOI waveguides for mid-infrared wavelengths around 2 µm,” J. Opt. 19(2), 025801 (2017).
[Crossref]

Halir, R.

Haodong, Q.

M.-S. Rouifed, C. G. Littlejohns, G. X. Tina, Q. Haodong, T. Hu, Z. Zhang, C. Liu, G. T. Reed, and H. Wang, “Low loss SOI waveguides and MMIs at the MIR wavelength of 2 µm,” IEEE Photonics Technol. Lett. 28(24), 2827–2829 (2016).
[Crossref]

Harjanne, M.

Harris, N. C.

Hatakeyama, T.

Hattasan, N.

N. Hattasan, B. Kuyken, F. Leo, E. M. Ryckeboer, D. Vermeulen, and G. Roelkens, “High-efficiency SOI fiber-to-chip grating couplers and low-loss waveguides for the short-wave infrared,” IEEE Photonics Technol. Lett. 24(17), 1536–1538 (2012).
[Crossref]

He, J.

Hochberg, M.

Hong, C.-K.

C.-K. Hong, Z.-Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59(18), 2044–2046 (1987).
[Crossref]

Horng, J.

Howland, G. A.

S. F. Preble, M. L. Fanto, J. A. Steidle, C. C. Tison, G. A. Howland, Z. Wang, and P. M. Alsing, “On-chip quantum interference from a single silicon ring-resonator source,” Phys. Rev. Appl. 4(2), 021001 (2015).
[Crossref]

Hu, J.

M. Prost, Y.-C. Ling, S. Cakmakyapan, Y. Zhang, K. Zhang, J. Hu, Y. Zhang, and S. B. Yoo, “MWIR solid-state optical phased array beam steering using germanium-silicon photonic platform,” in Optical Fiber Communication Conference, (Optical Society of America, 2019), pp. M4E–3.

Hu, T.

M.-S. Rouifed, C. G. Littlejohns, G. X. Tina, Q. Haodong, T. Hu, Z. Zhang, C. Liu, G. T. Reed, and H. Wang, “Low loss SOI waveguides and MMIs at the MIR wavelength of 2 µm,” IEEE Photonics Technol. Lett. 28(24), 2827–2829 (2016).
[Crossref]

Hu, Y.

Huang, Y.-P.

Y. M. Sua, H. Fan, A. Shahverdi, J.-Y. Chen, and Y.-P. Huang, “Direct generation and detection of quantum correlated photons with 3.2 um wavelength spacing,” Sci. Rep. 7(1), 17494 (2017).
[Crossref]

Husko, C. A.

C. A. Husko, A. S. Clark, M. J. Collins, A. De Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, “Multi-photon absorption limits to heralded single photon sources,” Sci. Rep. 3(1), 3087 (2013).
[Crossref]

Huy, K. P.

Iizuka, N.

J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, “On-chip quantum interference between silicon photon-pair sources,” Nat. Photonics 8(2), 104–108 (2014).
[Crossref]

Jaberansary, E.

M. M. Milošević, M. Nedeljkovic, T. M. Ben Masaud, E. Jaberansary, H. M. Chong, N. G. Emerson, G. T. Reed, and G. Z. Mashanovich, “Silicon waveguides and devices for the mid-infrared,” Appl. Phys. Lett. 101(12), 121105 (2012).
[Crossref]

Jalali, B.

B. Jalali, “Silicon photonics: Nonlinear optics in the mid-infrared,” Nat. Photonics 4(8), 506–508 (2010).
[Crossref]

Janz, S.

Ji, W.

Ji, X.

Jin, H.

H. Jin, F. Liu, P. Xu, J. Xia, M. Zhong, Y. Yuan, J. Zhou, Y. Gong, W. Wang, and S. Zhu, “On-chip generation and manipulation of entangled photons based on reconfigurable lithium-niobate waveguide circuits,” Phys. Rev. Lett. 113(10), 103601 (2014).
[Crossref]

Jung, U.

D. H. Lee, S. J. Choo, U. Jung, K. W. Lee, K. W. Kim, and J. H. Park, “Low-loss silicon waveguides with sidewall roughness reduction using a SiO2 hard mask and fluorine-based dry etching,” J. Micromech. Microeng. 25(1), 015003 (2015).
[Crossref]

Kalyanaraman, R.

H. Garcia and R. Kalyanaraman, “Phonon-assisted two-photon absorption in the presence of a DC-field: the nonlinear Franz–Keldysh effect in indirect gap semiconductors,” J. Phys. B: At., Mol. Opt. Phys. 39(12), 2737–2746 (2006).
[Crossref]

Kang, J.-H.

Kapulainen, M.

Kaspar, S.

S. Kaspar, M. Rattunde, T. Topper, R. Moser, S. Adler, C. Manz, K. Kohler, and J. Wagner, “Recent Advances in 2-µm GaSb-Based Semiconductor Disk Laser—Power Scaling, Narrow-Linewidth and Short-Pulse Operation,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1501908 (2013).
[Crossref]

Khokhar, A.

Kim, K. W.

D. H. Lee, S. J. Choo, U. Jung, K. W. Lee, K. W. Kim, and J. H. Park, “Low-loss silicon waveguides with sidewall roughness reduction using a SiO2 hard mask and fluorine-based dry etching,” J. Micromech. Microeng. 25(1), 015003 (2015).
[Crossref]

Knights, A. P.

D. E. Hagan and A. P. Knights, “Mechanisms for optical loss in SOI waveguides for mid-infrared wavelengths around 2 µm,” J. Opt. 19(2), 025801 (2017).
[Crossref]

Kohler, K.

S. Kaspar, M. Rattunde, T. Topper, R. Moser, S. Adler, C. Manz, K. Kohler, and J. Wagner, “Recent Advances in 2-µm GaSb-Based Semiconductor Disk Laser—Power Scaling, Narrow-Linewidth and Short-Pulse Operation,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1501908 (2013).
[Crossref]

Kou, R.

Krauss, T. F.

C. A. Husko, A. S. Clark, M. J. Collins, A. De Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, “Multi-photon absorption limits to heralded single photon sources,” Sci. Rep. 3(1), 3087 (2013).
[Crossref]

Kues, M.

S. Prabhakar, T. Shields, A. C. Dada, M. Ebrahim, G. G. Taylor, D. Morozov, K. Erotokritou, S. Miki, M. Yabuno, H. Terai, C. Gawith, M. Kues, L. Caspani, R. H. Hadfield, and M. Clerici, “Two-photon quantum interference and entanglement at 2.1 µm,” Sci. Adv. 6(13), eaay5195 (2020).
[Crossref]

Kumar, P.

Kumar, R.

Kuyken, B.

N. Hattasan, B. Kuyken, F. Leo, E. M. Ryckeboer, D. Vermeulen, and G. Roelkens, “High-efficiency SOI fiber-to-chip grating couplers and low-loss waveguides for the short-wave infrared,” IEEE Photonics Technol. Lett. 24(17), 1536–1538 (2012).
[Crossref]

B. Kuyken, X. Liu, R. M. Osgood, R. Baets, G. Roelkens, and W. M. Green, “Mid-infrared to telecom-band supercontinuum generation in highly nonlinear silicon-on-insulator wire waveguides,” Opt. Express 19(21), 20172–20181 (2011).
[Crossref]

Laing, A.

S. Paesani, Y. Ding, R. Santagati, L. Chakhmakhchyan, C. Vigliar, K. Rottwitt, L. K. Oxenløwe, J. Wang, M. G. Thompson, and A. Laing, “Generation and sampling of quantum states of light in a silicon chip,” Nat. Phys. 15(9), 925–929 (2019).
[Crossref]

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360(6386), 285–291 (2018).
[Crossref]

Lamontagne, B.

Lapointe, J.

Lau, R. K.

A. G. Griffith, R. K. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6(1), 6299 (2015).
[Crossref]

Laval, S.

F. Grillot, L. Vivien, S. Laval, D. Pascal, and E. Cassan, “Size influence on the propagation loss induced by sidewall roughness in ultrasmall soi waveguides,” IEEE Photonics Technol. Lett. 16(7), 1661–1663 (2004).
[Crossref]

Lee, D. H.

D. H. Lee, S. J. Choo, U. Jung, K. W. Lee, K. W. Kim, and J. H. Park, “Low-loss silicon waveguides with sidewall roughness reduction using a SiO2 hard mask and fluorine-based dry etching,” J. Micromech. Microeng. 25(1), 015003 (2015).
[Crossref]

Lee, K. F.

Lee, K. W.

D. H. Lee, S. J. Choo, U. Jung, K. W. Lee, K. W. Kim, and J. H. Park, “Low-loss silicon waveguides with sidewall roughness reduction using a SiO2 hard mask and fluorine-based dry etching,” J. Micromech. Microeng. 25(1), 015003 (2015).
[Crossref]

Lee, Y. H. D.

A. G. Griffith, R. K. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6(1), 6299 (2015).
[Crossref]

Lehoucq, G.

C. A. Husko, A. S. Clark, M. J. Collins, A. De Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, “Multi-photon absorption limits to heralded single photon sources,” Sci. Rep. 3(1), 3087 (2013).
[Crossref]

Leo, F.

N. Hattasan, B. Kuyken, F. Leo, E. M. Ryckeboer, D. Vermeulen, and G. Roelkens, “High-efficiency SOI fiber-to-chip grating couplers and low-loss waveguides for the short-wave infrared,” IEEE Photonics Technol. Lett. 24(17), 1536–1538 (2012).
[Crossref]

Li, L.

Z. Sheng, Z. Wang, C. Qiu, L. Li, A. Pang, A. Wu, X. Wang, S. Zou, and F. Gan, “A compact and low-loss MMI coupler fabricated with CMOS technology,” IEEE Photonics J. 4(6), 2272–2277 (2012).
[Crossref]

Ling, Y.-C.

M. Prost, Y.-C. Ling, S. Cakmakyapan, Y. Zhang, K. Zhang, J. Hu, Y. Zhang, and S. B. Yoo, “MWIR solid-state optical phased array beam steering using germanium-silicon photonic platform,” in Optical Fiber Communication Conference, (Optical Society of America, 2019), pp. M4E–3.

Lipson, M.

M. Yu, Y. Okawachi, A. G. Griffith, N. Picqué, M. Lipson, and A. L. Gaeta, “Silicon-chip-based mid-infrared dual-comb spectroscopy,” Nat. Commun. 9(1), 1869 (2018).
[Crossref]

S. A. Miller, M. Yu, X. Ji, A. G. Griffith, J. Cardenas, A. L. Gaeta, and M. Lipson, “Low-loss silicon platform for broadband mid-infrared photonics,” Optica 4(7), 707–712 (2017).
[Crossref]

X. Ji, F. A. Barbosa, S. P. Roberts, A. Dutt, J. Cardenas, Y. Okawachi, A. Bryant, A. L. Gaeta, and M. Lipson, “Ultra-low-loss on-chip resonators with sub-milliwatt parametric oscillation threshold,” Optica 4(6), 619–624 (2017).
[Crossref]

A. G. Griffith, R. K. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6(1), 6299 (2015).
[Crossref]

J. Cardenas, C. B. Poitras, J. T. Robinson, K. Preston, L. Chen, and M. Lipson, “Low loss etchless silicon photonic waveguides,” Opt. Express 17(6), 4752–4757 (2009).
[Crossref]

J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14(25), 12388–12393 (2006).
[Crossref]

S. Ramelow, A. Farsi, S. Clemmen, D. Orquiza, K. Luke, M. Lipson, and A. L. Gaeta, “Silicon-nitride platform for narrowband entangled photon generation,” arXiv preprint arXiv:1508.04358 (2015).

Liscidini, M.

M. Liscidini and J. Sipe, “Stimulated emission tomography,” Phys. Rev. Lett. 111(19), 193602 (2013).
[Crossref]

Littlejohns, C. G.

M.-S. Rouifed, C. G. Littlejohns, G. X. Tina, Q. Haodong, T. Hu, Z. Zhang, C. Liu, G. T. Reed, and H. Wang, “Low loss SOI waveguides and MMIs at the MIR wavelength of 2 µm,” IEEE Photonics Technol. Lett. 28(24), 2827–2829 (2016).
[Crossref]

Liu, C.

M.-S. Rouifed, C. G. Littlejohns, G. X. Tina, Q. Haodong, T. Hu, Z. Zhang, C. Liu, G. T. Reed, and H. Wang, “Low loss SOI waveguides and MMIs at the MIR wavelength of 2 µm,” IEEE Photonics Technol. Lett. 28(24), 2827–2829 (2016).
[Crossref]

Liu, F.

H. Jin, F. Liu, P. Xu, J. Xia, M. Zhong, Y. Yuan, J. Zhou, Y. Gong, W. Wang, and S. Zhu, “On-chip generation and manipulation of entangled photons based on reconfigurable lithium-niobate waveguide circuits,” Phys. Rev. Lett. 113(10), 103601 (2014).
[Crossref]

Liu, X.

B. Kuyken, X. Liu, R. M. Osgood, R. Baets, G. Roelkens, and W. M. Green, “Mid-infrared to telecom-band supercontinuum generation in highly nonlinear silicon-on-insulator wire waveguides,” Opt. Express 19(21), 20172–20181 (2011).
[Crossref]

X. Liu, R. M. Osgood Jr, Y. A. Vlasov, and W. M. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics 4(8), 557–560 (2010).
[Crossref]

Lockwood, D. J.

L. Pavesi and D. J. Lockwood, Silicon photonics III: Systems and applications, vol. 122 (Springer Science & Business Media, 2016).

Luke, K.

S. Ramelow, A. Farsi, S. Clemmen, D. Orquiza, K. Luke, M. Lipson, and A. L. Gaeta, “Silicon-nitride platform for narrowband entangled photon generation,” arXiv preprint arXiv:1508.04358 (2015).

Mancinelli, M.

M. Mancinelli, A. Trenti, S. Piccione, G. Fontana, J. S. Dam, P. Tidemand-Lichtenberg, C. Pedersen, and L. Pavesi, “Mid-infrared coincidence measurements on twin photons at room temperature,” Nat. Commun. 8(1), 15184 (2017).
[Crossref]

Mancinska, L.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360(6386), 285–291 (2018).
[Crossref]

Mandel, L.

C.-K. Hong, Z.-Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59(18), 2044–2046 (1987).
[Crossref]

Manz, C.

S. Kaspar, M. Rattunde, T. Topper, R. Moser, S. Adler, C. Manz, K. Kohler, and J. Wagner, “Recent Advances in 2-µm GaSb-Based Semiconductor Disk Laser—Power Scaling, Narrow-Linewidth and Short-Pulse Operation,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1501908 (2013).
[Crossref]

Marshall, G. D.

J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, “On-chip quantum interference between silicon photon-pair sources,” Nat. Photonics 8(2), 104–108 (2014).
[Crossref]

Marsili, F.

F. Marsili, F. Bellei, F. Najafi, A. E. Dane, E. A. Dauler, R. J. Molnar, and K. K. Berggren, “Efficient single photon detection from 500 nm to 5 µm wavelength,” Nano Lett. 12(9), 4799–4804 (2012).
[Crossref]

Martini, R.

Mashanovich, G.

Mashanovich, G. Z.

M. M. Milošević, M. Nedeljkovic, T. M. Ben Masaud, E. Jaberansary, H. M. Chong, N. G. Emerson, G. T. Reed, and G. Z. Mashanovich, “Silicon waveguides and devices for the mid-infrared,” Appl. Phys. Lett. 101(12), 121105 (2012).
[Crossref]

Massar, S.

Matthews, J. C.

J. C. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3(6), 346–350 (2009).
[Crossref]

McCracken, R. A.

McGroddy, J. C.

J. F. Reintjes and J. C. McGroddy, “Indirect two-photon transitions in si at 1.06 µm,” Phys. Rev. Lett. 30(19), 901–903 (1973).
[Crossref]

Meyer, T. A.

M. Cardona, T. A. Meyer, and M. L. W. Thewalt, “Temperature Dependence of the Energy Gap of Semiconductors in the Low-Temperature Limit,” Phys. Rev. Lett. 92(19), 196403 (2004).
[Crossref]

Miki, S.

S. Prabhakar, T. Shields, A. C. Dada, M. Ebrahim, G. G. Taylor, D. Morozov, K. Erotokritou, S. Miki, M. Yabuno, H. Terai, C. Gawith, M. Kues, L. Caspani, R. H. Hadfield, and M. Clerici, “Two-photon quantum interference and entanglement at 2.1 µm,” Sci. Adv. 6(13), eaay5195 (2020).
[Crossref]

M. Piekarek, D. Bonneau, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “High-extinction ratio integrated photonic filters for silicon quantum photonics,” Opt. Lett. 42(4), 815–818 (2017).
[Crossref]

Miller, S. A.

Miloševic, M. M.

M. M. Milošević, M. Nedeljkovic, T. M. Ben Masaud, E. Jaberansary, H. M. Chong, N. G. Emerson, G. T. Reed, and G. Z. Mashanovich, “Silicon waveguides and devices for the mid-infrared,” Appl. Phys. Lett. 101(12), 121105 (2012).
[Crossref]

Mizaikoff, B.

M. Sieger and B. Mizaikoff, “Toward on-chip mid-infrared sensors,” Anal. Chem. 88(11), 5562–5573 (2016).
[Crossref]

Mohanty, A.

A. G. Griffith, R. K. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6(1), 6299 (2015).
[Crossref]

Molnar, R. J.

F. Marsili, F. Bellei, F. Najafi, A. E. Dane, E. A. Dauler, R. J. Molnar, and K. K. Berggren, “Efficient single photon detection from 500 nm to 5 µm wavelength,” Nano Lett. 12(9), 4799–4804 (2012).
[Crossref]

Mookherjea, S.

Morozov, D.

S. Prabhakar, T. Shields, A. C. Dada, M. Ebrahim, G. G. Taylor, D. Morozov, K. Erotokritou, S. Miki, M. Yabuno, H. Terai, C. Gawith, M. Kues, L. Caspani, R. H. Hadfield, and M. Clerici, “Two-photon quantum interference and entanglement at 2.1 µm,” Sci. Adv. 6(13), eaay5195 (2020).
[Crossref]

Moser, R.

S. Kaspar, M. Rattunde, T. Topper, R. Moser, S. Adler, C. Manz, K. Kohler, and J. Wagner, “Recent Advances in 2-µm GaSb-Based Semiconductor Disk Laser—Power Scaling, Narrow-Linewidth and Short-Pulse Operation,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1501908 (2013).
[Crossref]

Najafi, F.

F. Marsili, F. Bellei, F. Najafi, A. E. Dane, E. A. Dauler, R. J. Molnar, and K. K. Berggren, “Efficient single photon detection from 500 nm to 5 µm wavelength,” Nano Lett. 12(9), 4799–4804 (2012).
[Crossref]

Natarajan, C. M.

M. Piekarek, D. Bonneau, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “High-extinction ratio integrated photonic filters for silicon quantum photonics,” Opt. Lett. 42(4), 815–818 (2017).
[Crossref]

J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, “On-chip quantum interference between silicon photon-pair sources,” Nat. Photonics 8(2), 104–108 (2014).
[Crossref]

C. M. Natarajan, M. G. Tanner, and R. H. Hadfield, “Superconducting nanowire single-photon detectors: physics and applications,” Supercond. Sci. Technol. 25(6), 063001 (2012).
[Crossref]

Nedeljkovic, M.

M. Nedeljkovic, A. Khokhar, Y. Hu, X. Chen, J. S. Penades, S. Stankovic, H. Chong, D. Thomson, F. Gardes, G. Reed, and G. Mashanovich, “Silicon photonic devices and platforms for the mid-infrared,” Opt. Mater. Express 3(9), 1205–1214 (2013).
[Crossref]

M. M. Milošević, M. Nedeljkovic, T. M. Ben Masaud, E. Jaberansary, H. M. Chong, N. G. Emerson, G. T. Reed, and G. Z. Mashanovich, “Silicon waveguides and devices for the mid-infrared,” Appl. Phys. Lett. 101(12), 121105 (2012).
[Crossref]

O’Brien, J. L.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360(6386), 285–291 (2018).
[Crossref]

M. Piekarek, D. Bonneau, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “High-extinction ratio integrated photonic filters for silicon quantum photonics,” Opt. Lett. 42(4), 815–818 (2017).
[Crossref]

J. W. Silverstone, D. Bonneau, J. L. O’Brien, and M. G. Thompson, “Silicon quantum photonics,” IEEE J. Sel. Top. Quantum Electron. 22(6), 390–402 (2016).
[Crossref]

J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, “On-chip quantum interference between silicon photon-pair sources,” Nat. Photonics 8(2), 104–108 (2014).
[Crossref]

J. C. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3(6), 346–350 (2009).
[Crossref]

J. L. O’Brien, A. Furusawa, and J. Vučković, “Photonic quantum technologies,” Nat. Photonics 3(12), 687–695 (2009).
[Crossref]

Ohira, K.

J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, “On-chip quantum interference between silicon photon-pair sources,” Nat. Photonics 8(2), 104–108 (2014).
[Crossref]

Okawachi, Y.

M. Yu, Y. Okawachi, A. G. Griffith, N. Picqué, M. Lipson, and A. L. Gaeta, “Silicon-chip-based mid-infrared dual-comb spectroscopy,” Nat. Commun. 9(1), 1869 (2018).
[Crossref]

X. Ji, F. A. Barbosa, S. P. Roberts, A. Dutt, J. Cardenas, Y. Okawachi, A. Bryant, A. L. Gaeta, and M. Lipson, “Ultra-low-loss on-chip resonators with sub-milliwatt parametric oscillation threshold,” Optica 4(6), 619–624 (2017).
[Crossref]

A. G. Griffith, R. K. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6(1), 6299 (2015).
[Crossref]

Orquiza, D.

S. Ramelow, A. Farsi, S. Clemmen, D. Orquiza, K. Luke, M. Lipson, and A. L. Gaeta, “Silicon-nitride platform for narrowband entangled photon generation,” arXiv preprint arXiv:1508.04358 (2015).

Ortega-Moñux, A.

Osgood, R. M.

Osgood Jr, R. M.

X. Liu, R. M. Osgood Jr, Y. A. Vlasov, and W. M. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics 4(8), 557–560 (2010).
[Crossref]

Ou, Z.-Y.

C.-K. Hong, Z.-Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59(18), 2044–2046 (1987).
[Crossref]

Oxenløwe, L. K.

S. Paesani, Y. Ding, R. Santagati, L. Chakhmakhchyan, C. Vigliar, K. Rottwitt, L. K. Oxenløwe, J. Wang, M. G. Thompson, and A. Laing, “Generation and sampling of quantum states of light in a silicon chip,” Nat. Phys. 15(9), 925–929 (2019).
[Crossref]

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360(6386), 285–291 (2018).
[Crossref]

Paesani, S.

S. Paesani, Y. Ding, R. Santagati, L. Chakhmakhchyan, C. Vigliar, K. Rottwitt, L. K. Oxenløwe, J. Wang, M. G. Thompson, and A. Laing, “Generation and sampling of quantum states of light in a silicon chip,” Nat. Phys. 15(9), 925–929 (2019).
[Crossref]

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360(6386), 285–291 (2018).
[Crossref]

Pang, A.

Z. Sheng, Z. Wang, C. Qiu, L. Li, A. Pang, A. Wu, X. Wang, S. Zou, and F. Gan, “A compact and low-loss MMI coupler fabricated with CMOS technology,” IEEE Photonics J. 4(6), 2272–2277 (2012).
[Crossref]

Park, J. H.

D. H. Lee, S. J. Choo, U. Jung, K. W. Lee, K. W. Kim, and J. H. Park, “Low-loss silicon waveguides with sidewall roughness reduction using a SiO2 hard mask and fluorine-based dry etching,” J. Micromech. Microeng. 25(1), 015003 (2015).
[Crossref]

Pascal, D.

F. Grillot, L. Vivien, S. Laval, D. Pascal, and E. Cassan, “Size influence on the propagation loss induced by sidewall roughness in ultrasmall soi waveguides,” IEEE Photonics Technol. Lett. 16(7), 1661–1663 (2004).
[Crossref]

Pavesi, L.

M. Mancinelli, A. Trenti, S. Piccione, G. Fontana, J. S. Dam, P. Tidemand-Lichtenberg, C. Pedersen, and L. Pavesi, “Mid-infrared coincidence measurements on twin photons at room temperature,” Nat. Commun. 8(1), 15184 (2017).
[Crossref]

L. Pavesi and D. J. Lockwood, Silicon photonics III: Systems and applications, vol. 122 (Springer Science & Business Media, 2016).

Pedersen, C.

M. Mancinelli, A. Trenti, S. Piccione, G. Fontana, J. S. Dam, P. Tidemand-Lichtenberg, C. Pedersen, and L. Pavesi, “Mid-infrared coincidence measurements on twin photons at room temperature,” Nat. Commun. 8(1), 15184 (2017).
[Crossref]

Penades, J. S.

Phare, C. T.

A. G. Griffith, R. K. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6(1), 6299 (2015).
[Crossref]

Piccione, S.

M. Mancinelli, A. Trenti, S. Piccione, G. Fontana, J. S. Dam, P. Tidemand-Lichtenberg, C. Pedersen, and L. Pavesi, “Mid-infrared coincidence measurements on twin photons at room temperature,” Nat. Commun. 8(1), 15184 (2017).
[Crossref]

Picqué, N.

M. Yu, Y. Okawachi, A. G. Griffith, N. Picqué, M. Lipson, and A. L. Gaeta, “Silicon-chip-based mid-infrared dual-comb spectroscopy,” Nat. Commun. 9(1), 1869 (2018).
[Crossref]

Piekarek, M.

Poitras, C. B.

A. G. Griffith, R. K. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6(1), 6299 (2015).
[Crossref]

J. Cardenas, C. B. Poitras, J. T. Robinson, K. Preston, L. Chen, and M. Lipson, “Low loss etchless silicon photonic waveguides,” Opt. Express 17(6), 4752–4757 (2009).
[Crossref]

Politi, A.

J. C. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3(6), 346–350 (2009).
[Crossref]

Prabhakar, S.

S. Prabhakar, T. Shields, A. C. Dada, M. Ebrahim, G. G. Taylor, D. Morozov, K. Erotokritou, S. Miki, M. Yabuno, H. Terai, C. Gawith, M. Kues, L. Caspani, R. H. Hadfield, and M. Clerici, “Two-photon quantum interference and entanglement at 2.1 µm,” Sci. Adv. 6(13), eaay5195 (2020).
[Crossref]

Prabhu, M.

Preble, S. F.

S. F. Preble, M. L. Fanto, J. A. Steidle, C. C. Tison, G. A. Howland, Z. Wang, and P. M. Alsing, “On-chip quantum interference from a single silicon ring-resonator source,” Phys. Rev. Appl. 4(2), 021001 (2015).
[Crossref]

Premaratne, M.

Preston, K.

Prost, M.

M. Prost, Y.-C. Ling, S. Cakmakyapan, Y. Zhang, K. Zhang, J. Hu, Y. Zhang, and S. B. Yoo, “MWIR solid-state optical phased array beam steering using germanium-silicon photonic platform,” in Optical Fiber Communication Conference, (Optical Society of America, 2019), pp. M4E–3.

Qian, G.

Qiu, C.

Z. Sheng, Z. Wang, C. Qiu, L. Li, A. Pang, A. Wu, X. Wang, S. Zou, and F. Gan, “A compact and low-loss MMI coupler fabricated with CMOS technology,” IEEE Photonics J. 4(6), 2272–2277 (2012).
[Crossref]

Ramelow, S.

S. Ramelow, A. Farsi, S. Clemmen, D. Orquiza, K. Luke, M. Lipson, and A. L. Gaeta, “Silicon-nitride platform for narrowband entangled photon generation,” arXiv preprint arXiv:1508.04358 (2015).

Rarity, J. G.

J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, “On-chip quantum interference between silicon photon-pair sources,” Nat. Photonics 8(2), 104–108 (2014).
[Crossref]

Rattunde, M.

S. Kaspar, M. Rattunde, T. Topper, R. Moser, S. Adler, C. Manz, K. Kohler, and J. Wagner, “Recent Advances in 2-µm GaSb-Based Semiconductor Disk Laser—Power Scaling, Narrow-Linewidth and Short-Pulse Operation,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1501908 (2013).
[Crossref]

Reed, G.

Reed, G. T.

M.-S. Rouifed, C. G. Littlejohns, G. X. Tina, Q. Haodong, T. Hu, Z. Zhang, C. Liu, G. T. Reed, and H. Wang, “Low loss SOI waveguides and MMIs at the MIR wavelength of 2 µm,” IEEE Photonics Technol. Lett. 28(24), 2827–2829 (2016).
[Crossref]

M. M. Milošević, M. Nedeljkovic, T. M. Ben Masaud, E. Jaberansary, H. M. Chong, N. G. Emerson, G. T. Reed, and G. Z. Mashanovich, “Silicon waveguides and devices for the mid-infrared,” Appl. Phys. Lett. 101(12), 121105 (2012).
[Crossref]

Reintjes, J. F.

J. F. Reintjes and J. C. McGroddy, “Indirect two-photon transitions in si at 1.06 µm,” Phys. Rev. Lett. 30(19), 901–903 (1973).
[Crossref]

Rey, I. H.

C. A. Husko, A. S. Clark, M. J. Collins, A. De Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, “Multi-photon absorption limits to heralded single photon sources,” Sci. Rep. 3(1), 3087 (2013).
[Crossref]

Roberts, S. P.

Robinson, J. T.

Roelkens, G.

N. Hattasan, B. Kuyken, F. Leo, E. M. Ryckeboer, D. Vermeulen, and G. Roelkens, “High-efficiency SOI fiber-to-chip grating couplers and low-loss waveguides for the short-wave infrared,” IEEE Photonics Technol. Lett. 24(17), 1536–1538 (2012).
[Crossref]

B. Kuyken, X. Liu, R. M. Osgood, R. Baets, G. Roelkens, and W. M. Green, “Mid-infrared to telecom-band supercontinuum generation in highly nonlinear silicon-on-insulator wire waveguides,” Opt. Express 19(21), 20172–20181 (2011).
[Crossref]

Rotenberg, N.

A. D. Bristow, N. Rotenberg, and H. M. Van Driel, “Two-photon absorption and kerr coefficients of silicon for 850–2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
[Crossref]

Rottwitt, K.

S. Paesani, Y. Ding, R. Santagati, L. Chakhmakhchyan, C. Vigliar, K. Rottwitt, L. K. Oxenløwe, J. Wang, M. G. Thompson, and A. Laing, “Generation and sampling of quantum states of light in a silicon chip,” Nat. Phys. 15(9), 925–929 (2019).
[Crossref]

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360(6386), 285–291 (2018).
[Crossref]

Rouifed, M.-S.

M.-S. Rouifed, C. G. Littlejohns, G. X. Tina, Q. Haodong, T. Hu, Z. Zhang, C. Liu, G. T. Reed, and H. Wang, “Low loss SOI waveguides and MMIs at the MIR wavelength of 2 µm,” IEEE Photonics Technol. Lett. 28(24), 2827–2829 (2016).
[Crossref]

Rukhlenko, I. D.

Ryckeboer, E. M.

N. Hattasan, B. Kuyken, F. Leo, E. M. Ryckeboer, D. Vermeulen, and G. Roelkens, “High-efficiency SOI fiber-to-chip grating couplers and low-loss waveguides for the short-wave infrared,” IEEE Photonics Technol. Lett. 24(17), 1536–1538 (2012).
[Crossref]

Sahin, D.

G. F. Sinclair, N. A. Tyler, D. Sahin, J. Barreto, and M. G. Thompson, “Temperature dependence of the kerr nonlinearity and two-photon absorption in a silicon waveguide at 1.55 µm,” Phys. Rev. Appl. 11(4), 044084 (2019).
[Crossref]

Salavrakos, A.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360(6386), 285–291 (2018).
[Crossref]

Santagati, R.

J. C. Adcock, C. Vigliar, R. Santagati, J. W. Silverstone, and M. G. Thompson, “Programmable four-photon graph states on a silicon chip,” Nat. Commun. 10(1), 3528 (2019).
[Crossref]

S. Paesani, Y. Ding, R. Santagati, L. Chakhmakhchyan, C. Vigliar, K. Rottwitt, L. K. Oxenløwe, J. Wang, M. G. Thompson, and A. Laing, “Generation and sampling of quantum states of light in a silicon chip,” Nat. Phys. 15(9), 925–929 (2019).
[Crossref]

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360(6386), 285–291 (2018).
[Crossref]

Sasaki, M.

Savanier, M.

Schmid, J. H.

Schmidt, B. S.

Shahverdi, A.

Y. M. Sua, H. Fan, A. Shahverdi, J.-Y. Chen, and Y.-P. Huang, “Direct generation and detection of quantum correlated photons with 3.2 um wavelength spacing,” Sci. Rep. 7(1), 17494 (2017).
[Crossref]

Sharping, J. E.

Sheng, Z.

Z. Sheng, Z. Wang, C. Qiu, L. Li, A. Pang, A. Wu, X. Wang, S. Zou, and F. Gan, “A compact and low-loss MMI coupler fabricated with CMOS technology,” IEEE Photonics J. 4(6), 2272–2277 (2012).
[Crossref]

Shields, T.

S. Prabhakar, T. Shields, A. C. Dada, M. Ebrahim, G. G. Taylor, D. Morozov, K. Erotokritou, S. Miki, M. Yabuno, H. Terai, C. Gawith, M. Kues, L. Caspani, R. H. Hadfield, and M. Clerici, “Two-photon quantum interference and entanglement at 2.1 µm,” Sci. Adv. 6(13), eaay5195 (2020).
[Crossref]

Sieger, M.

M. Sieger and B. Mizaikoff, “Toward on-chip mid-infrared sensors,” Anal. Chem. 88(11), 5562–5573 (2016).
[Crossref]

Silverstone, J. W.

J. C. Adcock, C. Vigliar, R. Santagati, J. W. Silverstone, and M. G. Thompson, “Programmable four-photon graph states on a silicon chip,” Nat. Commun. 10(1), 3528 (2019).
[Crossref]

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360(6386), 285–291 (2018).
[Crossref]

J. W. Silverstone, D. Bonneau, J. L. O’Brien, and M. G. Thompson, “Silicon quantum photonics,” IEEE J. Sel. Top. Quantum Electron. 22(6), 390–402 (2016).
[Crossref]

J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, “On-chip quantum interference between silicon photon-pair sources,” Nat. Photonics 8(2), 104–108 (2014).
[Crossref]

Sinclair, G. F.

G. F. Sinclair, N. A. Tyler, D. Sahin, J. Barreto, and M. G. Thompson, “Temperature dependence of the kerr nonlinearity and two-photon absorption in a silicon waveguide at 1.55 µm,” Phys. Rev. Appl. 11(4), 044084 (2019).
[Crossref]

Sipe, J.

M. Liscidini and J. Sipe, “Stimulated emission tomography,” Phys. Rev. Lett. 111(19), 193602 (2013).
[Crossref]

Skrzypczyk, P.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360(6386), 285–291 (2018).
[Crossref]

Smith, A. M.

Smith, D. R.

P. Cheben, R. Halir, J. H. Schmid, H. A. Atwater, and D. R. Smith, “Subwavelength integrated photonics,” Nature 560(7720), 565–572 (2018).
[Crossref]

Stankovic, S.

Stefanov, A.

J. C. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3(6), 346–350 (2009).
[Crossref]

Steidle, J. A.

S. F. Preble, M. L. Fanto, J. A. Steidle, C. C. Tison, G. A. Howland, Z. Wang, and P. M. Alsing, “On-chip quantum interference from a single silicon ring-resonator source,” Phys. Rev. Appl. 4(2), 021001 (2015).
[Crossref]

Sua, Y. M.

Y. M. Sua, H. Fan, A. Shahverdi, J.-Y. Chen, and Y.-P. Huang, “Direct generation and detection of quantum correlated photons with 3.2 um wavelength spacing,” Sci. Rep. 7(1), 17494 (2017).
[Crossref]

Suzuki, N.

J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, “On-chip quantum interference between silicon photon-pair sources,” Nat. Photonics 8(2), 104–108 (2014).
[Crossref]

Tan, D. T.

Tanner, M. G.

M. Piekarek, D. Bonneau, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “High-extinction ratio integrated photonic filters for silicon quantum photonics,” Opt. Lett. 42(4), 815–818 (2017).
[Crossref]

J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, “On-chip quantum interference between silicon photon-pair sources,” Nat. Photonics 8(2), 104–108 (2014).
[Crossref]

C. M. Natarajan, M. G. Tanner, and R. H. Hadfield, “Superconducting nanowire single-photon detectors: physics and applications,” Supercond. Sci. Technol. 25(6), 063001 (2012).
[Crossref]

Taylor, G. G.

S. Prabhakar, T. Shields, A. C. Dada, M. Ebrahim, G. G. Taylor, D. Morozov, K. Erotokritou, S. Miki, M. Yabuno, H. Terai, C. Gawith, M. Kues, L. Caspani, R. H. Hadfield, and M. Clerici, “Two-photon quantum interference and entanglement at 2.1 µm,” Sci. Adv. 6(13), eaay5195 (2020).
[Crossref]

Terai, H.

S. Prabhakar, T. Shields, A. C. Dada, M. Ebrahim, G. G. Taylor, D. Morozov, K. Erotokritou, S. Miki, M. Yabuno, H. Terai, C. Gawith, M. Kues, L. Caspani, R. H. Hadfield, and M. Clerici, “Two-photon quantum interference and entanglement at 2.1 µm,” Sci. Adv. 6(13), eaay5195 (2020).
[Crossref]

M. Piekarek, D. Bonneau, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “High-extinction ratio integrated photonic filters for silicon quantum photonics,” Opt. Lett. 42(4), 815–818 (2017).
[Crossref]

Thewalt, M. L. W.

M. Cardona, T. A. Meyer, and M. L. W. Thewalt, “Temperature Dependence of the Energy Gap of Semiconductors in the Low-Temperature Limit,” Phys. Rev. Lett. 92(19), 196403 (2004).
[Crossref]

Thompson, M. G.

J. C. Adcock, C. Vigliar, R. Santagati, J. W. Silverstone, and M. G. Thompson, “Programmable four-photon graph states on a silicon chip,” Nat. Commun. 10(1), 3528 (2019).
[Crossref]

S. Paesani, Y. Ding, R. Santagati, L. Chakhmakhchyan, C. Vigliar, K. Rottwitt, L. K. Oxenløwe, J. Wang, M. G. Thompson, and A. Laing, “Generation and sampling of quantum states of light in a silicon chip,” Nat. Phys. 15(9), 925–929 (2019).
[Crossref]

G. F. Sinclair, N. A. Tyler, D. Sahin, J. Barreto, and M. G. Thompson, “Temperature dependence of the kerr nonlinearity and two-photon absorption in a silicon waveguide at 1.55 µm,” Phys. Rev. Appl. 11(4), 044084 (2019).
[Crossref]

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360(6386), 285–291 (2018).
[Crossref]

M. Piekarek, D. Bonneau, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “High-extinction ratio integrated photonic filters for silicon quantum photonics,” Opt. Lett. 42(4), 815–818 (2017).
[Crossref]

J. W. Silverstone, D. Bonneau, J. L. O’Brien, and M. G. Thompson, “Silicon quantum photonics,” IEEE J. Sel. Top. Quantum Electron. 22(6), 390–402 (2016).
[Crossref]

J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, “On-chip quantum interference between silicon photon-pair sources,” Nat. Photonics 8(2), 104–108 (2014).
[Crossref]

Thomson, D.

Tidemand-Lichtenberg, P.

M. Mancinelli, A. Trenti, S. Piccione, G. Fontana, J. S. Dam, P. Tidemand-Lichtenberg, C. Pedersen, and L. Pavesi, “Mid-infrared coincidence measurements on twin photons at room temperature,” Nat. Commun. 8(1), 15184 (2017).
[Crossref]

Tina, G. X.

M.-S. Rouifed, C. G. Littlejohns, G. X. Tina, Q. Haodong, T. Hu, Z. Zhang, C. Liu, G. T. Reed, and H. Wang, “Low loss SOI waveguides and MMIs at the MIR wavelength of 2 µm,” IEEE Photonics Technol. Lett. 28(24), 2827–2829 (2016).
[Crossref]

Tison, C. C.

N. C. Harris, J. Carolan, D. Bunandar, M. Prabhu, M. Hochberg, T. Baehr-Jones, M. L. Fanto, A. M. Smith, C. C. Tison, P. M. Alsing, and D. Englund, “Linear programmable nanophotonic processors,” Optica 5(12), 1623 (2018).
[Crossref]

S. F. Preble, M. L. Fanto, J. A. Steidle, C. C. Tison, G. A. Howland, Z. Wang, and P. M. Alsing, “On-chip quantum interference from a single silicon ring-resonator source,” Phys. Rev. Appl. 4(2), 021001 (2015).
[Crossref]

Topper, T.

S. Kaspar, M. Rattunde, T. Topper, R. Moser, S. Adler, C. Manz, K. Kohler, and J. Wagner, “Recent Advances in 2-µm GaSb-Based Semiconductor Disk Laser—Power Scaling, Narrow-Linewidth and Short-Pulse Operation,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1501908 (2013).
[Crossref]

Trenti, A.

M. Mancinelli, A. Trenti, S. Piccione, G. Fontana, J. S. Dam, P. Tidemand-Lichtenberg, C. Pedersen, and L. Pavesi, “Mid-infrared coincidence measurements on twin photons at room temperature,” Nat. Commun. 8(1), 15184 (2017).
[Crossref]

Tura, J.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360(6386), 285–291 (2018).
[Crossref]

Turner, A. C.

Tyler, N. A.

G. F. Sinclair, N. A. Tyler, D. Sahin, J. Barreto, and M. G. Thompson, “Temperature dependence of the kerr nonlinearity and two-photon absorption in a silicon waveguide at 1.55 µm,” Phys. Rev. Appl. 11(4), 044084 (2019).
[Crossref]

Van Driel, H. M.

A. D. Bristow, N. Rotenberg, and H. M. Van Driel, “Two-photon absorption and kerr coefficients of silicon for 850–2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
[Crossref]

Venkatram, N.

Vermeulen, D.

N. Hattasan, B. Kuyken, F. Leo, E. M. Ryckeboer, D. Vermeulen, and G. Roelkens, “High-efficiency SOI fiber-to-chip grating couplers and low-loss waveguides for the short-wave infrared,” IEEE Photonics Technol. Lett. 24(17), 1536–1538 (2012).
[Crossref]

Vigliar, C.

J. C. Adcock, C. Vigliar, R. Santagati, J. W. Silverstone, and M. G. Thompson, “Programmable four-photon graph states on a silicon chip,” Nat. Commun. 10(1), 3528 (2019).
[Crossref]

S. Paesani, Y. Ding, R. Santagati, L. Chakhmakhchyan, C. Vigliar, K. Rottwitt, L. K. Oxenløwe, J. Wang, M. G. Thompson, and A. Laing, “Generation and sampling of quantum states of light in a silicon chip,” Nat. Phys. 15(9), 925–929 (2019).
[Crossref]

Vivien, L.

F. Grillot, L. Vivien, S. Laval, D. Pascal, and E. Cassan, “Size influence on the propagation loss induced by sidewall roughness in ultrasmall soi waveguides,” IEEE Photonics Technol. Lett. 16(7), 1661–1663 (2004).
[Crossref]

Vlasov, Y. A.

X. Liu, R. M. Osgood Jr, Y. A. Vlasov, and W. M. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics 4(8), 557–560 (2010).
[Crossref]

Vuckovic, J.

J. L. O’Brien, A. Furusawa, and J. Vučković, “Photonic quantum technologies,” Nat. Photonics 3(12), 687–695 (2009).
[Crossref]

Wagner, J.

S. Kaspar, M. Rattunde, T. Topper, R. Moser, S. Adler, C. Manz, K. Kohler, and J. Wagner, “Recent Advances in 2-µm GaSb-Based Semiconductor Disk Laser—Power Scaling, Narrow-Linewidth and Short-Pulse Operation,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1501908 (2013).
[Crossref]

Wang, F.

Wang, H.

M.-S. Rouifed, C. G. Littlejohns, G. X. Tina, Q. Haodong, T. Hu, Z. Zhang, C. Liu, G. T. Reed, and H. Wang, “Low loss SOI waveguides and MMIs at the MIR wavelength of 2 µm,” IEEE Photonics Technol. Lett. 28(24), 2827–2829 (2016).
[Crossref]

Wang, J.

S. Paesani, Y. Ding, R. Santagati, L. Chakhmakhchyan, C. Vigliar, K. Rottwitt, L. K. Oxenløwe, J. Wang, M. G. Thompson, and A. Laing, “Generation and sampling of quantum states of light in a silicon chip,” Nat. Phys. 15(9), 925–929 (2019).
[Crossref]

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360(6386), 285–291 (2018).
[Crossref]

Wang, S.

Wang, T.

Wang, W.

H. Jin, F. Liu, P. Xu, J. Xia, M. Zhong, Y. Yuan, J. Zhou, Y. Gong, W. Wang, and S. Zhu, “On-chip generation and manipulation of entangled photons based on reconfigurable lithium-niobate waveguide circuits,” Phys. Rev. Lett. 113(10), 103601 (2014).
[Crossref]

Wang, X.

Z. Sheng, Z. Wang, C. Qiu, L. Li, A. Pang, A. Wu, X. Wang, S. Zou, and F. Gan, “A compact and low-loss MMI coupler fabricated with CMOS technology,” IEEE Photonics J. 4(6), 2272–2277 (2012).
[Crossref]

Wang, Y.

Wang, Z.

S. F. Preble, M. L. Fanto, J. A. Steidle, C. C. Tison, G. A. Howland, Z. Wang, and P. M. Alsing, “On-chip quantum interference from a single silicon ring-resonator source,” Phys. Rev. Appl. 4(2), 021001 (2015).
[Crossref]

Z. Sheng, Z. Wang, C. Qiu, L. Li, A. Pang, A. Wu, X. Wang, S. Zou, and F. Gan, “A compact and low-loss MMI coupler fabricated with CMOS technology,” IEEE Photonics J. 4(6), 2272–2277 (2012).
[Crossref]

Whittaker, E. A.

Wu, A.

Z. Sheng, Z. Wang, C. Qiu, L. Li, A. Pang, A. Wu, X. Wang, S. Zou, and F. Gan, “A compact and low-loss MMI coupler fabricated with CMOS technology,” IEEE Photonics J. 4(6), 2272–2277 (2012).
[Crossref]

Xia, J.

H. Jin, F. Liu, P. Xu, J. Xia, M. Zhong, Y. Yuan, J. Zhou, Y. Gong, W. Wang, and S. Zhu, “On-chip generation and manipulation of entangled photons based on reconfigurable lithium-niobate waveguide circuits,” Phys. Rev. Lett. 113(10), 103601 (2014).
[Crossref]

Xiong, C.

J. He, B. A. Bell, A. Casas-Bedoya, Y. Zhang, A. S. Clark, C. Xiong, and B. J. Eggleton, “Ultracompact quantum splitter of degenerate photon pairs,” Optica 2(9), 779–782 (2015).
[Crossref]

C. A. Husko, A. S. Clark, M. J. Collins, A. De Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, “Multi-photon absorption limits to heralded single photon sources,” Sci. Rep. 3(1), 3087 (2013).
[Crossref]

Xu, D.-X.

Xu, P.

H. Jin, F. Liu, P. Xu, J. Xia, M. Zhong, Y. Yuan, J. Zhou, Y. Gong, W. Wang, and S. Zhu, “On-chip generation and manipulation of entangled photons based on reconfigurable lithium-niobate waveguide circuits,” Phys. Rev. Lett. 113(10), 103601 (2014).
[Crossref]

Xu, X.

Y. Zou, S. Chakravarty, C.-J. Chung, X. Xu, and R. T. Chen, “Mid-infrared silicon photonic waveguides and devices [Invited],” Photonics Res. 6(4), 254–276 (2018).
[Crossref]

Yabuno, M.

S. Prabhakar, T. Shields, A. C. Dada, M. Ebrahim, G. G. Taylor, D. Morozov, K. Erotokritou, S. Miki, M. Yabuno, H. Terai, C. Gawith, M. Kues, L. Caspani, R. H. Hadfield, and M. Clerici, “Two-photon quantum interference and entanglement at 2.1 µm,” Sci. Adv. 6(13), eaay5195 (2020).
[Crossref]

Yamashita, T.

Yin, L.

Ylinen, S.

Yoo, S. B.

M. Prost, Y.-C. Ling, S. Cakmakyapan, Y. Zhang, K. Zhang, J. Hu, Y. Zhang, and S. B. Yoo, “MWIR solid-state optical phased array beam steering using germanium-silicon photonic platform,” in Optical Fiber Communication Conference, (Optical Society of America, 2019), pp. M4E–3.

Yoshida, H.

J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, “On-chip quantum interference between silicon photon-pair sources,” Nat. Photonics 8(2), 104–108 (2014).
[Crossref]

Yu, M.

M. Yu, Y. Okawachi, A. G. Griffith, N. Picqué, M. Lipson, and A. L. Gaeta, “Silicon-chip-based mid-infrared dual-comb spectroscopy,” Nat. Commun. 9(1), 1869 (2018).
[Crossref]

S. A. Miller, M. Yu, X. Ji, A. G. Griffith, J. Cardenas, A. L. Gaeta, and M. Lipson, “Low-loss silicon platform for broadband mid-infrared photonics,” Optica 4(7), 707–712 (2017).
[Crossref]

A. G. Griffith, R. K. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6(1), 6299 (2015).
[Crossref]

Yuan, Y.

H. Jin, F. Liu, P. Xu, J. Xia, M. Zhong, Y. Yuan, J. Zhou, Y. Gong, W. Wang, and S. Zhu, “On-chip generation and manipulation of entangled photons based on reconfigurable lithium-niobate waveguide circuits,” Phys. Rev. Lett. 113(10), 103601 (2014).
[Crossref]

Zhang, K.

M. Prost, Y.-C. Ling, S. Cakmakyapan, Y. Zhang, K. Zhang, J. Hu, Y. Zhang, and S. B. Yoo, “MWIR solid-state optical phased array beam steering using germanium-silicon photonic platform,” in Optical Fiber Communication Conference, (Optical Society of America, 2019), pp. M4E–3.

Zhang, X.

Zhang, Y.

J. He, B. A. Bell, A. Casas-Bedoya, Y. Zhang, A. S. Clark, C. Xiong, and B. J. Eggleton, “Ultracompact quantum splitter of degenerate photon pairs,” Optica 2(9), 779–782 (2015).
[Crossref]

M. Prost, Y.-C. Ling, S. Cakmakyapan, Y. Zhang, K. Zhang, J. Hu, Y. Zhang, and S. B. Yoo, “MWIR solid-state optical phased array beam steering using germanium-silicon photonic platform,” in Optical Fiber Communication Conference, (Optical Society of America, 2019), pp. M4E–3.

M. Prost, Y.-C. Ling, S. Cakmakyapan, Y. Zhang, K. Zhang, J. Hu, Y. Zhang, and S. B. Yoo, “MWIR solid-state optical phased array beam steering using germanium-silicon photonic platform,” in Optical Fiber Communication Conference, (Optical Society of America, 2019), pp. M4E–3.

Zhang, Z.

M.-S. Rouifed, C. G. Littlejohns, G. X. Tina, Q. Haodong, T. Hu, Z. Zhang, C. Liu, G. T. Reed, and H. Wang, “Low loss SOI waveguides and MMIs at the MIR wavelength of 2 µm,” IEEE Photonics Technol. Lett. 28(24), 2827–2829 (2016).
[Crossref]

Zhong, M.

H. Jin, F. Liu, P. Xu, J. Xia, M. Zhong, Y. Yuan, J. Zhou, Y. Gong, W. Wang, and S. Zhu, “On-chip generation and manipulation of entangled photons based on reconfigurable lithium-niobate waveguide circuits,” Phys. Rev. Lett. 113(10), 103601 (2014).
[Crossref]

Zhou, J.

H. Jin, F. Liu, P. Xu, J. Xia, M. Zhong, Y. Yuan, J. Zhou, Y. Gong, W. Wang, and S. Zhu, “On-chip generation and manipulation of entangled photons based on reconfigurable lithium-niobate waveguide circuits,” Phys. Rev. Lett. 113(10), 103601 (2014).
[Crossref]

Zhu, S.

H. Jin, F. Liu, P. Xu, J. Xia, M. Zhong, Y. Yuan, J. Zhou, Y. Gong, W. Wang, and S. Zhu, “On-chip generation and manipulation of entangled photons based on reconfigurable lithium-niobate waveguide circuits,” Phys. Rev. Lett. 113(10), 103601 (2014).
[Crossref]

Zou, S.

Z. Sheng, Z. Wang, C. Qiu, L. Li, A. Pang, A. Wu, X. Wang, S. Zou, and F. Gan, “A compact and low-loss MMI coupler fabricated with CMOS technology,” IEEE Photonics J. 4(6), 2272–2277 (2012).
[Crossref]

Zou, Y.

Y. Zou, S. Chakravarty, C.-J. Chung, X. Xu, and R. T. Chen, “Mid-infrared silicon photonic waveguides and devices [Invited],” Photonics Res. 6(4), 254–276 (2018).
[Crossref]

Anal. Chem. (1)

M. Sieger and B. Mizaikoff, “Toward on-chip mid-infrared sensors,” Anal. Chem. 88(11), 5562–5573 (2016).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

M. M. Milošević, M. Nedeljkovic, T. M. Ben Masaud, E. Jaberansary, H. M. Chong, N. G. Emerson, G. T. Reed, and G. Z. Mashanovich, “Silicon waveguides and devices for the mid-infrared,” Appl. Phys. Lett. 101(12), 121105 (2012).
[Crossref]

A. D. Bristow, N. Rotenberg, and H. M. Van Driel, “Two-photon absorption and kerr coefficients of silicon for 850–2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

J. W. Silverstone, D. Bonneau, J. L. O’Brien, and M. G. Thompson, “Silicon quantum photonics,” IEEE J. Sel. Top. Quantum Electron. 22(6), 390–402 (2016).
[Crossref]

S. Kaspar, M. Rattunde, T. Topper, R. Moser, S. Adler, C. Manz, K. Kohler, and J. Wagner, “Recent Advances in 2-µm GaSb-Based Semiconductor Disk Laser—Power Scaling, Narrow-Linewidth and Short-Pulse Operation,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1501908 (2013).
[Crossref]

IEEE Photonics J. (1)

Z. Sheng, Z. Wang, C. Qiu, L. Li, A. Pang, A. Wu, X. Wang, S. Zou, and F. Gan, “A compact and low-loss MMI coupler fabricated with CMOS technology,” IEEE Photonics J. 4(6), 2272–2277 (2012).
[Crossref]

IEEE Photonics Technol. Lett. (3)

M.-S. Rouifed, C. G. Littlejohns, G. X. Tina, Q. Haodong, T. Hu, Z. Zhang, C. Liu, G. T. Reed, and H. Wang, “Low loss SOI waveguides and MMIs at the MIR wavelength of 2 µm,” IEEE Photonics Technol. Lett. 28(24), 2827–2829 (2016).
[Crossref]

N. Hattasan, B. Kuyken, F. Leo, E. M. Ryckeboer, D. Vermeulen, and G. Roelkens, “High-efficiency SOI fiber-to-chip grating couplers and low-loss waveguides for the short-wave infrared,” IEEE Photonics Technol. Lett. 24(17), 1536–1538 (2012).
[Crossref]

F. Grillot, L. Vivien, S. Laval, D. Pascal, and E. Cassan, “Size influence on the propagation loss induced by sidewall roughness in ultrasmall soi waveguides,” IEEE Photonics Technol. Lett. 16(7), 1661–1663 (2004).
[Crossref]

J. Micromech. Microeng. (1)

D. H. Lee, S. J. Choo, U. Jung, K. W. Lee, K. W. Kim, and J. H. Park, “Low-loss silicon waveguides with sidewall roughness reduction using a SiO2 hard mask and fluorine-based dry etching,” J. Micromech. Microeng. 25(1), 015003 (2015).
[Crossref]

J. Opt. (1)

D. E. Hagan and A. P. Knights, “Mechanisms for optical loss in SOI waveguides for mid-infrared wavelengths around 2 µm,” J. Opt. 19(2), 025801 (2017).
[Crossref]

J. Opt. Soc. Am. B (1)

J. Phys. B: At., Mol. Opt. Phys. (1)

H. Garcia and R. Kalyanaraman, “Phonon-assisted two-photon absorption in the presence of a DC-field: the nonlinear Franz–Keldysh effect in indirect gap semiconductors,” J. Phys. B: At., Mol. Opt. Phys. 39(12), 2737–2746 (2006).
[Crossref]

Nano Lett. (1)

F. Marsili, F. Bellei, F. Najafi, A. E. Dane, E. A. Dauler, R. J. Molnar, and K. K. Berggren, “Efficient single photon detection from 500 nm to 5 µm wavelength,” Nano Lett. 12(9), 4799–4804 (2012).
[Crossref]

Nat. Commun. (4)

A. G. Griffith, R. K. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6(1), 6299 (2015).
[Crossref]

M. Yu, Y. Okawachi, A. G. Griffith, N. Picqué, M. Lipson, and A. L. Gaeta, “Silicon-chip-based mid-infrared dual-comb spectroscopy,” Nat. Commun. 9(1), 1869 (2018).
[Crossref]

M. Mancinelli, A. Trenti, S. Piccione, G. Fontana, J. S. Dam, P. Tidemand-Lichtenberg, C. Pedersen, and L. Pavesi, “Mid-infrared coincidence measurements on twin photons at room temperature,” Nat. Commun. 8(1), 15184 (2017).
[Crossref]

J. C. Adcock, C. Vigliar, R. Santagati, J. W. Silverstone, and M. G. Thompson, “Programmable four-photon graph states on a silicon chip,” Nat. Commun. 10(1), 3528 (2019).
[Crossref]

Nat. Photonics (5)

J. L. O’Brien, A. Furusawa, and J. Vučković, “Photonic quantum technologies,” Nat. Photonics 3(12), 687–695 (2009).
[Crossref]

B. Jalali, “Silicon photonics: Nonlinear optics in the mid-infrared,” Nat. Photonics 4(8), 506–508 (2010).
[Crossref]

X. Liu, R. M. Osgood Jr, Y. A. Vlasov, and W. M. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics 4(8), 557–560 (2010).
[Crossref]

J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, “On-chip quantum interference between silicon photon-pair sources,” Nat. Photonics 8(2), 104–108 (2014).
[Crossref]

J. C. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3(6), 346–350 (2009).
[Crossref]

Nat. Phys. (1)

S. Paesani, Y. Ding, R. Santagati, L. Chakhmakhchyan, C. Vigliar, K. Rottwitt, L. K. Oxenløwe, J. Wang, M. G. Thompson, and A. Laing, “Generation and sampling of quantum states of light in a silicon chip,” Nat. Phys. 15(9), 925–929 (2019).
[Crossref]

Nature (1)

P. Cheben, R. Halir, J. H. Schmid, H. A. Atwater, and D. R. Smith, “Subwavelength integrated photonics,” Nature 560(7720), 565–572 (2018).
[Crossref]

Opt. Express (9)

M. Cherchi, S. Ylinen, M. Harjanne, M. Kapulainen, and T. Aalto, “Dramatic size reduction of waveguide bends on a micron-scale silicon photonic platform,” Opt. Express 21(15), 17814–17823 (2013).
[Crossref]

M. Savanier, R. Kumar, and S. Mookherjea, “Photon pair generation from compact silicon microring resonators using microwatt-level pump powers,” Opt. Express 24(4), 3313–3328 (2016).
[Crossref]

J. Cardenas, C. B. Poitras, J. T. Robinson, K. Preston, L. Chen, and M. Lipson, “Low loss etchless silicon photonic waveguides,” Opt. Express 17(6), 4752–4757 (2009).
[Crossref]

J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14(25), 12388–12393 (2006).
[Crossref]

S. Clemmen, K. P. Huy, W. Bogaerts, R. G. Baets, P. Emplit, and S. Massar, “Continuous wave photon pair generation in silicon-on-insulator waveguides and ring resonators,” Opt. Express 17(19), 16558–16570 (2009).
[Crossref]

D. Benedikovic, P. Cheben, J. H. Schmid, D.-X. Xu, B. Lamontagne, S. Wang, J. Lapointe, R. Halir, A. Ortega-Moñux, S. Janz, and M. Dado, “Subwavelength index engineered surface grating coupler with sub-decibel efficiency for 220-nm silicon-on-insulator waveguides,” Opt. Express 23(17), 22628–22635 (2015).
[Crossref]

B. Kuyken, X. Liu, R. M. Osgood, R. Baets, G. Roelkens, and W. M. Green, “Mid-infrared to telecom-band supercontinuum generation in highly nonlinear silicon-on-insulator wire waveguides,” Opt. Express 19(21), 20172–20181 (2011).
[Crossref]

P. Corrigan, R. Martini, E. A. Whittaker, and C. Bethea, “Quantum cascade lasers and the kruse model in free space optical communication,” Opt. Express 17(6), 4355–4359 (2009).
[Crossref]

T. Wang, N. Venkatram, J. Gosciniak, Y. Cui, G. Qian, W. Ji, and D. T. Tan, “Multi-photon absorption and third-order nonlinearity in silicon at mid-infrared wavelengths,” Opt. Express 21(26), 32192–32198 (2013).
[Crossref]

Opt. Lett. (4)

Opt. Mater. Express (1)

Optica (4)

Photonics Res. (1)

Y. Zou, S. Chakravarty, C.-J. Chung, X. Xu, and R. T. Chen, “Mid-infrared silicon photonic waveguides and devices [Invited],” Photonics Res. 6(4), 254–276 (2018).
[Crossref]

Phys. Rev. Appl. (2)

G. F. Sinclair, N. A. Tyler, D. Sahin, J. Barreto, and M. G. Thompson, “Temperature dependence of the kerr nonlinearity and two-photon absorption in a silicon waveguide at 1.55 µm,” Phys. Rev. Appl. 11(4), 044084 (2019).
[Crossref]

S. F. Preble, M. L. Fanto, J. A. Steidle, C. C. Tison, G. A. Howland, Z. Wang, and P. M. Alsing, “On-chip quantum interference from a single silicon ring-resonator source,” Phys. Rev. Appl. 4(2), 021001 (2015).
[Crossref]

Phys. Rev. Lett. (5)

H. Jin, F. Liu, P. Xu, J. Xia, M. Zhong, Y. Yuan, J. Zhou, Y. Gong, W. Wang, and S. Zhu, “On-chip generation and manipulation of entangled photons based on reconfigurable lithium-niobate waveguide circuits,” Phys. Rev. Lett. 113(10), 103601 (2014).
[Crossref]

C.-K. Hong, Z.-Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59(18), 2044–2046 (1987).
[Crossref]

J. F. Reintjes and J. C. McGroddy, “Indirect two-photon transitions in si at 1.06 µm,” Phys. Rev. Lett. 30(19), 901–903 (1973).
[Crossref]

M. Liscidini and J. Sipe, “Stimulated emission tomography,” Phys. Rev. Lett. 111(19), 193602 (2013).
[Crossref]

M. Cardona, T. A. Meyer, and M. L. W. Thewalt, “Temperature Dependence of the Energy Gap of Semiconductors in the Low-Temperature Limit,” Phys. Rev. Lett. 92(19), 196403 (2004).
[Crossref]

Sci. Adv. (1)

S. Prabhakar, T. Shields, A. C. Dada, M. Ebrahim, G. G. Taylor, D. Morozov, K. Erotokritou, S. Miki, M. Yabuno, H. Terai, C. Gawith, M. Kues, L. Caspani, R. H. Hadfield, and M. Clerici, “Two-photon quantum interference and entanglement at 2.1 µm,” Sci. Adv. 6(13), eaay5195 (2020).
[Crossref]

Sci. Rep. (2)

Y. M. Sua, H. Fan, A. Shahverdi, J.-Y. Chen, and Y.-P. Huang, “Direct generation and detection of quantum correlated photons with 3.2 um wavelength spacing,” Sci. Rep. 7(1), 17494 (2017).
[Crossref]

C. A. Husko, A. S. Clark, M. J. Collins, A. De Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, “Multi-photon absorption limits to heralded single photon sources,” Sci. Rep. 3(1), 3087 (2013).
[Crossref]

Science (1)

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360(6386), 285–291 (2018).
[Crossref]

Supercond. Sci. Technol. (1)

C. M. Natarajan, M. G. Tanner, and R. H. Hadfield, “Superconducting nanowire single-photon detectors: physics and applications,” Supercond. Sci. Technol. 25(6), 063001 (2012).
[Crossref]

Other (3)

L. Pavesi and D. J. Lockwood, Silicon photonics III: Systems and applications, vol. 122 (Springer Science & Business Media, 2016).

S. Ramelow, A. Farsi, S. Clemmen, D. Orquiza, K. Luke, M. Lipson, and A. L. Gaeta, “Silicon-nitride platform for narrowband entangled photon generation,” arXiv preprint arXiv:1508.04358 (2015).

M. Prost, Y.-C. Ling, S. Cakmakyapan, Y. Zhang, K. Zhang, J. Hu, Y. Zhang, and S. B. Yoo, “MWIR solid-state optical phased array beam steering using germanium-silicon photonic platform,” in Optical Fiber Communication Conference, (Optical Society of America, 2019), pp. M4E–3.

Supplementary Material (1)

NameDescription
» Supplement 1       Supplemental Document

Data Availability

Data and computer code that support the findings of this study are available at the University of Bristol’s data repository, data.bris (Digital object identifier: 10.5523/bris.1ckssqmdmilj023w7f0gr36o06). Other information is available from the authors upon reasonable request.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1. Dispersion of key optical phenomena, relative to 1.55 µm values. Silicon intensity-dependent refractive index ( $n_2$ ), and two-photon absorption coefficient ( $\beta _{\textrm {TPA}}$ ) are shown, as well as simple Rayleigh scattering efficiency. Error bars represent one standard deviation of the mean of a Monte-Carlo-modelled distribution of system uncertainties. Values from Bristow et al. [15] and Wang et al. [16], both measured using the bulk Z-scan technique, are plotted in diamonds and squares. Waveguided measurements from Sinclair et al. [17] and our work are plotted as six- and five-pointed stars. Lines are: for $n_2$ , a guide for the eye; for βTPA, a model for two-photon absorption [18].
Fig. 2.
Fig. 2. Waveguide design, simulation and experimental verification of phase-matching. a, Scanning electron micrograph of the waveguide cross section. Scale bar $100~\textrm {nm}$ . b, Simulation of the fundamental transverse electric mode electric field intensity at $\lambda = 2.071$ µm. c, Simulations of the group velocity dispersion $\beta _2$ and effective modal area $A_{\textrm {eff}}$ varying the width of the source waveguide with a fixed height of $340~\textrm {nm}$ and side-wall angle of $15^{\circ }$ . d, Nonlinear refraction and absorption. The maximum self-phase $\phi _{NL}$ and the normalised device transmission $\eta$ (decreasing due to residual two-photon absorption) are shown versus peak pump power. e, Single grating coupler transmission spectrum. f, Measured normalised power spectral density (PSD) of broadband stimulated four-wave mixing. A stimulating seed laser (continuous wave, tuneable, $\lambda \leq 2.071$ µm) is swept on one side of the pulsed pump at $2.071$ µm, while spectra are collected from an OSA, showing the stimulated output on the other ( $\lambda \geq 2.071$ µm).
Fig. 3.
Fig. 3. Measurement of correlated photons and characterisation of superconducting detectors: a, Dark field optical micrograph of the waveguide (WG) source with vertical grating couplers (VGC); scale bar $50$ µm. b, Experimental configuration for correlated photon measurement. Polarisation controller (PC), input optical tap (9:1), photodiode (PD), beam splitter (1:1), output optical tap (99:1), superconducting nanowire single photon detector (SNSPD), time interval analyser (TIA). c, System detection efficiency (SDE) and dark count rate (DCR) with change in bias current measured at $\lambda = 2.07$ µm wavelength on detector $A$ . Error bars are dominated by uncertainty in the number of launched photons. d, SDE and DCR for detector $B$ . e, Spectral response of detector efficiencies at a fixed bias current of $8.4$ and $7.9$ µA for detectors $A$ and $B$ , respectively. A moving average window of five points has been applied to data and the error bars are the standard deviation of the points in the sampled moving average window. f, Sample coincidence histogram integrated for 540 seconds at $0.67$ -W peak pump power. The peak at zero delay corresponds to photon pairs generated in the same spontaneous four-wave mixing event. g, Measured coincidence-to-accidental ratio (CAR), net and raw coincidence rate with varying launched pump power. Error bars are one standard deviation of the random error in the measurement. The sample histogram in part f is indicated by a star.
Fig. 4.
Fig. 4. Experimental measurement of on-chip quantum interference: a, Dark-field optical micrograph of the time-reversed Hong-Ou-Mandel experiment. Multimode interference coupler (MMI), waveguides (7.4-mm, WGs), thermo-optic phase modulator (TOPM), directional coupler (DC), asymmetric Mach-Zehnder interferometer (AMZI), wirebond (WB). Scale bar 50 µm. b, Experimental scheme. A pump laser is polarisation controlled (PC), filtered with a double-pass monochromator, and coupled into the waveguide circuit, with a monitor photodiode (PD) at the input tap (9:1). A controller provides DC-voltage control of the on-chip quantum state. The signal and idler photons are demultiplexed, filtered and then detected with superconducting nanowire detectors (SNSPD) and a time interval analyser (TIA). c, Quantum and classical interference fringes with varying on-chip phase $\phi$ , with fitted accidental-subtracted (net) visibility $V = 0.993\pm 0.017$ .

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

γ = k 0 n 2 A e f f
| ψ = sin ϕ 2 ( | 0 s 0 i A | 1 s 1 i B | 1 s 1 i A | 0 s 0 i B ) + cos ϕ 2 ( | 1 s 0 i A | 0 s 1 i B + | 0 s 1 i A | 1 s 0 i B ) ,

Metrics