Abstract

Nonlinear wavelength conversion is essential for many classical and quantum pho-tonic applications. The underlying second-order nonlinear optical processes, however, generally exhibit limited spectral bandwidths that impact their application potential. Here we use a high-Q X-cut lithium niobate microdisk resonator to demonstrate both second-harmonic generation and spontaneous parametric down-conversion on chip. In particular, our lithium niobate microresonator, with its wide-range cyclic phase matching and rich optical mode structures, is able to achieve ultra-broadband spontaneous parametric down-conversion, with a bandwidth over 400 nm, inferred from recorded spectra of the down-converted photons. The produced biphoton pairs exhibit strong temporal correlation, with a coincidence-to-accidental ratio measured to be 43.1. Our device is promising for integrated quantum photonics where optical frequency could be used as a degree of freedom for signal processing.

© 2017 Optical Society of America

1. Introduction

Second-order optical nonlinearity manifests as various important processes such as second-harmonic generation (SHG), sum-/difference-frequency generation, parametric down-conversion, etc. [1], that underlie crucially a large variety of applications from photonic signal processing [2, 3], tunable coherent radiation [4–7], optical computing [8, 9], to quantum information processing [10–15]. Recently, significant efforts have been devoted to implementing second-order nonlinear photonics on a chip scale [16–28], which shows the great advantage of device engineering for integrated nonlinear photonic applications. Among various nonlinear media employed, lithium niobate (LN) is particularly attractive, given its significant second-order nonlinear susceptibility (χ(2)) and wide transparency window from violet to mid-infrared. Recent development of LN device nanofabrication technology has resulted in high-quality LN nanophotonic devices [24–35] that enable efficient nonlinear optical effects [23, 24, 26–28, 36].

The second-order nonlinear optical processes, however, generally exhibit limited spectral bandwidths due to the material dispersion of nonlinear media that impacts seriously the phase-matching condition, which becomes a major challenge for practical applications. This issue remains for on-chip devices, since current attention is primarily focused on device engineering to improve the efficiency of nonlinear optical processes [23, 24, 26–28, 35]. In this paper, we demonstrate an intriguing feature of second-order nonlinear processes in a high-Q X-cut LN microdisk resonator, whose rich optical mode structures are able to support extremely broadband spontaneous parametric down-conversion (SPDC) with a bandwidth over 400 nm that is significantly beyond conventional dispersion engineering and phase-matching approaches [16–28]. The remarkably broadband SPDC among multiple cavity mode families in our on-chip LN device is of great potential for integrated quantum photonic applications that could potentially utilize the frequency degree of freedom for information coding and processing [37,38].

Device characterization

The device employed is a microdisk resonator fabricated on an X-cut LN-on-insulator wafer. As shown in Fig. 1(a), the microdisk has a radius of 45 µm and a thickness of 300 nm, sitting on a 2-µm-high silica pedestal. The device is patterned by electron beam lithography with ZEP520A as the resist, etched by Argon-ion milling, and undercut by diluted hydrofluoric acid. The device exhibits very low optical losses, with two typical examples shown in Fig. 1(b) and 1(c), where the intrinsic optical Q’s are 1.7 ×106 in the telecom band and 6.4 ×105 in the visible. These optical Q’s in both bands, to our best knowledge, are the highest reported in on-chip LN microresonators to date [25–27, 31–35].

 figure: Fig. 1

Fig. 1 (a) Scanning electron microscope image of fabricated X-cut LN microdisks. (b) and (c) Transmission spectra of typical high-Q cavity resonances of the employed device in the telecom and visible bands, respectively. Both modes are quasi-TM polarized. Experimental data are shown in red and blue, and theoretical fittings are shown in black. (d) and (e) Schematics of the experimental setups for SHG and SPDC, respectively. VOA: variable optical attenuator; WDM: wavelength-division multiplexer; OSA: optical spectrum analyzer; LPF: longpass filter; BPF: bandpass filter; TBPF: tunable bandpass filter; SPD: single-photon detector.

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Experiments and results

The high optical quality of our device implies its great potential for cavity enhanced nonlinear optics. To explore this, we first set up an experiment for SHG. As shown in Fig. 1(d), pump light from a laser in the telecom band, is launched via a tapered optical fiber into the LN microresonator, where frequency-doubled light is generated and coupled out of the cavity together with the pump light. A 780/1550 interband wavelength-division multiplexer (WDM) is then employed to separate the pump and its second harmonic, with the pump light going to an InGaAs detector for mode monitoring and laser locking, and the second harmonic going to an optical spectrum analyzer (OSA) for characterization. Polarization of the pump wave is controlled by a polarization controller for optimal coupling to the pumped cavity mode. The pump power is controlled by variable optical attenuators (VOAs) to characterize the power dependent performance of SHG.

Second-order nonlinear optics could be studied in optical resonators via various phase-matching techniques [39, 40]. In an X-cut LN microresonator, where the optical axis is in the device plane, for a quasi-transverse-electric (quasi-TE) mode whose polarization lies dominantly in the device plane as well, the phase velocity oscillates sinusoidally in every round trip, with the oscillating amplitude determined by the material birefringence. In contrast, the phase velocity of a quasi-transverse-magnetic (quasi-TM) mode almost stays constant as light travels in the cavity, since the polarization remains nearly perpendicular to the device plane, in which the optical axis lies. As a result, SHG could take place through a special phase-matching scheme called cyclic phase matching [26, 39, 41, 42], where perfect phase matching between a quasi-TE mode and a quasi-TM mode is satisfied at four azimuthal angles of the microresonator, leading to significant optical frequency doubling, given that the energy conservation condition is also satisfied between the two involved modes. In our X-cut LN microdisk, we selected a cavity mode at 1549.32 nm in the telecom band as the pump mode, which is quasi-TE polarized. The pump mode exhibits a loaded optical Q of 1.2 ×105, with its transmission spectrum shown in Fig. 2(a) and 2(c). When launching optical power into this mode, we observed coherent radiation produced at the second harmonic whose emission spectrum is shown in Fig. 3(a). Optical mode characterization of the passive cavity in the spectral region around the second-harmonic frequency [Fig. 2(b) and 2(d)] shows that the second harmonic corresponds to a quasi-TM mode at 774.66 nm with a loaded optical Q of 2.2 ×105, which corresponds to a linewidth of 3.5 pm. Figure 3(b) plots the power dependence of the SHG signal, exhibiting a clear quadratic relation, which further confirms that the visible signal is produced by SHG originating from the χ(2) nonlinearity. From Fig. 3(b), we obtain a SHG efficiency of 3.6×10−6/mW. This value is lower than those obtained in other LN microresonators [25–27] potentially because the mode overlap, the phase-matching condition and/or the light extraction were not specifically optimized in our device. We expect that future optimization of the device would be able to significantly increase the SHG efficiency.

 figure: Fig. 2

Fig. 2 Optical mode characterization of the LN microresonator. (a) Transmission spectrum of the device in the telecom band, for quasi-TE polarization. (b) Transmission spectrum of the device in the visible band, for quasi-TM polarization. (c) Detailed transmission spectrum of the fundamental cavity mode used for SHG. (d) Detailed transmission spectrum of the second-harmonic mode. In (c) and (d), experimental data are shown in red and blue, and theoretical fittings are shown in black.

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 figure: Fig. 3

Fig. 3 Second-harmonic generation in the LN microresonator. (a) Recorded spectrum of the SHG signal in the visible, produced by pump light in the telecom band. (b) Power dependence of the SHG signal on the fundamental pump.

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The demonstration of SHG above readily implies the application of our device for SPDC, which forms the foundation for photonic quantum information processing [10–15]. To explore the characteristics of SPDC, we conducted an experiment with the setup schematically shown in Fig. 1(e). Pump light in the visible is launched into the cavity mode at 774.66 nm and the down-converted light is coupled out of the LN microdisk through the same fiber taper. The down-converted light was separated from the pump by a 780/1550 WDM and a longpass filter (with a cutoff wavelength of 1100 nm), and was then sent to a spectrometer for spectral characterization. Figure 4(a) shows the recorded photoluminescence (PL) spectrum of the down-converted signal. Surprisingly, the SPDC spectrum exhibits a large number of emission lines over a broad spectral range from below 1400 nm to nearly 1600 nm, which is far beyond our expectation.

 figure: Fig. 4

Fig. 4 Broadband SPDC. (a) Recorded SPDC spectrum, generated by a pump wave at 774.66 nm in the visible. The spectrometer used for recording the spectrum has a cutoff wavelength around 1590 nm. The pump power is 115 µW. (b) Detailed SPDC spectrum in the wavelength range of 1505–1595 nm, showing multiple pairs of emission lines symmetrically located around the degenerate SPDC signal at 1549.32 nm, indicated by the black arrow. Blue and red arrows highlight two conjugate mode families. Two big arrows indicate a pair of strong peaks, one at 1517.85 nm and the other at 1582.12 nm. Blue and red dashed boxes indicate two coarse WDM channels, which are later used to select two conjugate SPDC wavebands for characterizing the temporal correlation of the broadband biphotons. (c) Polarization properties of the SPDC, where the PL spectra for TE and TM polarizations are shown in blue and red, respectively. The spectrum of TE polarization is shifted along the vertical axis for better comparison with the TM polarization. Inset: experimental setup for characterizing the polarization properties of SPDC, from point A shown in Fig. 1(e).

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The physical reason for the broadband SPDC lies in its intrinsic nature of energy conservation among interacting photons, since a photon at frequency 2ω can be converted into two photons at frequencies ω + Δω and ω − Δω, where Δω could be nonzero as long as phase matching (momentum conservation) is satisfied. This is particularly the case in our X-cut LN microdisk that exhibits rich mode structures. With cyclic phase matching, our device is able to induce nonlinear interaction between the visible pump mode and many telecom mode pairs from multiple mode families, resulting in remarkably broadband SPDC, in contrast to a Z-cut LN optical resonator that generally supports narrow-band SPDC [14, 43].

The detected SPDC spectrum spans from below 1400 nm all the way up to 1590 nm, the cutoff wavelength of the spectrometer. Because of energy conservation, a signal photon detected around 1370 nm implies an idler photon produced around 1783 nm (which is beyond the spectral response of our spectrometer). This infers a total SPDC bandwidth of about 400 nm. Such a large bandwidth of SPDC is significantly beyond those obtained by conventional phase-matching approaches that generally exhibit bandwidths of about tens of nanometers [15, 20, 28, 44, 45]. Only chirped nonlinear gratings [46] are able to provide a SPDC bandwidth comparable to that demonstrated by our device.

To investigate the conjugate photon pairs generated from SPDC, we take a detailed look at the spectral region with a total bandwidth of ∼100 nm around the fundamental mode at 1549.32 nm, which corresponds to half of the pump frequency. Figure 4(b) shows that two groups of equally spaced strong PL peaks (indicated by blue and red arrows) are located symmetrically around the fundamental mode, with many small peaks covering the whole spectrum due to the dense modes of the LN microresonator. Detailed polarization analysis shows that the two groups of strong peaks originate from two mode families with different polarizations. As shown in Fig. 4(c), the strong emission lines at wavelengths below 1549.32 nm belong to a quasi-TE mode family which shares the same polarization with the fundamental mode at 1549.32 nm. In contrast, those with wavelengths longer than 1549.32 nm come from a quasi-TM mode family that has the same polarization with the pump mode at 774.66 nm. This indicates that SPDC involving these two telecom mode families is a type-II process, where a quasi-TM visible pump photon produces a pair of photons with orthogonal quasi-TM and quasi-TE polarizations.

During a SPDC event, two down-converted photons are created simultaneously and thus exhibit strong temporal correlation, which underlies crucially many quantum photonic functionalities [47, 48]. To investigate such correlation, we set up coincidence counting experiments as shown in Fig. 1(e), where the down-converted photons are directed to two InGaAs single-photon detectors (SPDs) whose output signals are analyzed to obtain the temporal correlation of the generated photon pairs. We first selected two strong emission lines at wavelengths of 1517.85 and 1582.12 nm [see Fig. 4(b)], whose sum frequency is equal to the pump frequency, indicating that they are a pair of signal and idler photon modes produced via SPDC. As shown in Fig. 5(a), this pair of photon modes were separated by a bandpass filter (BPF) with one photon mode directed to the through port (with a pass-band of 1503-1519 nm) and the other to the reflection port. The two separated photon modes were further filtered by a pair of tunable bandpass filters (TBPFs) before they reached the SPDs.

 figure: Fig. 5

Fig. 5 Temporal correlation of the produced conjugate biphoton pairs. (a) and (b) Experimental setup, and coincidence counts as a function of relative time delay, for a single mode pair at wavelengths of 1517.85 and 1582.12 nm. Experimental data are shown as blue circles and a Gaussian fitting is plotted as a magenta curve. The single photons are detected by two InGaAs SPDs, with a gated time window of 40 ns, gate frequency of 2.5 MHz, quantum efficiency of 15%, and data acquisition time of 6 hours. No background subtraction is performed. The full width at half maximum (FWHM) of over 800 ps is due to detector timing jitter. (c) and (d) Experimental setup, and coincidence counts as a function of relative time delay, for broadband multiple mode pairs. The two selected wavebands have an identical bandwidth of 16 nm, with one centered at 1531 nm and the other centered at 1571 nm. In (a) and (c), SPDC signals are from point B shown in Fig. 1(e). Insets of (b) and (d) present accidental coincidence counts as functions of relative time delay, with experimental data shown as gray dots and theoretical fittings as magenta curves.

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Figure 5(b) plots the coincidence counting result, which shows clearly the dominant true coincidence of the signal and idler photons that overlap in time. The coincidence-to-accidental ratio (CAR) is measured to be 20.1, which is comparable to those obtained in other state-of-the-art nanophotonic devices [49], clearly demonstrating the strong temporal correlation of the produced biphotons. The current CAR value is primarily limited by accidental coincidence counts [Fig. 5(b), inset], in which detector dark counts play a fundamental role, since the generated photon pairs exhibit a relatively low flux. We expect that future reduction of detector dark counts (say, with superconducting SPDs) and improvement of light extraction from the device would significantly improve the CAR. Furthermore, we also performed coincidence counting for a set of multiple mode pairs to further characterize the property of the broadband SPDC. As shown in Fig. 5(c), we separated the down-converted light by a coarse WDM into two spectral bands, one centered at 1531 nm and the other centered at 1571 nm [see the dashed boxes in Fig. 4(b)], and each of them has a bandwidth of 16 nm covering multiple emission lines. The two bands of signal and idler modes were then directed to the SPDs for photon counting. Figure 5(d) shows the result, which, again, exhibits a clear dominant true coincidence when the time separation between the two bands is zero. The CAR is measured to be 43.1, clearly showing the strong correlation of photon pairs within the two selected wavebands. This value is higher than that obtained from the single mode pair [Fig. 5(b)], resulting mainly from two factors. The first factor is that in the case of multiple mode pairs, the overall flux of correlated photon pairs within the two 16-nm-bandwidth coarse WDM channels is higher, which leads to a larger number of true coincidence counts [Fig. 5(b) and 5(d)]. The other factor, however, lies in the fact that the recorded accidental coincidence counts are fewer when filtering is achieved by the coarse WDM [Fig. 5(b) and 5(d), insets], because in the single mode pair case, the used TBPFs are Fabry-Perot based, with a free spectral range (FSR) of 60 nm and a linewidth of 1.4 nm, and in the broadband SPDC signal at the BPF reflection port, besides the targeted idler photons at λidler = 1582.12 nm that matches the center of one pass-band of TBPF 2, some unwanted photons (at wavelengths around λj = λidler + j ×FSR, where j = ±1, ±2, …) also went through TBPF 2 and reached SPD 2, which makes an extra contribution to accidental coincidence counts. In fact, for the single mode pair, these extra accidental coincidence counts come from our broadband SPDC, and can be easily suppressed by a filter with a smaller linewidth to further increase the CAR. These CAR values directly confirm that the broadband multiple mode pairs observed in Fig. 4(a) and 4(b) are indeed produced by SPDC.

Conclusion

In conclusion, we have demonstrated on-chip SHG and SPDC in a high-Q X-cut LN microdisk resonator. We showed that the SPDC produced by the device exhibits an extremely large bandwidth up to 400 nm in the telecom band, which is significantly beyond those obtained in conventional devices. We performed coincidence photon counting to characterize the intrinsic correlation between the down-converted signal and idler mode pairs, with a CAR of 43.1 that directly confirms the physical origin of the down-converted photon pairs. The ultra-broadband SPDC observed in our device is of great potential for integrated quantum photonic applications that could utilize frequency as a degree of freedom for information coding and processing.

Funding

National Science Foundation (No. 1641099).

Acknowledgments

This work was performed in part at the Cornell NanoScale Facility, a member of the National Nanotechnology Coordinated Infrastructure (NNCI), which is supported by the National Science Foundation (Grant ECCS-1542081).

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References

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  1. R. Boyd, Nonlinear Optics3rd edn (Academic) (2008).
  2. C. Langrock, S. Kumar, J. E. McGeehan, A. Willner, and M. Fejer, “All-optical signal processing using χ(2) nonlinearities in guided-wave devices,” J. Lightwave Technol. 24, 2579 (2006).
    [Crossref]
  3. A. E. Willner, S. Khaleghi, M. R. Chitgarha, and O. F. Yilmaz, “All-optical signal processing,” J. Lightwave Technol. 32, 660 (2014).
    [Crossref]
  4. M. H. Dunn and M. Ebrahimzadeh, “Parametric generation of tunable light from continuous-wave to femtosecond pulses,” Science 286, 1513 (1999).
    [Crossref] [PubMed]
  5. M. M. Fejer, G. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631 (1992).
    [Crossref]
  6. Y.-F. Chen, S. Tsai, S. Wang, Y. Huang, T. Lin, and B. Wong, “Efficient generation of continuous-wave yellow light by single-pass sum-frequency mixing of a diode-pumped Nd:YVO4 dual-wavelength laser with periodically poled lithium niobate,” Opt. Lett. 27, 1809 (2002).
    [Crossref]
  7. C. Xu, H. Okayama, and M. Kawahara, “1.5 µm band efficient broadband wavelength conversion by difference frequency generation in a periodically domain-inverted LiNbO3 channel waveguide,” Appl. Phys. Lett. 63, 3559 (1993).
    [Crossref]
  8. T. Inagaki, Y. Haribara, K. Igarashi, T. Sonobe, S. Tamate, T. Honjo, A. Marandi, P. L. McMahon, T. Umeki, K. Enbutsu, O. Tadanaga, H. Takenouchi, K. Aihara, K.-I. Kawarabayashi, K. Inoue, S. Utsunomiya, and H. Takesue, “A coherent ising machine for 2000-node optimization problems,” Science 354, 603 (2016).
    [Crossref] [PubMed]
  9. P. L. McMahon, A. Marandi, Y. Haribara, R. Hamerly, C. Langrock, S. Tamate, T. Inagaki, H. Takesue, S. Utsunomiya, K. Aihara, R. L. Byer, M. M. Fejer, H. Mabuchi, and Y. Yamamoto, “A fully-programmable 100-spin coherent Ising machine with all-to-all connections,” Science 354, 614 (2016).
    [Crossref] [PubMed]
  10. M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. 3, 692 (2007).
    [Crossref]
  11. K. De Greve, L. Yu, P. L. McMahon, J. S. Pelc, C. M. Natarajan, N. Y. Kim, E. Abe, S. Maier, C. Schneider, M. Kamp, S. Höfling, R. H. Hadfield, A. Forchel, M. M. Fejer, and Y. Yamamoto, “Quantum-dot spin-photon entanglement via frequency downconversion to telecom wavelength,” Nature 491, 421 (2012).
    [Crossref] [PubMed]
  12. E. Saglamyurek, N. Sinclair, J. Jin, J. A. Slater, D. Oblak, W. Tittel, F. Bussières, M. George, R. Ricken, and W. Sohler, “Broadband waveguide quantum memory for entangled photons,” Nature 469, 512 (2011).
    [Crossref] [PubMed]
  13. F. Bussieres, C. Clausen, A. Tiranov, B. Korzh, V. B. Verma, S. W. Nam, F. Marsili, A. Ferrier, P. Goldner, H. Herrmann, C. Silberhorn, W. Sohler, M. Afzelius, and N. Gisin, “Quantum teleportation from a telecom-wavelength photon to a solid-state quantum memory,” Nat. Photon. 8, 775 (2014).
    [Crossref]
  14. M. Förtsch, J. Fürst, C. Wittmann, D. Strekalov, A. Aiello, M. V. Chekhova, C. Silberhorn, G. Leuchs, and C. Marquardt, “A versatile source of single photons for quantum information processing,” Nat. Commun. 41818 (2013).
    [Crossref] [PubMed]
  15. 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, 103601 (2014).
    [Crossref] [PubMed]
  16. C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, “Integrated GaN photonic circuits on silicon (100) for second harmonic generation,” Opt. Express 19, 10462 (2011).
    [Crossref] [PubMed]
  17. J. S. Levy, M. A. Foster, A. L. Gaeta, and M. Lipson, “Harmonic generation in silicon nitride ring resonators,” Opt. Express 19, 11415 (2011).
    [Crossref] [PubMed]
  18. P. S. Kuo and G. S. Solomon, “Second-harmonic generation using 4-bar quasi-phasematching in a GaAs microdisk cavity,” Nat. Commun. 53109 (2014).
    [Crossref]
  19. X. Guo, C.-L. Zou, and H. X. Tang, “Second-harmonic generation in aluminum nitride microrings with 2500%/W conversion efficiency,” Optica 3, 1126 (2016).
    [Crossref]
  20. X. Guo, C.-L. Zou, C. Schuck, H. Jung, R. Cheng, and H. X. Tang, “Parametric down-conversion photon-pair source on a nanophotonic chip,” Light Sci. Appl. 6, e16249 (2017).
    [Crossref]
  21. L. Chang, Y. Li, N. Volet, L. Wang, J. Peters, and J. E. Bowers, “Thin film wavelength converters for photonic integrated circuits,” Optica 3, 531 (2016).
    [Crossref]
  22. A. Rao, M. Malinowski, A. Honardoost, J. R. Talukder, P. Rabiei, P. Delfyett, and S. Fathpour, “Second-harmonic generation in periodically-poled thin film lithium niobate wafer-bonded on silicon,” Opt. Express 24, 29941 (2016).
    [Crossref]
  23. A. Rao, J. Chiles, S. Khan, S. Toroghi, M. Malinowski, G. F. Camacho-González, and S. Fathpour, “Second-harmonic generation in single-mode integrated waveguides based on mode-shape modulation,” Appl. Phys. Lett. 110, 111109 (2017).
    [Crossref]
  24. C. Wang, X. Xiong, N. Andrade, V. Venkataraman, X.-F. Ren, G.-C. Guo, and M. Lončar, “Second harmonic generation in nano-structured thin-film lithium niobate waveguides,” Opt. Express 25, 6963 (2017).
    [Crossref] [PubMed]
  25. C. Wang, M. J. Burek, Z. Lin, H. A. Atikian, V. Venkataraman, I.-C. Huang, P. Stark, and M. Lončar, “Integrated high quality factor lithium niobate microdisk resonators,” Opt. Express 22, 30924 (2014).
    [Crossref]
  26. J. Lin, Y. Xu, J. Ni, M. Wang, Z. Fang, L. Qiao, W. Fang, and Y. Cheng, “Phase-matched second-harmonic generation in an on-chip LiNbO3 microresonator,” Phys. Rev. Appl. 6, 014002 (2016).
    [Crossref]
  27. J. Moore, J. K. Douglas, I. W. Frank, T. A. Friedmann, R. Camacho, and M. Eichenfield, “Efficient second harmonic generation in lithium niobate on insulator,” Proc. Conf. Lasers and Electro-Optics (CLEO), pp. STh3P.1 (2016).
  28. I. W. Frank, J. Moore, J. K. Douglas, R. Camacho, and M. Eichenfield, “Entangled photon generation in lithium niobate microdisk resonators through spontaneous parametric down conversion,” Proc. Conf. Lasers and Electro-Optics (CLEO), pp. SM2E.6 (2016).
  29. A. Guarino, G. Poberaj, D. Rezzonico, R. Degl’Innocenti, and P. Günter, “Electro-optically tunable microring resonators in lithium niobate,” Nat. Photon. 1, 407 (2007).
    [Crossref]
  30. G. Poberaj, H. Hu, W. Sohler, and P. Guenter, “Lithium niobate on insulator (LNOI) for micro-photonic devices,” Laser Photon. Rev. 6, 488 (2012).
    [Crossref]
  31. T.-J. Wang, J.-Y. He, C.-A. Lee, and H. Niu, “High-quality LiNbO3 microdisk resonators by undercut etching and surface tension reshaping,” Opt. Express 20, 2811 (2012).
  32. J. Lin, Y. Xu, Z. Fang, M. Wang, J. Song, N. Wang, L. Qiao, W. Fang, and Y. Cheng, “Fabrication of high-Q lithium niobate microresonators using femtosecond laser micromachining,” Sci. Rep. 5, 8072 (2015).
    [Crossref] [PubMed]
  33. J. Wang, F. Bo, S. Wan, W. Li, F. Gao, J. Li, G. Zhang, and J. Xu, “High-Q lithium niobate microdisk resonators on a chip for efficient electro-optic modulation,” Opt. Express 23, 23072 (2015).
    [Crossref] [PubMed]
  34. W. C. Jiang and Q. Lin, “Chip-scale cavity optomechanics in lithium niobate,” Sci. Rep. 6, 36920 (2016).
    [Crossref] [PubMed]
  35. C. Wang, M. Zhang, B. Stern, M. Lipson, and M. Loncar, “Nanophotonic lithium niobate electro-optic modulators,” arXiv:1701.06470 (2017).
  36. X. Sun, H. Liang, R. Luo, W. C. Jiang, X.-C. Zhang, and Q. Lin, “Nonlinear optical oscillation dynamics in high-Q lithium niobate microresonators,” Opt. Express 25, 13504 (2017).
    [Crossref] [PubMed]
  37. S. Ramelow, L. Ratschbacher, A. Fedrizzi, N. Langford, and A. Zeilinger, “Discrete tunable color entanglement,” Phys. Rev. Lett. 103, 253601 (2009).
    [Crossref]
  38. C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176 (2016).
    [Crossref] [PubMed]
  39. D. V. Strekalov, C. Marquardt, A. B. Matsko, H. G. L. Schwefel, and G. Leuchs, “Nonlinear and quantum optics with whispering gallery resonators,” J. Opt. 18, 123002 (2016).
    [Crossref]
  40. I. Breunig, “Three-wave mixing in whispering gallery resonators,” Laser Photon. Rev. 10, 569 (2016).
    [Crossref]
  41. G. Lin, J. U. Fürst, D. V. Strekalov, and N. Yu, “Wide-range cyclic phase matching and second harmonic generation in whispering gallery resonators,” Appl. Phys. Lett. 103, 181107 (2013).
    [Crossref]
  42. J. Fürst, B. Sturman, K. Buse, and I. Breunig, “Whispering gallery resonators with broken axial symmetry: Theory and experiment,” Opt. Express 2, 20143 (2016).
    [Crossref]
  43. M. Förtsch, G. Schunk, J. U. Fürst, D. Strekalov, T. Gerrits, M. J. Stevens, F. Sedlmeir, H. G. L. Schwefel, S. W. Nam, G. Leuchs, and C. Marquardt, “Highly efficient generation of single-mode photon pairs from a crystalline whispering-gallery-mode resonator source,” Phys. Rev. A 91, 23812 (2015).
    [Crossref]
  44. S. Tanzilli, W. Tittel, H. De Riedmatten, H. Zbinden, P. Baldi, M. DeMicheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18, 155 (2002).
    [Crossref]
  45. G. Fujii, N. Namekata, M. Motoya, S. Kurimura, and S. Inoue, “Bright narrowband source of photon pairs at optical telecommunication wavelengths using a type-II periodically poled lithium niobate waveguide,” Opt. Express 15, 12769 (2007).
    [Crossref] [PubMed]
  46. M. B. Nasr, S. Carrasco, B. E. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100, 183601 (2008).
    [Crossref] [PubMed]
  47. N. Gisin and R. Thew, “Quantum communication,” Nat. Photon. 1, 165 (2007).
    [Crossref]
  48. J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777 (2012).
    [Crossref]
  49. D. Grassani, S. Azzini, M. Liscidini, M. Galli, M. J. Strain, M. Sorel, J. Sipe, and D. Bajoni, “Micrometer-scale integrated silicon source of time-energy entangled photons,” Optica 2, 88 (2015).
    [Crossref]

2017 (4)

X. Guo, C.-L. Zou, C. Schuck, H. Jung, R. Cheng, and H. X. Tang, “Parametric down-conversion photon-pair source on a nanophotonic chip,” Light Sci. Appl. 6, e16249 (2017).
[Crossref]

A. Rao, J. Chiles, S. Khan, S. Toroghi, M. Malinowski, G. F. Camacho-González, and S. Fathpour, “Second-harmonic generation in single-mode integrated waveguides based on mode-shape modulation,” Appl. Phys. Lett. 110, 111109 (2017).
[Crossref]

C. Wang, X. Xiong, N. Andrade, V. Venkataraman, X.-F. Ren, G.-C. Guo, and M. Lončar, “Second harmonic generation in nano-structured thin-film lithium niobate waveguides,” Opt. Express 25, 6963 (2017).
[Crossref] [PubMed]

X. Sun, H. Liang, R. Luo, W. C. Jiang, X.-C. Zhang, and Q. Lin, “Nonlinear optical oscillation dynamics in high-Q lithium niobate microresonators,” Opt. Express 25, 13504 (2017).
[Crossref] [PubMed]

2016 (11)

X. Guo, C.-L. Zou, and H. X. Tang, “Second-harmonic generation in aluminum nitride microrings with 2500%/W conversion efficiency,” Optica 3, 1126 (2016).
[Crossref]

W. C. Jiang and Q. Lin, “Chip-scale cavity optomechanics in lithium niobate,” Sci. Rep. 6, 36920 (2016).
[Crossref] [PubMed]

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176 (2016).
[Crossref] [PubMed]

D. V. Strekalov, C. Marquardt, A. B. Matsko, H. G. L. Schwefel, and G. Leuchs, “Nonlinear and quantum optics with whispering gallery resonators,” J. Opt. 18, 123002 (2016).
[Crossref]

I. Breunig, “Three-wave mixing in whispering gallery resonators,” Laser Photon. Rev. 10, 569 (2016).
[Crossref]

J. Lin, Y. Xu, J. Ni, M. Wang, Z. Fang, L. Qiao, W. Fang, and Y. Cheng, “Phase-matched second-harmonic generation in an on-chip LiNbO3 microresonator,” Phys. Rev. Appl. 6, 014002 (2016).
[Crossref]

L. Chang, Y. Li, N. Volet, L. Wang, J. Peters, and J. E. Bowers, “Thin film wavelength converters for photonic integrated circuits,” Optica 3, 531 (2016).
[Crossref]

A. Rao, M. Malinowski, A. Honardoost, J. R. Talukder, P. Rabiei, P. Delfyett, and S. Fathpour, “Second-harmonic generation in periodically-poled thin film lithium niobate wafer-bonded on silicon,” Opt. Express 24, 29941 (2016).
[Crossref]

T. Inagaki, Y. Haribara, K. Igarashi, T. Sonobe, S. Tamate, T. Honjo, A. Marandi, P. L. McMahon, T. Umeki, K. Enbutsu, O. Tadanaga, H. Takenouchi, K. Aihara, K.-I. Kawarabayashi, K. Inoue, S. Utsunomiya, and H. Takesue, “A coherent ising machine for 2000-node optimization problems,” Science 354, 603 (2016).
[Crossref] [PubMed]

P. L. McMahon, A. Marandi, Y. Haribara, R. Hamerly, C. Langrock, S. Tamate, T. Inagaki, H. Takesue, S. Utsunomiya, K. Aihara, R. L. Byer, M. M. Fejer, H. Mabuchi, and Y. Yamamoto, “A fully-programmable 100-spin coherent Ising machine with all-to-all connections,” Science 354, 614 (2016).
[Crossref] [PubMed]

J. Fürst, B. Sturman, K. Buse, and I. Breunig, “Whispering gallery resonators with broken axial symmetry: Theory and experiment,” Opt. Express 2, 20143 (2016).
[Crossref]

2015 (4)

M. Förtsch, G. Schunk, J. U. Fürst, D. Strekalov, T. Gerrits, M. J. Stevens, F. Sedlmeir, H. G. L. Schwefel, S. W. Nam, G. Leuchs, and C. Marquardt, “Highly efficient generation of single-mode photon pairs from a crystalline whispering-gallery-mode resonator source,” Phys. Rev. A 91, 23812 (2015).
[Crossref]

D. Grassani, S. Azzini, M. Liscidini, M. Galli, M. J. Strain, M. Sorel, J. Sipe, and D. Bajoni, “Micrometer-scale integrated silicon source of time-energy entangled photons,” Optica 2, 88 (2015).
[Crossref]

J. Lin, Y. Xu, Z. Fang, M. Wang, J. Song, N. Wang, L. Qiao, W. Fang, and Y. Cheng, “Fabrication of high-Q lithium niobate microresonators using femtosecond laser micromachining,” Sci. Rep. 5, 8072 (2015).
[Crossref] [PubMed]

J. Wang, F. Bo, S. Wan, W. Li, F. Gao, J. Li, G. Zhang, and J. Xu, “High-Q lithium niobate microdisk resonators on a chip for efficient electro-optic modulation,” Opt. Express 23, 23072 (2015).
[Crossref] [PubMed]

2014 (5)

C. Wang, M. J. Burek, Z. Lin, H. A. Atikian, V. Venkataraman, I.-C. Huang, P. Stark, and M. Lončar, “Integrated high quality factor lithium niobate microdisk resonators,” Opt. Express 22, 30924 (2014).
[Crossref]

A. E. Willner, S. Khaleghi, M. R. Chitgarha, and O. F. Yilmaz, “All-optical signal processing,” J. Lightwave Technol. 32, 660 (2014).
[Crossref]

P. S. Kuo and G. S. Solomon, “Second-harmonic generation using 4-bar quasi-phasematching in a GaAs microdisk cavity,” Nat. Commun. 53109 (2014).
[Crossref]

F. Bussieres, C. Clausen, A. Tiranov, B. Korzh, V. B. Verma, S. W. Nam, F. Marsili, A. Ferrier, P. Goldner, H. Herrmann, C. Silberhorn, W. Sohler, M. Afzelius, and N. Gisin, “Quantum teleportation from a telecom-wavelength photon to a solid-state quantum memory,” Nat. Photon. 8, 775 (2014).
[Crossref]

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, 103601 (2014).
[Crossref] [PubMed]

2013 (2)

M. Förtsch, J. Fürst, C. Wittmann, D. Strekalov, A. Aiello, M. V. Chekhova, C. Silberhorn, G. Leuchs, and C. Marquardt, “A versatile source of single photons for quantum information processing,” Nat. Commun. 41818 (2013).
[Crossref] [PubMed]

G. Lin, J. U. Fürst, D. V. Strekalov, and N. Yu, “Wide-range cyclic phase matching and second harmonic generation in whispering gallery resonators,” Appl. Phys. Lett. 103, 181107 (2013).
[Crossref]

2012 (4)

G. Poberaj, H. Hu, W. Sohler, and P. Guenter, “Lithium niobate on insulator (LNOI) for micro-photonic devices,” Laser Photon. Rev. 6, 488 (2012).
[Crossref]

T.-J. Wang, J.-Y. He, C.-A. Lee, and H. Niu, “High-quality LiNbO3 microdisk resonators by undercut etching and surface tension reshaping,” Opt. Express 20, 2811 (2012).

K. De Greve, L. Yu, P. L. McMahon, J. S. Pelc, C. M. Natarajan, N. Y. Kim, E. Abe, S. Maier, C. Schneider, M. Kamp, S. Höfling, R. H. Hadfield, A. Forchel, M. M. Fejer, and Y. Yamamoto, “Quantum-dot spin-photon entanglement via frequency downconversion to telecom wavelength,” Nature 491, 421 (2012).
[Crossref] [PubMed]

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777 (2012).
[Crossref]

2011 (3)

2009 (1)

S. Ramelow, L. Ratschbacher, A. Fedrizzi, N. Langford, and A. Zeilinger, “Discrete tunable color entanglement,” Phys. Rev. Lett. 103, 253601 (2009).
[Crossref]

2008 (1)

M. B. Nasr, S. Carrasco, B. E. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100, 183601 (2008).
[Crossref] [PubMed]

2007 (4)

N. Gisin and R. Thew, “Quantum communication,” Nat. Photon. 1, 165 (2007).
[Crossref]

G. Fujii, N. Namekata, M. Motoya, S. Kurimura, and S. Inoue, “Bright narrowband source of photon pairs at optical telecommunication wavelengths using a type-II periodically poled lithium niobate waveguide,” Opt. Express 15, 12769 (2007).
[Crossref] [PubMed]

A. Guarino, G. Poberaj, D. Rezzonico, R. Degl’Innocenti, and P. Günter, “Electro-optically tunable microring resonators in lithium niobate,” Nat. Photon. 1, 407 (2007).
[Crossref]

M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. 3, 692 (2007).
[Crossref]

2006 (1)

2002 (2)

1999 (1)

M. H. Dunn and M. Ebrahimzadeh, “Parametric generation of tunable light from continuous-wave to femtosecond pulses,” Science 286, 1513 (1999).
[Crossref] [PubMed]

1993 (1)

C. Xu, H. Okayama, and M. Kawahara, “1.5 µm band efficient broadband wavelength conversion by difference frequency generation in a periodically domain-inverted LiNbO3 channel waveguide,” Appl. Phys. Lett. 63, 3559 (1993).
[Crossref]

1992 (1)

M. M. Fejer, G. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631 (1992).
[Crossref]

Abe, E.

K. De Greve, L. Yu, P. L. McMahon, J. S. Pelc, C. M. Natarajan, N. Y. Kim, E. Abe, S. Maier, C. Schneider, M. Kamp, S. Höfling, R. H. Hadfield, A. Forchel, M. M. Fejer, and Y. Yamamoto, “Quantum-dot spin-photon entanglement via frequency downconversion to telecom wavelength,” Nature 491, 421 (2012).
[Crossref] [PubMed]

Afzelius, M.

F. Bussieres, C. Clausen, A. Tiranov, B. Korzh, V. B. Verma, S. W. Nam, F. Marsili, A. Ferrier, P. Goldner, H. Herrmann, C. Silberhorn, W. Sohler, M. Afzelius, and N. Gisin, “Quantum teleportation from a telecom-wavelength photon to a solid-state quantum memory,” Nat. Photon. 8, 775 (2014).
[Crossref]

Aiello, A.

M. Förtsch, J. Fürst, C. Wittmann, D. Strekalov, A. Aiello, M. V. Chekhova, C. Silberhorn, G. Leuchs, and C. Marquardt, “A versatile source of single photons for quantum information processing,” Nat. Commun. 41818 (2013).
[Crossref] [PubMed]

Aihara, K.

T. Inagaki, Y. Haribara, K. Igarashi, T. Sonobe, S. Tamate, T. Honjo, A. Marandi, P. L. McMahon, T. Umeki, K. Enbutsu, O. Tadanaga, H. Takenouchi, K. Aihara, K.-I. Kawarabayashi, K. Inoue, S. Utsunomiya, and H. Takesue, “A coherent ising machine for 2000-node optimization problems,” Science 354, 603 (2016).
[Crossref] [PubMed]

P. L. McMahon, A. Marandi, Y. Haribara, R. Hamerly, C. Langrock, S. Tamate, T. Inagaki, H. Takesue, S. Utsunomiya, K. Aihara, R. L. Byer, M. M. Fejer, H. Mabuchi, and Y. Yamamoto, “A fully-programmable 100-spin coherent Ising machine with all-to-all connections,” Science 354, 614 (2016).
[Crossref] [PubMed]

Andrade, N.

Atikian, H. A.

Azzini, S.

Bajoni, D.

Baldi, P.

S. Tanzilli, W. Tittel, H. De Riedmatten, H. Zbinden, P. Baldi, M. DeMicheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18, 155 (2002).
[Crossref]

Beveratos, A.

M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. 3, 692 (2007).
[Crossref]

Bo, F.

Bowers, J. E.

Boyd, R.

R. Boyd, Nonlinear Optics3rd edn (Academic) (2008).

Breunig, I.

I. Breunig, “Three-wave mixing in whispering gallery resonators,” Laser Photon. Rev. 10, 569 (2016).
[Crossref]

J. Fürst, B. Sturman, K. Buse, and I. Breunig, “Whispering gallery resonators with broken axial symmetry: Theory and experiment,” Opt. Express 2, 20143 (2016).
[Crossref]

Bromberg, Y.

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176 (2016).
[Crossref] [PubMed]

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Figures (5)

Fig. 1
Fig. 1 (a) Scanning electron microscope image of fabricated X-cut LN microdisks. (b) and (c) Transmission spectra of typical high-Q cavity resonances of the employed device in the telecom and visible bands, respectively. Both modes are quasi-TM polarized. Experimental data are shown in red and blue, and theoretical fittings are shown in black. (d) and (e) Schematics of the experimental setups for SHG and SPDC, respectively. VOA: variable optical attenuator; WDM: wavelength-division multiplexer; OSA: optical spectrum analyzer; LPF: longpass filter; BPF: bandpass filter; TBPF: tunable bandpass filter; SPD: single-photon detector.
Fig. 2
Fig. 2 Optical mode characterization of the LN microresonator. (a) Transmission spectrum of the device in the telecom band, for quasi-TE polarization. (b) Transmission spectrum of the device in the visible band, for quasi-TM polarization. (c) Detailed transmission spectrum of the fundamental cavity mode used for SHG. (d) Detailed transmission spectrum of the second-harmonic mode. In (c) and (d), experimental data are shown in red and blue, and theoretical fittings are shown in black.
Fig. 3
Fig. 3 Second-harmonic generation in the LN microresonator. (a) Recorded spectrum of the SHG signal in the visible, produced by pump light in the telecom band. (b) Power dependence of the SHG signal on the fundamental pump.
Fig. 4
Fig. 4 Broadband SPDC. (a) Recorded SPDC spectrum, generated by a pump wave at 774.66 nm in the visible. The spectrometer used for recording the spectrum has a cutoff wavelength around 1590 nm. The pump power is 115 µW. (b) Detailed SPDC spectrum in the wavelength range of 1505–1595 nm, showing multiple pairs of emission lines symmetrically located around the degenerate SPDC signal at 1549.32 nm, indicated by the black arrow. Blue and red arrows highlight two conjugate mode families. Two big arrows indicate a pair of strong peaks, one at 1517.85 nm and the other at 1582.12 nm. Blue and red dashed boxes indicate two coarse WDM channels, which are later used to select two conjugate SPDC wavebands for characterizing the temporal correlation of the broadband biphotons. (c) Polarization properties of the SPDC, where the PL spectra for TE and TM polarizations are shown in blue and red, respectively. The spectrum of TE polarization is shifted along the vertical axis for better comparison with the TM polarization. Inset: experimental setup for characterizing the polarization properties of SPDC, from point A shown in Fig. 1(e).
Fig. 5
Fig. 5 Temporal correlation of the produced conjugate biphoton pairs. (a) and (b) Experimental setup, and coincidence counts as a function of relative time delay, for a single mode pair at wavelengths of 1517.85 and 1582.12 nm. Experimental data are shown as blue circles and a Gaussian fitting is plotted as a magenta curve. The single photons are detected by two InGaAs SPDs, with a gated time window of 40 ns, gate frequency of 2.5 MHz, quantum efficiency of 15%, and data acquisition time of 6 hours. No background subtraction is performed. The full width at half maximum (FWHM) of over 800 ps is due to detector timing jitter. (c) and (d) Experimental setup, and coincidence counts as a function of relative time delay, for broadband multiple mode pairs. The two selected wavebands have an identical bandwidth of 16 nm, with one centered at 1531 nm and the other centered at 1571 nm. In (a) and (c), SPDC signals are from point B shown in Fig. 1(e). Insets of (b) and (d) present accidental coincidence counts as functions of relative time delay, with experimental data shown as gray dots and theoretical fittings as magenta curves.

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