Abstract

We present an approach for generating widely separated first sidebands based solely on the four-wave-mixing process in optical parametric oscillators built on complementary metal–oxide–semiconductor-compatible photonic chips. Using higher-order transverse modes to perform dispersion engineering, we obtain zero-group-velocity dispersion near 796 nm. By pumping the chip in the normal dispersion region, at 795.6 nm, we generate a signal field in the visible band (at 546.2 nm) and the corresponding idler field in the telecom band (at 1465.3 nm), corresponding to a frequency span of approximately 346 THz. We show that the spectral position of signal and idler can be tailored by exploiting a delicate balance between second- and fourth-order dispersion terms. Furthermore, we explicitly demonstrate a change in the parametric oscillation dynamics when moving the pump field from the anomalous to normal dispersion, where the chip ceases producing multiple sidebands adjacent to the pump field and generates widely separated single sidebands. This provides a chip-scale platform for generating single-sideband fields separated by more than one octave, covering the visible and telecom spectral regions.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

An optical parametric oscillator (OPO) based on four-wave mixing (FWM) converts pairs of pump photons into pairs of nondegenerate photons at symmetric sidebands on either side of the pumped cavity mode. The mechanisms responsible for the efficient generation of these beams in waveguides are nonlinearity and dispersion, which can be used to build a tunable light source. The ability to tune the pump frequency and accurately control the waveguide dispersion enables control of the frequency detuning of the generated sidebands. Silicon nitride (${{\rm Si}_{3}}{{\rm N}_{4}}$) planar microrings are attractive devices for integrated light generation because of their compatibility with complementary metal–oxide–semiconductor (CMOS) technology, broad transparency window, and ability to tailor ring-waveguide dispersion for the parametric process over several bands, e.g., mid-infrared [1], telecom [2], and near-infrared [3].

However, for shorter wavelengths, the strong normal dispersion of the material decreases the influence of the waveguide geometry on the effective dispersion of the fundamental mode, preventing the observation of intrinsic parametric oscillation with a pump close to the visible band. Other methods have been used to produce visible light using various cascaded processes to assist the FWM. It was demonstrated in whispering gallery mode ${{\rm MgF}_2}$ resonators that multiple bright beams were generated from ultraviolet (UV) to the near-infrared assisted by stimulated Raman scattering [4]. Similarly, using aluminum nitride (AIN) microrings with intrinsic Pockels effects in addition to Kerr nonlinearity or surface-induced second-order nonlinearity in ${{\rm Si}_3}{{\rm N}_4}$, cascaded FWM oscillation through second-harmonic, sum-frequency generation, and third-harmonic generation produced multiple lines in the visible [57].

A recent development on FWM in silicon photonics enabled the configuration of OPOs and amplifiers coupling very distinct wavelengths [8,9]. Using ${{\rm Si}_3}{{\rm N}_4}$ and air as the core and clad for ring-resonator waveguides, respectively, and exciting the fundamental transverse-electric (TE) mode into the resonator with a pump laser at 900 nm, Lu et al. [8] could produce red light at 700 nm and the corresponding idler pair at 1300 nm with sub-milliwatt threshold power, corresponding to a separation of 192 THz between sidebands. In a recent paper [10], using a similar configuration, but now with a pump field at around 770 nm, distinct geometries were explored to achieve visible light generation, presenting a larger frequency separation between sidebands of the order of 274 THz. The formalism employed is based on frequency and momentum conservation with additional requirements to avoid other competition processes that are phase-matched as well as distinct nonlinear processes. For instance, the essential requirement is to pump the resonator in a spectral region described by normal dispersion to avoid close-to-pump modulation instability.

Here, we present a detailed calculation of the total dispersion involving higher-order transverse modes for the direct generation of fields widely separated in frequency solely using the FWM process, exploring the role of the medium Kerr effect combined with the dispersion coefficients in ${{\rm Si}_3}{{\rm N}_4}$ devices covered in silicon dioxide (${{\rm SiO}_{2}}$) cladding. We concentrate on the importance of the fourth-order dispersion term to achieve phase-matching when the geometry is characterized by normal dispersion. Using frequency and time-domain simulations, we obtained the essential parameters of the resonator based on its geometry to describe the oscillation process. With a pump close to the atomic rubidium 795 nm line, the resonator generated the signal and idler in the visible and telecom bands, respectively, leading to a record separation between sidebands of 346 THz.

2. DISPERSION ENGINEERING USING HIGH-ORDER TRANSVERSE MODES

The FWM process is usually started with modest input power when the group-velocity dispersion (GVD) is anomalous, and a broad frequency comb is generated when the pump wavelength is centered near the zero-GVD point, allowing phase-matching over a wide range of wavelengths [13,11,12]. However, anomalous dispersion is not a crucial condition for the onset of parametric oscillation in a resonator. It was shown that pump power and laser detuning allow phase-matching with positive gain even in the normal dispersion regime [13,14]. Another way to observe oscillation in normal dispersion is to use mode-coupling-induced effective dispersion [15]. The coupling between different modes can disrupt the separation of resonant frequencies and lead to local anomalous dispersion [16]. In this work, we show that a balance between the first two even terms of frequency dispersion (i.e., ${\beta _2}$ an ${\beta _4}$) can trigger parametric oscillation in a normal GVD regime (${\beta _2} \gt 0$) if ${\beta _4}$ is negative, leading to different dynamics, where the first generated sidebands appear widely separated from the pump. The contribution from ${\beta _4}$ on the onset of a parametric process was already investigated in optical fibers [17], silica microspheres [18], ${{\rm Si}_3}{{\rm N}_4}$ waveguides at the mid-infrared [19], and recently at crystalline AlN on sapphire microrings [20]. Here, we used a higher-order transverse mode in ${{\rm Si}_3}{{\rm N}_4}$ microrings to shift the zero-GVD wavelength to near 796 nm [21], leading to phase-matching at the visible and infrared bands for a pump field in the normal dispersion regime. In general, we observed that these distant sidebands are generated when the signal of ${\beta _2}$ is positive but close to zero-GVD, and the fourth-order dispersion term ${\beta _4}$ is negative and sufficiently strong to have a significant contribution.

To understand the relationship between dispersion and phase-matching, we used a theoretical model based on a modified Lugiato–Lefever equation, which describes the propagation of the intracavity field in the microring [13,22]. The model predicts that the maximum gain of the parametric process will occur at sideband frequencies that lead the following nonlinear phase mismatching condition to zero:

$$\Delta \kappa = {\delta _0} - L\sum\limits_{n = 2,4, \ldots} \frac{{{\beta _n}}}{{n!}}{\Omega ^n} - 2\gamma L{P_0},$$
where ${\delta _0}$ is the phase detuning between pump frequency ${\omega _0}$ and cavity resonance, $L$ is the cavity length, $\Omega \equiv \omega - {\omega _0}$ is the sideband detuning, $\gamma$ is the nonlinear parameter, ${P_0}$ is the circulating power within the microcavity, and ${\beta _n}$ is the $n$ th-order dispersion coefficient of the Taylor expansion of the propagation constant $\beta (\Omega) = \sum_{n = 0}^\infty {\beta _n}{\Omega ^n}/n!$ and is given by ${\beta _n} = ({d^n}\beta /d{\omega ^n}{)|_{\omega = {\omega _0}}}$ for ($n = 1,2, \ldots$). As discussed in [22], the phase mismatch $\Delta \kappa$ and the gain coefficient depend only on the even-order dispersion terms. Considering just the second-order dispersion term, to achieve the phase-matching condition, anomalous dispersion (${\beta _2} \lt 0$) is required at zero detuning. However, a significant anomalous fourth-order dispersion term releases the need for cavity detuning to achieve phase-matching at normal GVD. As previously noticed [23], the sideband frequencies satisfy approximately the linear phase-matching condition $\Omega _{{\rm pm}}^2 \approx - 12{\beta _2}/{\beta _4}$. Therefore, a wider frequency difference for sideband amplification must occur when ${\beta _2}$ and ${\beta _4}$ have opposite signals, and we have experimentally observed that they can be as separated from the pump as ${\sim}{\omega _0}/2$. However, if ${\beta _2}$ is negative and ${\beta _4}$ is positive, modulation instability close to the pump occurs preferentially. These sideband modes oscillate when the pump power into the microring is larger than the oscillation threshold power [22]:
$$P_0^{{\rm th}} = \frac{\alpha}{{\gamma L}}{\left({1 - \frac{{\Omega _{{\rm pm}}^2}}{{\omega _0^2}}} \right)^{- 1}},$$
where $\alpha$ is the total cavity loss in a roundtrip and is related to the loaded quality factor (${Q}$) in the critical coupling regime by $Q = {\omega _0}/(2\alpha \rm FSR)$. The term $\alpha /(\gamma L)$ is the required power to initiate oscillation for the usual anomalous dispersion geometry [24]. The extra term, which depends explicitly on the phase-matched frequency, increases the minimum required power, as the first sideband frequencies become more separated from the pump. In principle, there is no upper limit in the sideband modes separation as long as the regarded fields satisfy the phase-matching condition in Eq. (1). In ${{\rm Si}_3}{{\rm N}_4}$ resonators, the limiting factor will be the transparency region of the material, which grows in absorption at shorter wavelengths, particularly in the UV. On the other hand, the absorption on the ${{\rm SiO}_2}$ cladding could be a limiting factor for operation at longer wavelengths, as it begins to increase at the mid-infrared [25]. However, depending on the waveguide geometry and curvature radius, its effect can be minimized by reducing the overlap of the field with the oxide clad [26]. It is also important to remark that at shorter wavelengths the roughness of the sidewalls gives further contribution to the scattering of light, since the pattern distance of the irregularities is comparable with the wavelength, considerably increasing the threshold power [27].

The calculation of the GVD is based on the material dispersion and waveguide geometry for a specific optical mode, which in turn involves the frequency, polarization, and its transverse spatial profile. The material dispersion is usually described by a normal GVD, and the waveguide geometry must be designed to add a relevant contribution to the dispersion in order to compensate for the positive value of ${\beta _2}$. In the case of a ${{\rm Si}_3}{{\rm N}_4}$-oxide resonator, the zero-GVD wavelength for the fundamental mode can be shifted to a limit value close to 1 µm [3,28]. For shorter wavelengths, in particular in the visible band, the contribution from material dispersion is dominant, and it is especially challenging to reach anomalous GVD for the fundamental mode. However, the influence of material depends on how the mode is transversely distributed in the waveguide, and, considering higher-order modes, we can look for a geometry with anomalous GVD at shorter wavelengths.

For a waveguide made of ${{\rm Si}_3}{{\rm N}_4}$ with refraction index (${{n}_{0}} \sim {2}{.02}$) clad in ${{\rm SiO}_{2}}$ (${{n}_{0}} \sim 1.45$), the high contrast in the refractive index allows high confinement, leading to an enhancement of the nonlinear process. We calculated the dependence of zero-GVD wavelength for different widths of a waveguide with a thickness of 730 nm. We used preconditioned block-iterative eigensolvers in a plane wave basis [29] to simulate the first three quasi-transverse-magnetic (TM) modes in a straight waveguide. The finite curvature radius was taken into account by the corresponding map on the refraction index distribution over the geometry, following the treatment presented in [30]. For the ${{\rm TM}_1}$ mode in a waveguide cross section of $730 \times 2000\;{\rm nm} $, the zero-GVD wavelength is around 800 nm. Figure 1(a) shows the calculated values of ${\beta _2}$ and ${\beta _4}$ for this geometry in terms of the vacuum wavelength.

 figure: Fig. 1.

Fig. 1. Simulation of the dispersion coefficients: (a) second- and fourth-order terms of the Taylor expansion of the propagation constant for the ${{\rm TM}_1}$ mode in a microresonator with the cross section of ${730} \times {2000}\;{\rm nm}$. (b) Phase mismatching calculation for the simulated values of ${\beta _2}$ and ${\beta _4}$, evaluated for pump wavelength of 795 nm, zero detuning, and power close to the measured oscillation threshold of 150 mW.

Download Full Size | PPT Slide | PDF

A waveguide with this dimension is multimode for a pump wavelength around 800 nm and supports at least the first three transverse spatial modes. This waveguide will constitute the microresonator, built as a ring of radius of 132 µm. To excite a particularly high-order mode into the resonator, phase-matching between the waveguide (through-port) and the resonator is necessary. With the fundamental mode at the input port, in order to couple the ${{\rm TM}_1}$ mode into the ring, the width of the waveguide must be narrower than the width of the resonator. We found that the width of the coupling waveguide must be 900 nm for an almost perfect phase-matching, see Fig. 2(c).

 figure: Fig. 2.

Fig. 2. (a) Schematic description of the experimental setup, a cw laser is used as the pump. (b) Spectral measurement of microcavity resonances by microheater sweeping. The inset shows a measurement of the cavity bandwidth by laser scanning. (c) Concept of the mode conversion at the bus waveguide and microring coupling.

Download Full Size | PPT Slide | PDF

3. EXPERIMENTAL SETUP

The experimental setup for generation and characterization of the parametric sidebands is illustrated in Fig. 2(a). A continuous-wave Ti:sapphire laser with a narrow linewidth (${\lt}\;{100}\;{\rm kHz}$) was used as the pump. The laser center wavelength is manually tuned through a birefringent filter from approximately 766 nm to 803 nm. In addition, there is also fine tuning spanning 10 GHz, controlled by a piezoelectric actuator, which allowed us to investigate the ${Q}$-factor of the rings. The maximum output power of the laser is 1.4 W, which corresponds to approximately 1 W at the input of the chip. A small part of this power is shared with a reference cavity with a free spectral range (FSR) of 1 GHz. Comparing the FSR of the reference cavity with the microresonator bandwidth, we could measure the loaded ${Q}$, see the inset of Fig. 2(b). The input coupling between the light and waveguide was performed in free space, where an inverse taper facilitated the mode-matching with a ${60} \times$ aspheric lens, achieving an efficiency of ${-}{3}\;{\rm dB}$. The light was coupled out of the chip using a ${40} \times$ aspheric lens, where a small part of it was sent to a detector to observe the resonance in an oscilloscope. Almost all of the light was coupled in a multimode optical fiber and sent to an optical spectrum analyzer (OSA). The polarization of the pump mode was controlled with a set of quarter-half-quarter waveplates before coupling.

The resonator optical mode depends on the effective refractive index ${{n}_{0}}$, which describes the transverse spatial distribution and how much it extends to the cladding, and the integer longitudinal mode index $m$. For a fixed number $m$, the resonant frequency of the fundamental mode is the lowest, followed by frequencies of higher modes in the increasing order of the transverse index (i.e., ${{\rm TM}_{1}}$, ${{\rm TM}_{2}},\ldots$). Therefore, if the fundamental mode is excited in the waveguide with a single-frequency laser source, all resonator modes will have necessarily a different longitudinal index. However, because each resonator mode has a distinct FSR, if the resonances are clearly separated at the pump frequency, the distance between two or more modes at some other frequency may be smaller than the sum of their bandwidths, causing a shift in resonances with different $m$, but these degeneracies would be accidental [31]. With a pump wavelength at 795 nm, we observe in Fig. 2(b) the excitation of only the first three transverse modes at the 2 µm ring during the scan of the cavity resonance using platinum microheaters [32].

The simulated dispersion coefficients ${\beta _2} = {19}\,\,{{\rm ps}^{2}}\,{{\rm km}^{- {1}}}$ and ${\beta _4} = - {2} \times {{10}^{- {4}}}\,\,{{\rm ps}^{4}}\,{{\rm km}^{- {1}}}$ satisfy the phase-matching condition at a sideband frequency of ${\sim}\;{170}\;{\rm THz}$, and, when used with the ${{\rm Si}_3}{{\rm N}_4}$ nonlinearity $\gamma \approx {1}\,\,{{\rm W}^{- {1}}}\,{{\rm m}^{- {1}}}$, we obtain a threshold power of 8.9 W within the microring, which is equivalent to 136 mW in the bus waveguide. Experimentally, the measured oscillation power threshold was 150 mW in the bus waveguide, which is in good agreement with the theoretical prediction. The discrepancy can be explained by the increased absorption of the signal. The estimation of the coefficient $\alpha$ was based on the width of the cavity resonance at the pump wavelength, and the model assumes it as constant over the full spectrum. However, the signal mode at a shorter wavelength is closer to the strong absorption region of ${{\rm Si}_3}{{\rm N}_4}$ at the UV [33] and should have, consequently, more absorption than at the pump wavelength.

 figure: Fig. 3.

Fig. 3. Parametric oscillation at visible and telecom wavelengths in a microring using the high-order mode ${{\rm TM}_1}$. (a) The data at shorter wavelengths ($\lt 600\,\,{\rm nm}$) were taken with a low-resolution spectrometer, (b) whereas the data from 600 to ${\sim}\;{1560}\;{\rm nm}$ were detected directly from the chip output by an OSA. The peak at 1092.3 nm is an artifice of the OSA, showing the second-order diffraction signal of the 546 nm mode. The corresponding idler pair is observed at 1465.3 nm. For the spectrum in (a) and (b), the estimated pump power in the bus waveguide was 175 mW (17% above the oscillation threshold). (c) Measured (markers) and theoretical (solid lines) FSRs and (d) measured loaded ${Q}$-factor of the three coupled modes ${{\rm TM}_0}$, ${{\rm TM}_1}$, and ${{\rm TM}_2}$. The dashed lines are a guide to the eyes. (e) Measured (blue marker) and FDTD simulation (red line) of the total dispersion. The inset compares the shape of the curve with the experimental tendency.

Download Full Size | PPT Slide | PDF

4. ULTRA-WIDE SINGLE SIDEBANDS GENERATION

We focus now on the necessary conditions for the generation of pairs of modes at distant wavelengths. The simulation of the ${\beta _2}$ coefficient depicted in Fig. 1(a) shows that the zero-GVD occurs slightly above 800 nm for our geometry. Therefore, we expected two different oscillatory regimes depending on the pump wavelength. For wavelengths longer than 800 nm, the device is described by anomalous dispersion, which satisfies the phase-matching condition for small detunings, and ${\beta _4}$ has a minor overall contribution, see Eq. (1), regularly leading to the occurrence of a frequency comb around the pump wavelength [21]. However, for wavelengths shorter than the zero-GVD, the dynamics of the oscillation change. The phase-matching involving only ${\beta _2}$ ceases, and the negative value of ${\beta _4}$ is required to achieve phase-matching at larger detunings. The phase mismatching curve for a pump wavelength at 795 nm is observed in Fig. 1(b). We can see a small region of phase-matching around the pump frequency and two crossings at remote frequencies. The simulation predicts a new oscillatory regime, where the signal appears at 548 nm and the corresponding idler at 1447 nm.

Experimentally, we observed a change in the oscillatory regime around 796 nm, which we attributed as the zero-GVD. The model correctly describes the experimental data in Figs. 3(a) and 3(b), which show the measured electromagnetic spectrum at the output of the chip when the resonator is pumped by the laser at the TM polarization, with a wavelength of 795.6 nm and power level of 175 mW in the bus waveguide. In this case, the pump field is in the normal dispersion regime, and we observed a signal appearing at 545 nm, which was measured with a low-resolution spectrometer. Since we were using distinct equipment for idler, pump (OSA), and signal (spectrometer) modes, the observed power is normalized to the peak intensity for each piece of equipment. The corresponding idler pair is observed at 1465.3 nm, close to another zero-GVD point in the telecom band (${\sim}\;{1600}\;{\rm nm}$). The same OSA could not detect the signal at around 545 nm due to a limitation in the frequency range of the equipment. Still, its presence could be noted due to the second-order diffraction peak of the OSA at 1092.3 nm, represented by a small peak in Fig. 3(b) between the pump and idler. We confirmed this by splitting the output beam from the chip in a dichroic mirror (DMLP650, from Thorlabs), transmitting the pump plus idler fields, and reflecting the signal. When we collect the transmitted light into a fiber and send it to the OSA, we notice that the small peak at 1092.3 nm vanishes. The better resolution of the OSA predicts a signal at 546.2 nm. The frequency separation between the sidebands and pump is 174 THz, which is in good agreement with the calculated ${\Omega _{{\rm pm}}}$. The 2.4% discrepancy to the theory can be attributed to small variations in the fabrication process. This oscillatory regime could be observed by the naked eye from the direct scattering of green light off the chip. Both generated modes have the same TM polarization at the output of the chip. As the pump power is increased up to $P = 1.2P_0^{{\rm th}}$, there is a corresponding linear increase in the idler power, with conversion of approximately 1% of the pump power. However, the signal power remains considerably lower, on the range of tens of microwatts (µW) (see Supplement 1). This strong power unbalance can be attributed to a larger absorption in the visible band, an increase in side-top walls scattering at shorter wavelengths, and, most important, a different output coupling efficiency of the signal and idler. We chose a resonator with critical coupling concerning the pump field; therefore, the coupling strengths for the generated modes are different since the wavelengths are very distinct. The signal (idler) is expected to be undercoupled (overcoupled), consistent with the observed unbalance.

To confirm which transverse mode has generated these sidebands, we measured the resonant frequencies for each of the coupled modes to compare with the simulated FSRs. For this purpose, we actively stabilized the temperature of the chip to reduce thermal fluctuations. With the temperature control, the frequency variation of resonances was ${\sim}\;{150}\;{\rm MHz}$. Figure 3(c) compares the measured FSRs with the simulation for the three modes. We calculated the FSRs based on the size of the resonator and the simulation of the group velocity. As we can see, the FSR linear behavior agrees well with the simulation, except at the extremities. For the fundamental mode, the FSR agrees well with the simulation until approximately 800 nm, and, at the very end, we observe a slight downshift on the tendency. On the other hand, for the mode ${{\rm TM}_1}$, we can see an upshift on the slope at approximately the same wavelength.

For shorter wavelengths, we measured a considerable drop of the FSR tendency for both modes ${{\rm TM}_1}$ and ${{\rm TM}_2}$. For the mode ${{\rm TM}_1}$, the FSR is reduced for wavelengths shorter than 775 nm and seems to stabilize at 770 nm with ${\sim}\;{3}\;{\rm GHz}$ below the average value. This amount is superior to what we expected from avoided TM–TE interactions between modes of the same order [16]. The geometry of the ring resonator is highly multimode and supports more modes than those discerned at 795 nm. Besides, at wavelengths far from the phase-matching region between the through-port and resonator, modes of even higher orders are expected to emerge. Near the spectral region where the deviations in the FSRs started, we began to perceive the rise of different modes with a low extinction ratio. Reasonably, these modes could produce the crossings observed. We observed similar effects in the measurement of the ${ Q}$-factor, as can be seen in Fig. 3(d). At the same wavelength that we begin to follow the FSR reduction for the mode ${{\rm TM}_1}$, we also measured a drop in the ${Q}$-factor. The mode ${{\rm TM}_2}$ has a similar behavior. We attributed these effects to a mode crossing with other family modes [31]. As expected, the ${Q}$ of the ${{\rm TM}_0}$ is the highest at ${\sim}\;{3}$, followed by the ${{\rm TM}_1} \sim 1.2$ and ${{\rm TM}_2} \sim 0.4 \times {10^6}$.

The parametric sidebands generated here are more than one octave apart, and the absence of modes between them suggests a different dynamic of the parametric oscillation when compared with a FWM process in the anomalous dispersion regime. It requires normal GVD and negative fourth-order dispersion with a pump frequency close to the zero-GVD point. To verify that, we used the finite-difference time-domain (FDTD) method [34] to compute the total dispersion ${\omega _\mu} -$${\omega _0} - {D_1}\mu = {D_2}{\mu ^2}/2! + {D_3}{\mu ^3}/3! + {D_4}{\mu ^4}/4! + \ldots$, where $\mu$ is the mode number, ${D_1}/2\pi$ is the FSR, ${D_2}$ is related to ${\beta _2}$ via ${D_2} = - (c/{n_0})D_1^2{\beta _2}$, and ${D_3}$ and ${D_4}$ are related to higher dispersion terms [35]. For our geometry, with a pump wavelength at 795 nm and mode ${{\rm TM}_1}$, we have a typical curve, where the second-order dispersion coefficient is small, and higher-order dispersion has a significant contribution, see Fig. 3(e). The solid line and markers are simulated and measured dispersion, respectively. In the plot, we neglected the measured resonances below 775 nm in Fig. 3(c), due to the mode crossing. After this, the dispersion agrees well with the calculation, as we can see in the inset of Fig. 3(e). For the pump mode ($\mu= 0$), the GVD is still normal, as is indicated by the concave shape of the curve. It is worth mentioning that the obtained dispersion parameters using the FDTD method, through ${{D}_2}$ and ${{D}_4}$, were slightly different from the values obtained with the frequency-domain method and closer to the experimental observations.

5. DYNAMICS OF OSCILLATION

The signal of ${\beta _2}$ determines the characteristics of oscillation we observed, leading to rich dynamics depending on both the wavelength and pump power. When pumping the same resonator at wavelengths longer than the zero-GVD, the geometry of the resonator is described by anomalous dispersion, and we witnessed oscillations of bright fields at various cavity modes from nearly 700 until 1050 nm, as shown in Fig. 4(a). When pumping at 797.2 nm, we could produce a full frequency comb, where all cavity modes inside the spectral gain bandwidth are filled with bright beams, as shown in Fig. 4(b). The frequency comb spans 143 THz, and, although we have not studied the RF noise on this device, the result is consistent with the generation of a frequency comb in a soliton state observed by Zhao et al. [21] using the high-order ${{\rm TE}_1}$ mode with a pump field at around 780 nm.

 figure: Fig. 4.

Fig. 4. Experimentally measured spectra for different pump wavelengths: (a) ${\lambda _p} = 799.5\;{\rm nm} $, (b) ${\lambda _p} = 797.2\;{\rm nm} $, and (c) ${\lambda _p} = 795.6\;{\rm nm} $. For all of these measurements, we used the same TM polarization and maximum pump power of 1 W, which corresponds to approximately 500 mW in the bus waveguide.

Download Full Size | PPT Slide | PDF

Figure 4(c) shows the generated spectrum when pumping the resonator at 795.6 nm. The transition from an oscillation where many cavity modes are populated with bright beams to the generation of a single bright field with great separation in frequency from the pump was evident because it ceased emitting red light corresponding to the bright fields on the blue tail of the frequency comb at around 700 nm and began emitting an intense green light. The crossing of the zero-GVD describes the transition. The switch on the signal of ${\beta _2}$ does not satisfy the phase-matching condition anymore for sidebands close to the pump. A similar observation was described in [8]. However, the negative value of ${\beta _4}$ takes an essential place on the nonlinear phase-matching described by Eq. (1), driving the generation of the first fields widely separated from the pump. The first idler field appears at 1465.3 nm in the telecom S-band, as can be observed in Fig. 4(c). Interestingly, the idler can act as a second pump at anomalous dispersion, generating a clustered frequency comb around it for high pump power [36].

Keeping the pump wavelength at 795.6 nm, we explore the structure of the idler field at distinct pump powers, as is shown in Fig. 5. With a pump power of 225 mW, the ring resonator produced a clustered comb in a telecom band centered at 1465.3 nm, spanning from approximately 1430 to 1510 nm, as shown in the inset of the top part figure. When the pump power is reduced to 200 mW, the device still produces some modes, although with a reduced density. Further reducing the pump power, the device produces only a single bright idler field. We can also observe a strong peak around 1591 nm related to the second-order diffraction peak of the OSA for the pump field at 795.6 nm. This peak is always detected regardless of the power, polarization, or device, being just an artifact of our equipment.

 figure: Fig. 5.

Fig. 5. Measured OPO spectra of widely separated sidebands with and without clustered frequency combs. For all measurements, we pumped the same cavity mode at TM polarization while changing the pump power. With 180 mW of pump power, the device produces only a single bright field at 1465.3 nm. The weak and strong signals at 1092.3 and ${\sim}{1591}\;{\rm nm}$ are second-order responses from the signal (546.2 nm) and pump (795.6 nm) in the OSA grating, respectively.

Download Full Size | PPT Slide | PDF

6. CONCLUSION

In conclusion, we have shown that the high-order ${{\rm TM}_1}$ mode in ${{\rm Si}_3}{{\rm N}_4}$ microresonators can tailor the zero-GVD point to a wavelength close to 795 nm, an attractive wavelength associated with the Rb D1 absorption line. Moreover, it is known that the generation of sidebands associated with the ${\beta _4}$ dispersion coefficient term can be widely tuned [1820]. We presented the guidance on building silicon-chip-based devices to produce single sidebands at specific spectral regions, where the separation between the signal and idler covers 346 THz, with a wavelength ratio of 2.68. It is far enough for one of the fields to sit in the visible range, while the other lays on the telecom S-band.

The developed method can find interesting applications in quantum communications. It is especially interesting at the visible band due to the possibility of sharing nonclassical information between different alkali atoms. As it was shown experimentally, the first generated sidebands in the microring exhibit quantum correlations in amplitude [37], and it also predicted bi and tripartite entanglement above the threshold [38].

Funding

Conselho Nacional de Desenvolvimento Científico e Tecnológico; Coordenação de Aperfeiçoamento de Pessoal de Nível Superior; Fundação de Amparo à Pesquisa do Estado de São Paulo (2015/18834-0); Sprint-UVa FAPESP (2016/50468-7); National Science Foundation (NNCI-2025233, OMA-1936345); Air Force Office of Scientific Research (FA8650-20-1-0297).

Acknowledgment

We acknowledge funding from Conselho Nacional de Desenvolvimento Científico e Tecnológico; Coordenação de Aperfeiçoamento de Pessoal de Nível Superior; Fundação de Amparo à Pesquisa do Estado de São Paulo (2015/18834-0) and Sprint-UVa FAPESP (2016/50468-7). The work by YZ, XJ, ML, and ALG was performed in part at the Cornell NanoScale Facility, a member of the National Nanotechnology Coordinated Infrastructure (NNCI), which was supported by the National Science Foundation (Grant No. NNCI-2025233). These authors also acknowledge support from the Air Force Office of Scientific Research (FA8650-20-1-0297) and the National Science Foundation (OMA-1936345).

Disclosures

The authors declare no conflicts of interest.

Supplemental document

See Supplement 1 for supporting content.

REFERENCES

1. K. Luke, Y. Okawachi, M. R. Lamont, A. L. Gaeta, and M. Lipson, “Broadband mid-infrared frequency comb generation in a Si3N4 microresonator,” Opt. Lett. 40, 4823–4826 (2015). [CrossRef]  

2. J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2010). [CrossRef]  

3. K. Saha, Y. Okawachi, J. S. Levy, R. K. W. Lau, K. Luke, M. A. Foster, M. Lipson, and A. L. Gaeta, “Broadband parametric frequency comb generation with a 1-µm pump source,” Opt. Express 20, 26935–26941 (2012). [CrossRef]  

4. W. Liang, A. A. Savchenkov, Z. Xie, J. F. McMillan, J. Burkhart, V. S. Ilchenko, C. W. Wong, A. B. Matsko, and L. Maleki, “Miniature multioctave light source based on a monolithic microcavity,” Optica 2, 40–47 (2015). [CrossRef]  

5. H. Jung, R. Stoll, X. Guo, D. Fischer, and H. X. Tang, “Green, red, and IR frequency comb line generation from single IR pump in AlN microring resonator,” Optica 1, 396–399 (2014). [CrossRef]  

6. S. Miller, K. Luke, Y. Okawachi, J. Cardenas, A. L. Gaeta, and M. Lipson, “On-chip frequency comb generation at visible wavelengths via simultaneous second- and third-order optical nonlinearities,” Opt. Express 22, 26517–26525 (2014). [CrossRef]  

7. L. Wang, L. Chang, N. Volet, M. H. Pfeiffer, M. Zervas, H. Guo, T. J. Kippenberg, and J. E. Bowers, “Frequency comb generation in the green using silicon nitride microresonators,” Laser Photon. Rev. 10, 631–638 (2016). [CrossRef]  

8. X. Lu, G. Moille, A. Singh, Q. Li, D. A. Westly, A. Rao, S.-P. Yu, T. C. Briles, S. B. Papp, and K. Srinivasan, “Milliwatt-threshold visible–telecom optical parametric oscillation using silicon nanophotonics,” Optica 6, 1535–1541 (2019). [CrossRef]  

9. X. Lu, G. Moille, Q. Li, D. A. Westly, A. Singh, A. Rao, S. P. Yu, T. C. Briles, S. B. Papp, and K. Srinivasan, “Efficient telecom-to-visible spectral translation through ultralow power nonlinear nanophotonics,” Nat. Photonics 13, 593–601 (2019). [CrossRef]  

10. X. Lu, G. Moille, A. Rao, D. A. Westly, and K. Srinivasan, “On-chip optical parametric oscillation into the visible: generating red, orange, yellow, and green from a near-infrared pump,” Optica 7, 1417–1425 (2020). [CrossRef]  

11. P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007). [CrossRef]  

12. A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Kerr combs with selectable central frequency,” Nat. Photonics 5, 293–296 (2011). [CrossRef]  

13. M. Haelterman, S. Trillo, and S. Wabnitz, “Additive-modulation-instability ring laser in the normal dispersion regime of a fiber,” Opt. Lett. 17, 745–747 (1992). [CrossRef]  

14. S. Coen and M. Haelterman, “Modulational instability induced by cavity boundary conditions in a normally dispersive optical fiber,” Phys. Rev. Lett. 79, 4139–4142 (1997). [CrossRef]  

15. S. W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D. L. Kwong, L. Maleki, and C. W. Wong, “Mode-locked ultrashort pulse generation from on-chip normal dispersion microresonators,” Phys. Rev. Lett. 114, 053901 (2015). [CrossRef]  

16. S. Ramelow, A. Farsi, S. Clemmen, J. S. Levy, A. R. Johnson, Y. Okawachi, M. R. E. Lamont, M. Lipson, and A. L. Gaeta, “Strong polarization mode coupling in microresonators,” Opt. Lett. 39, 5134–5137 (2014). [CrossRef]  

17. J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. Knight, W. J. Wadsworth, and P. St.J. Russell, “Scalar modulation instability in the normal dispersion regime by use of a photonic crystal fiber,” Opt. Lett. 28, 2225–2227 (2003). [CrossRef]  

18. N. L. B. Sayson, H. Pham, K. E. Webb, L. S. Trainor, H. G. Schwefel, S. Coen, M. Erkintalo, and S. G. Murdoch, “Widely-tunable optical parametric oscillation in MgF2 microresonators,” in Conference on Lasers and Electro-Optics (2018).

19. A. S. Koligy, D. D. Hickstein, A. Lind, D. R. Carlson, H. Timmers, N. Nader, D. L. Maser, D. Westly, K. Srinivasan, S. B. Papp, and S. A. Diddams, “Tunable mid-infrared generation via wide-band four-wave mixing in silicon nitride waveguides,” Opt. Lett. 43, 4220–4223 (2018). [CrossRef]  

20. Y. Tang, Z. Gong, X. Liu, and H. X. Tang, “Widely separated optical Kerr parametric oscillation in AlN microrings,” Opt. Lett. 45, 1124–1127 (2020). [CrossRef]  

21. Y. Zhao, X. Ji, B. Y. Kim, P. S. Donvalkar, J. K. Jang, C. Joshi, M. Yu, C. Joshi, R. R. Domeneguetti, F. A. S. Barbosa, P. Nussenzveig, Y. Okawachi, M. Lipson, and A. L. Gaeta, “Visible nonlinear photonics via high-order-mode dispersion engineering,” Optica 7, 135–141 (2020). [CrossRef]  

22. Y. Okawachi, M. R. E. Lamont, K. Luke, D. O. Carvalho, M. Yu, M. Lipson, and A. L. Gaeta, “Bandwidth shaping of microresonator-based frequency combs via dispersion engineering,” Opt. Lett. 39, 3535–3538 (2014). [CrossRef]  

23. S. J. Garth and C. Pask, “Four-photon mixing and dispersion in single-mode fibers,” Opt. Lett. 11, 380–382 (1986). [CrossRef]  

24. V. Torres-Company, D. Castelló-Lurbe, and E. Silvestre, “Comparative analysis of spectral coherence in microresonator frequency combs,” Opt. Express 22, 4678–4691 (2014). [CrossRef]  

25. R. Kitamura, L. Pilon, and M. Jonasz, “Optical constants of silica glass from extreme ultraviolet to far infrared at near room temperature,” Appl. Opt. 46, 8118–8133 (2007). [CrossRef]  

26. 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, 707–712 (2017). [CrossRef]  

27. X. Ji, F. A. S. 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, 619–624 (2017). [CrossRef]  

28. M. Karpov, M. H. Pfeiffer, J. Liu, A. Lukashchuk, and T. J. Kippenberg, “Photonic chip-based soliton frequency combs covering the biological imaging window,” Nat. Commun. 9, 1146 (2018). [CrossRef]  

29. S. Johnson and J. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001). [CrossRef]  

30. R. T. Schermer and J. H. Cole, “Improved bend loss formula verified for optical fiber by simulation and experiment,” IEEE J. Quantum Electron. 43, 899–909 (2007). [CrossRef]  

31. T. Carmon, H. G. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100, 103905 (2008). [CrossRef]  

32. X. Xue, Y. Xuan, C. Wang, P.-H. Wang, Y. Liu, B. Niu, D. E. Leaird, M. Qi, and A. M. Weiner, “Thermal tuning of Kerr frequency combs in silicon nitride microring resonators,” Opt. Express 24, 687–698 (2016). [CrossRef]  

33. H. R. Philipp, “Optical properties of silicon nitride,” J. Electrochem. Soc. 120, 295 (1973). [CrossRef]  

34. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010). [CrossRef]  

35. V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016). [CrossRef]  

36. A. B. Matsko, A. A. Savchenkov, S.-W. Huang, and L. Maleki, “Clustered frequency comb,” Opt. Lett. 41, 5102–5105 (2016). [CrossRef]  

37. A. Dutt, K. Luke, S. Manipatruni, A. L. Gaeta, P. Nussenzveig, and M. Lipson, “On-chip optical squeezing,” Phys. Rev. Appl. 3, 044005 (2015). [CrossRef]  

38. C. González-Arciniegas, N. Treps, and P. Nussenzveig, “Third-order nonlinearity OPO: Schmidt mode decomposition and tripartite entanglement,” Opt. Lett. 42, 4865–4868 (2017). [CrossRef]  

References

  • View by:

  1. K. Luke, Y. Okawachi, M. R. Lamont, A. L. Gaeta, and M. Lipson, “Broadband mid-infrared frequency comb generation in a Si3N4 microresonator,” Opt. Lett. 40, 4823–4826 (2015).
    [Crossref]
  2. J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2010).
    [Crossref]
  3. K. Saha, Y. Okawachi, J. S. Levy, R. K. W. Lau, K. Luke, M. A. Foster, M. Lipson, and A. L. Gaeta, “Broadband parametric frequency comb generation with a 1-µm pump source,” Opt. Express 20, 26935–26941 (2012).
    [Crossref]
  4. W. Liang, A. A. Savchenkov, Z. Xie, J. F. McMillan, J. Burkhart, V. S. Ilchenko, C. W. Wong, A. B. Matsko, and L. Maleki, “Miniature multioctave light source based on a monolithic microcavity,” Optica 2, 40–47 (2015).
    [Crossref]
  5. H. Jung, R. Stoll, X. Guo, D. Fischer, and H. X. Tang, “Green, red, and IR frequency comb line generation from single IR pump in AlN microring resonator,” Optica 1, 396–399 (2014).
    [Crossref]
  6. S. Miller, K. Luke, Y. Okawachi, J. Cardenas, A. L. Gaeta, and M. Lipson, “On-chip frequency comb generation at visible wavelengths via simultaneous second- and third-order optical nonlinearities,” Opt. Express 22, 26517–26525 (2014).
    [Crossref]
  7. L. Wang, L. Chang, N. Volet, M. H. Pfeiffer, M. Zervas, H. Guo, T. J. Kippenberg, and J. E. Bowers, “Frequency comb generation in the green using silicon nitride microresonators,” Laser Photon. Rev. 10, 631–638 (2016).
    [Crossref]
  8. X. Lu, G. Moille, A. Singh, Q. Li, D. A. Westly, A. Rao, S.-P. Yu, T. C. Briles, S. B. Papp, and K. Srinivasan, “Milliwatt-threshold visible–telecom optical parametric oscillation using silicon nanophotonics,” Optica 6, 1535–1541 (2019).
    [Crossref]
  9. X. Lu, G. Moille, Q. Li, D. A. Westly, A. Singh, A. Rao, S. P. Yu, T. C. Briles, S. B. Papp, and K. Srinivasan, “Efficient telecom-to-visible spectral translation through ultralow power nonlinear nanophotonics,” Nat. Photonics 13, 593–601 (2019).
    [Crossref]
  10. X. Lu, G. Moille, A. Rao, D. A. Westly, and K. Srinivasan, “On-chip optical parametric oscillation into the visible: generating red, orange, yellow, and green from a near-infrared pump,” Optica 7, 1417–1425 (2020).
    [Crossref]
  11. P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
    [Crossref]
  12. A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Kerr combs with selectable central frequency,” Nat. Photonics 5, 293–296 (2011).
    [Crossref]
  13. M. Haelterman, S. Trillo, and S. Wabnitz, “Additive-modulation-instability ring laser in the normal dispersion regime of a fiber,” Opt. Lett. 17, 745–747 (1992).
    [Crossref]
  14. S. Coen and M. Haelterman, “Modulational instability induced by cavity boundary conditions in a normally dispersive optical fiber,” Phys. Rev. Lett. 79, 4139–4142 (1997).
    [Crossref]
  15. S. W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D. L. Kwong, L. Maleki, and C. W. Wong, “Mode-locked ultrashort pulse generation from on-chip normal dispersion microresonators,” Phys. Rev. Lett. 114, 053901 (2015).
    [Crossref]
  16. S. Ramelow, A. Farsi, S. Clemmen, J. S. Levy, A. R. Johnson, Y. Okawachi, M. R. E. Lamont, M. Lipson, and A. L. Gaeta, “Strong polarization mode coupling in microresonators,” Opt. Lett. 39, 5134–5137 (2014).
    [Crossref]
  17. J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. Knight, W. J. Wadsworth, and P. St.J. Russell, “Scalar modulation instability in the normal dispersion regime by use of a photonic crystal fiber,” Opt. Lett. 28, 2225–2227 (2003).
    [Crossref]
  18. N. L. B. Sayson, H. Pham, K. E. Webb, L. S. Trainor, H. G. Schwefel, S. Coen, M. Erkintalo, and S. G. Murdoch, “Widely-tunable optical parametric oscillation in MgF2 microresonators,” in Conference on Lasers and Electro-Optics (2018).
  19. A. S. Koligy, D. D. Hickstein, A. Lind, D. R. Carlson, H. Timmers, N. Nader, D. L. Maser, D. Westly, K. Srinivasan, S. B. Papp, and S. A. Diddams, “Tunable mid-infrared generation via wide-band four-wave mixing in silicon nitride waveguides,” Opt. Lett. 43, 4220–4223 (2018).
    [Crossref]
  20. Y. Tang, Z. Gong, X. Liu, and H. X. Tang, “Widely separated optical Kerr parametric oscillation in AlN microrings,” Opt. Lett. 45, 1124–1127 (2020).
    [Crossref]
  21. Y. Zhao, X. Ji, B. Y. Kim, P. S. Donvalkar, J. K. Jang, C. Joshi, M. Yu, C. Joshi, R. R. Domeneguetti, F. A. S. Barbosa, P. Nussenzveig, Y. Okawachi, M. Lipson, and A. L. Gaeta, “Visible nonlinear photonics via high-order-mode dispersion engineering,” Optica 7, 135–141 (2020).
    [Crossref]
  22. Y. Okawachi, M. R. E. Lamont, K. Luke, D. O. Carvalho, M. Yu, M. Lipson, and A. L. Gaeta, “Bandwidth shaping of microresonator-based frequency combs via dispersion engineering,” Opt. Lett. 39, 3535–3538 (2014).
    [Crossref]
  23. S. J. Garth and C. Pask, “Four-photon mixing and dispersion in single-mode fibers,” Opt. Lett. 11, 380–382 (1986).
    [Crossref]
  24. V. Torres-Company, D. Castelló-Lurbe, and E. Silvestre, “Comparative analysis of spectral coherence in microresonator frequency combs,” Opt. Express 22, 4678–4691 (2014).
    [Crossref]
  25. R. Kitamura, L. Pilon, and M. Jonasz, “Optical constants of silica glass from extreme ultraviolet to far infrared at near room temperature,” Appl. Opt. 46, 8118–8133 (2007).
    [Crossref]
  26. 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, 707–712 (2017).
    [Crossref]
  27. X. Ji, F. A. S. 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, 619–624 (2017).
    [Crossref]
  28. M. Karpov, M. H. Pfeiffer, J. Liu, A. Lukashchuk, and T. J. Kippenberg, “Photonic chip-based soliton frequency combs covering the biological imaging window,” Nat. Commun. 9, 1146 (2018).
    [Crossref]
  29. S. Johnson and J. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
    [Crossref]
  30. R. T. Schermer and J. H. Cole, “Improved bend loss formula verified for optical fiber by simulation and experiment,” IEEE J. Quantum Electron. 43, 899–909 (2007).
    [Crossref]
  31. T. Carmon, H. G. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100, 103905 (2008).
    [Crossref]
  32. X. Xue, Y. Xuan, C. Wang, P.-H. Wang, Y. Liu, B. Niu, D. E. Leaird, M. Qi, and A. M. Weiner, “Thermal tuning of Kerr frequency combs in silicon nitride microring resonators,” Opt. Express 24, 687–698 (2016).
    [Crossref]
  33. H. R. Philipp, “Optical properties of silicon nitride,” J. Electrochem. Soc. 120, 295 (1973).
    [Crossref]
  34. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
    [Crossref]
  35. V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).
    [Crossref]
  36. A. B. Matsko, A. A. Savchenkov, S.-W. Huang, and L. Maleki, “Clustered frequency comb,” Opt. Lett. 41, 5102–5105 (2016).
    [Crossref]
  37. A. Dutt, K. Luke, S. Manipatruni, A. L. Gaeta, P. Nussenzveig, and M. Lipson, “On-chip optical squeezing,” Phys. Rev. Appl. 3, 044005 (2015).
    [Crossref]
  38. C. González-Arciniegas, N. Treps, and P. Nussenzveig, “Third-order nonlinearity OPO: Schmidt mode decomposition and tripartite entanglement,” Opt. Lett. 42, 4865–4868 (2017).
    [Crossref]

2020 (3)

2019 (2)

X. Lu, G. Moille, A. Singh, Q. Li, D. A. Westly, A. Rao, S.-P. Yu, T. C. Briles, S. B. Papp, and K. Srinivasan, “Milliwatt-threshold visible–telecom optical parametric oscillation using silicon nanophotonics,” Optica 6, 1535–1541 (2019).
[Crossref]

X. Lu, G. Moille, Q. Li, D. A. Westly, A. Singh, A. Rao, S. P. Yu, T. C. Briles, S. B. Papp, and K. Srinivasan, “Efficient telecom-to-visible spectral translation through ultralow power nonlinear nanophotonics,” Nat. Photonics 13, 593–601 (2019).
[Crossref]

2018 (2)

2017 (3)

2016 (4)

X. Xue, Y. Xuan, C. Wang, P.-H. Wang, Y. Liu, B. Niu, D. E. Leaird, M. Qi, and A. M. Weiner, “Thermal tuning of Kerr frequency combs in silicon nitride microring resonators,” Opt. Express 24, 687–698 (2016).
[Crossref]

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).
[Crossref]

A. B. Matsko, A. A. Savchenkov, S.-W. Huang, and L. Maleki, “Clustered frequency comb,” Opt. Lett. 41, 5102–5105 (2016).
[Crossref]

L. Wang, L. Chang, N. Volet, M. H. Pfeiffer, M. Zervas, H. Guo, T. J. Kippenberg, and J. E. Bowers, “Frequency comb generation in the green using silicon nitride microresonators,” Laser Photon. Rev. 10, 631–638 (2016).
[Crossref]

2015 (4)

K. Luke, Y. Okawachi, M. R. Lamont, A. L. Gaeta, and M. Lipson, “Broadband mid-infrared frequency comb generation in a Si3N4 microresonator,” Opt. Lett. 40, 4823–4826 (2015).
[Crossref]

W. Liang, A. A. Savchenkov, Z. Xie, J. F. McMillan, J. Burkhart, V. S. Ilchenko, C. W. Wong, A. B. Matsko, and L. Maleki, “Miniature multioctave light source based on a monolithic microcavity,” Optica 2, 40–47 (2015).
[Crossref]

S. W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D. L. Kwong, L. Maleki, and C. W. Wong, “Mode-locked ultrashort pulse generation from on-chip normal dispersion microresonators,” Phys. Rev. Lett. 114, 053901 (2015).
[Crossref]

A. Dutt, K. Luke, S. Manipatruni, A. L. Gaeta, P. Nussenzveig, and M. Lipson, “On-chip optical squeezing,” Phys. Rev. Appl. 3, 044005 (2015).
[Crossref]

2014 (5)

2012 (1)

2011 (1)

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Kerr combs with selectable central frequency,” Nat. Photonics 5, 293–296 (2011).
[Crossref]

2010 (2)

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2010).
[Crossref]

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

2008 (1)

T. Carmon, H. G. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100, 103905 (2008).
[Crossref]

2007 (3)

R. T. Schermer and J. H. Cole, “Improved bend loss formula verified for optical fiber by simulation and experiment,” IEEE J. Quantum Electron. 43, 899–909 (2007).
[Crossref]

R. Kitamura, L. Pilon, and M. Jonasz, “Optical constants of silica glass from extreme ultraviolet to far infrared at near room temperature,” Appl. Opt. 46, 8118–8133 (2007).
[Crossref]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

2003 (1)

2001 (1)

1997 (1)

S. Coen and M. Haelterman, “Modulational instability induced by cavity boundary conditions in a normally dispersive optical fiber,” Phys. Rev. Lett. 79, 4139–4142 (1997).
[Crossref]

1992 (1)

1986 (1)

1973 (1)

H. R. Philipp, “Optical properties of silicon nitride,” J. Electrochem. Soc. 120, 295 (1973).
[Crossref]

Arcizet, O.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

Barbosa, F. A. S.

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

Bowers, J. E.

L. Wang, L. Chang, N. Volet, M. H. Pfeiffer, M. Zervas, H. Guo, T. J. Kippenberg, and J. E. Bowers, “Frequency comb generation in the green using silicon nitride microresonators,” Laser Photon. Rev. 10, 631–638 (2016).
[Crossref]

Brasch, V.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).
[Crossref]

Briles, T. C.

X. Lu, G. Moille, A. Singh, Q. Li, D. A. Westly, A. Rao, S.-P. Yu, T. C. Briles, S. B. Papp, and K. Srinivasan, “Milliwatt-threshold visible–telecom optical parametric oscillation using silicon nanophotonics,” Optica 6, 1535–1541 (2019).
[Crossref]

X. Lu, G. Moille, Q. Li, D. A. Westly, A. Singh, A. Rao, S. P. Yu, T. C. Briles, S. B. Papp, and K. Srinivasan, “Efficient telecom-to-visible spectral translation through ultralow power nonlinear nanophotonics,” Nat. Photonics 13, 593–601 (2019).
[Crossref]

Bryant, A.

Burkhart, J.

Cardenas, J.

Carlson, D. R.

Carmon, T.

T. Carmon, H. G. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100, 103905 (2008).
[Crossref]

Carvalho, D. O.

Castelló-Lurbe, D.

Chang, L.

L. Wang, L. Chang, N. Volet, M. H. Pfeiffer, M. Zervas, H. Guo, T. J. Kippenberg, and J. E. Bowers, “Frequency comb generation in the green using silicon nitride microresonators,” Laser Photon. Rev. 10, 631–638 (2016).
[Crossref]

Clemmen, S.

Coen, S.

J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. Knight, W. J. Wadsworth, and P. St.J. Russell, “Scalar modulation instability in the normal dispersion regime by use of a photonic crystal fiber,” Opt. Lett. 28, 2225–2227 (2003).
[Crossref]

S. Coen and M. Haelterman, “Modulational instability induced by cavity boundary conditions in a normally dispersive optical fiber,” Phys. Rev. Lett. 79, 4139–4142 (1997).
[Crossref]

N. L. B. Sayson, H. Pham, K. E. Webb, L. S. Trainor, H. G. Schwefel, S. Coen, M. Erkintalo, and S. G. Murdoch, “Widely-tunable optical parametric oscillation in MgF2 microresonators,” in Conference on Lasers and Electro-Optics (2018).

Cole, J. H.

R. T. Schermer and J. H. Cole, “Improved bend loss formula verified for optical fiber by simulation and experiment,” IEEE J. Quantum Electron. 43, 899–909 (2007).
[Crossref]

Del’Haye, P.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

Diddams, S. A.

Domeneguetti, R. R.

Donvalkar, P. S.

Dutt, A.

Erkintalo, M.

N. L. B. Sayson, H. Pham, K. E. Webb, L. S. Trainor, H. G. Schwefel, S. Coen, M. Erkintalo, and S. G. Murdoch, “Widely-tunable optical parametric oscillation in MgF2 microresonators,” in Conference on Lasers and Electro-Optics (2018).

Farsi, A.

Fischer, D.

Foster, M. A.

K. Saha, Y. Okawachi, J. S. Levy, R. K. W. Lau, K. Luke, M. A. Foster, M. Lipson, and A. L. Gaeta, “Broadband parametric frequency comb generation with a 1-µm pump source,” Opt. Express 20, 26935–26941 (2012).
[Crossref]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2010).
[Crossref]

Gaeta, A. L.

Y. Zhao, X. Ji, B. Y. Kim, P. S. Donvalkar, J. K. Jang, C. Joshi, M. Yu, C. Joshi, R. R. Domeneguetti, F. A. S. Barbosa, P. Nussenzveig, Y. Okawachi, M. Lipson, and A. L. Gaeta, “Visible nonlinear photonics via high-order-mode dispersion engineering,” Optica 7, 135–141 (2020).
[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, 707–712 (2017).
[Crossref]

X. Ji, F. A. S. 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, 619–624 (2017).
[Crossref]

A. Dutt, K. Luke, S. Manipatruni, A. L. Gaeta, P. Nussenzveig, and M. Lipson, “On-chip optical squeezing,” Phys. Rev. Appl. 3, 044005 (2015).
[Crossref]

K. Luke, Y. Okawachi, M. R. Lamont, A. L. Gaeta, and M. Lipson, “Broadband mid-infrared frequency comb generation in a Si3N4 microresonator,” Opt. Lett. 40, 4823–4826 (2015).
[Crossref]

S. Miller, K. Luke, Y. Okawachi, J. Cardenas, A. L. Gaeta, and M. Lipson, “On-chip frequency comb generation at visible wavelengths via simultaneous second- and third-order optical nonlinearities,” Opt. Express 22, 26517–26525 (2014).
[Crossref]

S. Ramelow, A. Farsi, S. Clemmen, J. S. Levy, A. R. Johnson, Y. Okawachi, M. R. E. Lamont, M. Lipson, and A. L. Gaeta, “Strong polarization mode coupling in microresonators,” Opt. Lett. 39, 5134–5137 (2014).
[Crossref]

Y. Okawachi, M. R. E. Lamont, K. Luke, D. O. Carvalho, M. Yu, M. Lipson, and A. L. Gaeta, “Bandwidth shaping of microresonator-based frequency combs via dispersion engineering,” Opt. Lett. 39, 3535–3538 (2014).
[Crossref]

K. Saha, Y. Okawachi, J. S. Levy, R. K. W. Lau, K. Luke, M. A. Foster, M. Lipson, and A. L. Gaeta, “Broadband parametric frequency comb generation with a 1-µm pump source,” Opt. Express 20, 26935–26941 (2012).
[Crossref]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2010).
[Crossref]

Garth, S. J.

Geiselmann, M.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).
[Crossref]

Gondarenko, A.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2010).
[Crossref]

Gong, Z.

González-Arciniegas, C.

Gorodetsky, M. L.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).
[Crossref]

Griffith, A. G.

Guo, H.

L. Wang, L. Chang, N. Volet, M. H. Pfeiffer, M. Zervas, H. Guo, T. J. Kippenberg, and J. E. Bowers, “Frequency comb generation in the green using silicon nitride microresonators,” Laser Photon. Rev. 10, 631–638 (2016).
[Crossref]

Guo, X.

Haelterman, M.

S. Coen and M. Haelterman, “Modulational instability induced by cavity boundary conditions in a normally dispersive optical fiber,” Phys. Rev. Lett. 79, 4139–4142 (1997).
[Crossref]

M. Haelterman, S. Trillo, and S. Wabnitz, “Additive-modulation-instability ring laser in the normal dispersion regime of a fiber,” Opt. Lett. 17, 745–747 (1992).
[Crossref]

Harvey, J. D.

Herr, T.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).
[Crossref]

Hickstein, D. D.

Holzwarth, R.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

Huang, S. W.

S. W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D. L. Kwong, L. Maleki, and C. W. Wong, “Mode-locked ultrashort pulse generation from on-chip normal dispersion microresonators,” Phys. Rev. Lett. 114, 053901 (2015).
[Crossref]

Huang, S.-W.

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

Ilchenko, V. S.

W. Liang, A. A. Savchenkov, Z. Xie, J. F. McMillan, J. Burkhart, V. S. Ilchenko, C. W. Wong, A. B. Matsko, and L. Maleki, “Miniature multioctave light source based on a monolithic microcavity,” Optica 2, 40–47 (2015).
[Crossref]

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Kerr combs with selectable central frequency,” Nat. Photonics 5, 293–296 (2011).
[Crossref]

Jang, J. K.

Ji, X.

Joannopoulos, J.

Joannopoulos, J. D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

Johnson, A. R.

Johnson, S.

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

Jonasz, M.

Joshi, C.

Jung, H.

Karpov, M.

M. Karpov, M. H. Pfeiffer, J. Liu, A. Lukashchuk, and T. J. Kippenberg, “Photonic chip-based soliton frequency combs covering the biological imaging window,” Nat. Commun. 9, 1146 (2018).
[Crossref]

Kim, B. Y.

Kippenberg, T. J.

M. Karpov, M. H. Pfeiffer, J. Liu, A. Lukashchuk, and T. J. Kippenberg, “Photonic chip-based soliton frequency combs covering the biological imaging window,” Nat. Commun. 9, 1146 (2018).
[Crossref]

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).
[Crossref]

L. Wang, L. Chang, N. Volet, M. H. Pfeiffer, M. Zervas, H. Guo, T. J. Kippenberg, and J. E. Bowers, “Frequency comb generation in the green using silicon nitride microresonators,” Laser Photon. Rev. 10, 631–638 (2016).
[Crossref]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

Kitamura, R.

Knight, J.

Koligy, A. S.

Kwong, D. L.

S. W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D. L. Kwong, L. Maleki, and C. W. Wong, “Mode-locked ultrashort pulse generation from on-chip normal dispersion microresonators,” Phys. Rev. Lett. 114, 053901 (2015).
[Crossref]

Lamont, M. R.

Lamont, M. R. E.

Lau, R. K. W.

Leaird, D. E.

Leonhardt, R.

Levy, J. S.

Li, Q.

X. Lu, G. Moille, A. Singh, Q. Li, D. A. Westly, A. Rao, S.-P. Yu, T. C. Briles, S. B. Papp, and K. Srinivasan, “Milliwatt-threshold visible–telecom optical parametric oscillation using silicon nanophotonics,” Optica 6, 1535–1541 (2019).
[Crossref]

X. Lu, G. Moille, Q. Li, D. A. Westly, A. Singh, A. Rao, S. P. Yu, T. C. Briles, S. B. Papp, and K. Srinivasan, “Efficient telecom-to-visible spectral translation through ultralow power nonlinear nanophotonics,” Nat. Photonics 13, 593–601 (2019).
[Crossref]

Liang, W.

W. Liang, A. A. Savchenkov, Z. Xie, J. F. McMillan, J. Burkhart, V. S. Ilchenko, C. W. Wong, A. B. Matsko, and L. Maleki, “Miniature multioctave light source based on a monolithic microcavity,” Optica 2, 40–47 (2015).
[Crossref]

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Kerr combs with selectable central frequency,” Nat. Photonics 5, 293–296 (2011).
[Crossref]

Lihachev, G.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).
[Crossref]

Lind, A.

Lipson, M.

Y. Zhao, X. Ji, B. Y. Kim, P. S. Donvalkar, J. K. Jang, C. Joshi, M. Yu, C. Joshi, R. R. Domeneguetti, F. A. S. Barbosa, P. Nussenzveig, Y. Okawachi, M. Lipson, and A. L. Gaeta, “Visible nonlinear photonics via high-order-mode dispersion engineering,” Optica 7, 135–141 (2020).
[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, 707–712 (2017).
[Crossref]

X. Ji, F. A. S. 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, 619–624 (2017).
[Crossref]

A. Dutt, K. Luke, S. Manipatruni, A. L. Gaeta, P. Nussenzveig, and M. Lipson, “On-chip optical squeezing,” Phys. Rev. Appl. 3, 044005 (2015).
[Crossref]

K. Luke, Y. Okawachi, M. R. Lamont, A. L. Gaeta, and M. Lipson, “Broadband mid-infrared frequency comb generation in a Si3N4 microresonator,” Opt. Lett. 40, 4823–4826 (2015).
[Crossref]

S. Miller, K. Luke, Y. Okawachi, J. Cardenas, A. L. Gaeta, and M. Lipson, “On-chip frequency comb generation at visible wavelengths via simultaneous second- and third-order optical nonlinearities,” Opt. Express 22, 26517–26525 (2014).
[Crossref]

S. Ramelow, A. Farsi, S. Clemmen, J. S. Levy, A. R. Johnson, Y. Okawachi, M. R. E. Lamont, M. Lipson, and A. L. Gaeta, “Strong polarization mode coupling in microresonators,” Opt. Lett. 39, 5134–5137 (2014).
[Crossref]

Y. Okawachi, M. R. E. Lamont, K. Luke, D. O. Carvalho, M. Yu, M. Lipson, and A. L. Gaeta, “Bandwidth shaping of microresonator-based frequency combs via dispersion engineering,” Opt. Lett. 39, 3535–3538 (2014).
[Crossref]

K. Saha, Y. Okawachi, J. S. Levy, R. K. W. Lau, K. Luke, M. A. Foster, M. Lipson, and A. L. Gaeta, “Broadband parametric frequency comb generation with a 1-µm pump source,” Opt. Express 20, 26935–26941 (2012).
[Crossref]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2010).
[Crossref]

Liu, J.

M. Karpov, M. H. Pfeiffer, J. Liu, A. Lukashchuk, and T. J. Kippenberg, “Photonic chip-based soliton frequency combs covering the biological imaging window,” Nat. Commun. 9, 1146 (2018).
[Crossref]

Liu, X.

Liu, Y.

Lu, X.

Lukashchuk, A.

M. Karpov, M. H. Pfeiffer, J. Liu, A. Lukashchuk, and T. J. Kippenberg, “Photonic chip-based soliton frequency combs covering the biological imaging window,” Nat. Commun. 9, 1146 (2018).
[Crossref]

Luke, K.

Maleki, L.

A. B. Matsko, A. A. Savchenkov, S.-W. Huang, and L. Maleki, “Clustered frequency comb,” Opt. Lett. 41, 5102–5105 (2016).
[Crossref]

W. Liang, A. A. Savchenkov, Z. Xie, J. F. McMillan, J. Burkhart, V. S. Ilchenko, C. W. Wong, A. B. Matsko, and L. Maleki, “Miniature multioctave light source based on a monolithic microcavity,” Optica 2, 40–47 (2015).
[Crossref]

S. W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D. L. Kwong, L. Maleki, and C. W. Wong, “Mode-locked ultrashort pulse generation from on-chip normal dispersion microresonators,” Phys. Rev. Lett. 114, 053901 (2015).
[Crossref]

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Kerr combs with selectable central frequency,” Nat. Photonics 5, 293–296 (2011).
[Crossref]

Manipatruni, S.

A. Dutt, K. Luke, S. Manipatruni, A. L. Gaeta, P. Nussenzveig, and M. Lipson, “On-chip optical squeezing,” Phys. Rev. Appl. 3, 044005 (2015).
[Crossref]

Maser, D. L.

Matsko, A.

S. W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D. L. Kwong, L. Maleki, and C. W. Wong, “Mode-locked ultrashort pulse generation from on-chip normal dispersion microresonators,” Phys. Rev. Lett. 114, 053901 (2015).
[Crossref]

Matsko, A. B.

McMillan, J. F.

S. W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D. L. Kwong, L. Maleki, and C. W. Wong, “Mode-locked ultrashort pulse generation from on-chip normal dispersion microresonators,” Phys. Rev. Lett. 114, 053901 (2015).
[Crossref]

W. Liang, A. A. Savchenkov, Z. Xie, J. F. McMillan, J. Burkhart, V. S. Ilchenko, C. W. Wong, A. B. Matsko, and L. Maleki, “Miniature multioctave light source based on a monolithic microcavity,” Optica 2, 40–47 (2015).
[Crossref]

Miller, S.

Miller, S. A.

Moille, G.

Murdoch, S. G.

N. L. B. Sayson, H. Pham, K. E. Webb, L. S. Trainor, H. G. Schwefel, S. Coen, M. Erkintalo, and S. G. Murdoch, “Widely-tunable optical parametric oscillation in MgF2 microresonators,” in Conference on Lasers and Electro-Optics (2018).

Nader, N.

Niu, B.

Nussenzveig, P.

Okawachi, Y.

Y. Zhao, X. Ji, B. Y. Kim, P. S. Donvalkar, J. K. Jang, C. Joshi, M. Yu, C. Joshi, R. R. Domeneguetti, F. A. S. Barbosa, P. Nussenzveig, Y. Okawachi, M. Lipson, and A. L. Gaeta, “Visible nonlinear photonics via high-order-mode dispersion engineering,” Optica 7, 135–141 (2020).
[Crossref]

X. Ji, F. A. S. 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, 619–624 (2017).
[Crossref]

K. Luke, Y. Okawachi, M. R. Lamont, A. L. Gaeta, and M. Lipson, “Broadband mid-infrared frequency comb generation in a Si3N4 microresonator,” Opt. Lett. 40, 4823–4826 (2015).
[Crossref]

S. Miller, K. Luke, Y. Okawachi, J. Cardenas, A. L. Gaeta, and M. Lipson, “On-chip frequency comb generation at visible wavelengths via simultaneous second- and third-order optical nonlinearities,” Opt. Express 22, 26517–26525 (2014).
[Crossref]

S. Ramelow, A. Farsi, S. Clemmen, J. S. Levy, A. R. Johnson, Y. Okawachi, M. R. E. Lamont, M. Lipson, and A. L. Gaeta, “Strong polarization mode coupling in microresonators,” Opt. Lett. 39, 5134–5137 (2014).
[Crossref]

Y. Okawachi, M. R. E. Lamont, K. Luke, D. O. Carvalho, M. Yu, M. Lipson, and A. L. Gaeta, “Bandwidth shaping of microresonator-based frequency combs via dispersion engineering,” Opt. Lett. 39, 3535–3538 (2014).
[Crossref]

K. Saha, Y. Okawachi, J. S. Levy, R. K. W. Lau, K. Luke, M. A. Foster, M. Lipson, and A. L. Gaeta, “Broadband parametric frequency comb generation with a 1-µm pump source,” Opt. Express 20, 26935–26941 (2012).
[Crossref]

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

Oxborrow, M.

T. Carmon, H. G. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100, 103905 (2008).
[Crossref]

Papp, S. B.

Pask, C.

Pfeiffer, M. H.

M. Karpov, M. H. Pfeiffer, J. Liu, A. Lukashchuk, and T. J. Kippenberg, “Photonic chip-based soliton frequency combs covering the biological imaging window,” Nat. Commun. 9, 1146 (2018).
[Crossref]

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).
[Crossref]

L. Wang, L. Chang, N. Volet, M. H. Pfeiffer, M. Zervas, H. Guo, T. J. Kippenberg, and J. E. Bowers, “Frequency comb generation in the green using silicon nitride microresonators,” Laser Photon. Rev. 10, 631–638 (2016).
[Crossref]

Pham, H.

N. L. B. Sayson, H. Pham, K. E. Webb, L. S. Trainor, H. G. Schwefel, S. Coen, M. Erkintalo, and S. G. Murdoch, “Widely-tunable optical parametric oscillation in MgF2 microresonators,” in Conference on Lasers and Electro-Optics (2018).

Philipp, H. R.

H. R. Philipp, “Optical properties of silicon nitride,” J. Electrochem. Soc. 120, 295 (1973).
[Crossref]

Pilon, L.

Qi, M.

Ramelow, S.

Rao, A.

Roberts, S. P.

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

Russell, P. St.J.

Saha, K.

Savchenkov, A. A.

Sayson, N. L. B.

N. L. B. Sayson, H. Pham, K. E. Webb, L. S. Trainor, H. G. Schwefel, S. Coen, M. Erkintalo, and S. G. Murdoch, “Widely-tunable optical parametric oscillation in MgF2 microresonators,” in Conference on Lasers and Electro-Optics (2018).

Schermer, R. T.

R. T. Schermer and J. H. Cole, “Improved bend loss formula verified for optical fiber by simulation and experiment,” IEEE J. Quantum Electron. 43, 899–909 (2007).
[Crossref]

Schliesser, A.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

Schwefel, H. G.

T. Carmon, H. G. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100, 103905 (2008).
[Crossref]

N. L. B. Sayson, H. Pham, K. E. Webb, L. S. Trainor, H. G. Schwefel, S. Coen, M. Erkintalo, and S. G. Murdoch, “Widely-tunable optical parametric oscillation in MgF2 microresonators,” in Conference on Lasers and Electro-Optics (2018).

Seidel, D.

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Kerr combs with selectable central frequency,” Nat. Photonics 5, 293–296 (2011).
[Crossref]

Silvestre, E.

Singh, A.

X. Lu, G. Moille, Q. Li, D. A. Westly, A. Singh, A. Rao, S. P. Yu, T. C. Briles, S. B. Papp, and K. Srinivasan, “Efficient telecom-to-visible spectral translation through ultralow power nonlinear nanophotonics,” Nat. Photonics 13, 593–601 (2019).
[Crossref]

X. Lu, G. Moille, A. Singh, Q. Li, D. A. Westly, A. Rao, S.-P. Yu, T. C. Briles, S. B. Papp, and K. Srinivasan, “Milliwatt-threshold visible–telecom optical parametric oscillation using silicon nanophotonics,” Optica 6, 1535–1541 (2019).
[Crossref]

Srinivasan, K.

Stoll, R.

Stone, A. D.

T. Carmon, H. G. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100, 103905 (2008).
[Crossref]

Tang, H. X.

Tang, Y.

Timmers, H.

Torres-Company, V.

Trainor, L. S.

N. L. B. Sayson, H. Pham, K. E. Webb, L. S. Trainor, H. G. Schwefel, S. Coen, M. Erkintalo, and S. G. Murdoch, “Widely-tunable optical parametric oscillation in MgF2 microresonators,” in Conference on Lasers and Electro-Optics (2018).

Treps, N.

Trillo, S.

Turner-Foster, A. C.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2010).
[Crossref]

Vahala, K. J.

T. Carmon, H. G. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100, 103905 (2008).
[Crossref]

Volet, N.

L. Wang, L. Chang, N. Volet, M. H. Pfeiffer, M. Zervas, H. Guo, T. J. Kippenberg, and J. E. Bowers, “Frequency comb generation in the green using silicon nitride microresonators,” Laser Photon. Rev. 10, 631–638 (2016).
[Crossref]

Wabnitz, S.

Wadsworth, W. J.

Wang, C.

Wang, L.

L. Wang, L. Chang, N. Volet, M. H. Pfeiffer, M. Zervas, H. Guo, T. J. Kippenberg, and J. E. Bowers, “Frequency comb generation in the green using silicon nitride microresonators,” Laser Photon. Rev. 10, 631–638 (2016).
[Crossref]

Wang, P.-H.

Webb, K. E.

N. L. B. Sayson, H. Pham, K. E. Webb, L. S. Trainor, H. G. Schwefel, S. Coen, M. Erkintalo, and S. G. Murdoch, “Widely-tunable optical parametric oscillation in MgF2 microresonators,” in Conference on Lasers and Electro-Optics (2018).

Weiner, A. M.

Westly, D.

Westly, D. A.

Wilken, T.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

Wong, C. W.

S. W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D. L. Kwong, L. Maleki, and C. W. Wong, “Mode-locked ultrashort pulse generation from on-chip normal dispersion microresonators,” Phys. Rev. Lett. 114, 053901 (2015).
[Crossref]

W. Liang, A. A. Savchenkov, Z. Xie, J. F. McMillan, J. Burkhart, V. S. Ilchenko, C. W. Wong, A. B. Matsko, and L. Maleki, “Miniature multioctave light source based on a monolithic microcavity,” Optica 2, 40–47 (2015).
[Crossref]

Wong, G. K. L.

Xie, Z.

Xuan, Y.

Xue, X.

Yang, J.

S. W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D. L. Kwong, L. Maleki, and C. W. Wong, “Mode-locked ultrashort pulse generation from on-chip normal dispersion microresonators,” Phys. Rev. Lett. 114, 053901 (2015).
[Crossref]

Yang, L.

T. Carmon, H. G. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100, 103905 (2008).
[Crossref]

Yu, M.

Yu, S. P.

X. Lu, G. Moille, Q. Li, D. A. Westly, A. Singh, A. Rao, S. P. Yu, T. C. Briles, S. B. Papp, and K. Srinivasan, “Efficient telecom-to-visible spectral translation through ultralow power nonlinear nanophotonics,” Nat. Photonics 13, 593–601 (2019).
[Crossref]

Yu, S.-P.

Zervas, M.

L. Wang, L. Chang, N. Volet, M. H. Pfeiffer, M. Zervas, H. Guo, T. J. Kippenberg, and J. E. Bowers, “Frequency comb generation in the green using silicon nitride microresonators,” Laser Photon. Rev. 10, 631–638 (2016).
[Crossref]

Zhao, Y.

Zhou, H.

S. W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D. L. Kwong, L. Maleki, and C. W. Wong, “Mode-locked ultrashort pulse generation from on-chip normal dispersion microresonators,” Phys. Rev. Lett. 114, 053901 (2015).
[Crossref]

Appl. Opt. (1)

Comput. Phys. Commun. (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

IEEE J. Quantum Electron. (1)

R. T. Schermer and J. H. Cole, “Improved bend loss formula verified for optical fiber by simulation and experiment,” IEEE J. Quantum Electron. 43, 899–909 (2007).
[Crossref]

J. Electrochem. Soc. (1)

H. R. Philipp, “Optical properties of silicon nitride,” J. Electrochem. Soc. 120, 295 (1973).
[Crossref]

Laser Photon. Rev. (1)

L. Wang, L. Chang, N. Volet, M. H. Pfeiffer, M. Zervas, H. Guo, T. J. Kippenberg, and J. E. Bowers, “Frequency comb generation in the green using silicon nitride microresonators,” Laser Photon. Rev. 10, 631–638 (2016).
[Crossref]

Nat. Commun. (1)

M. Karpov, M. H. Pfeiffer, J. Liu, A. Lukashchuk, and T. J. Kippenberg, “Photonic chip-based soliton frequency combs covering the biological imaging window,” Nat. Commun. 9, 1146 (2018).
[Crossref]

Nat. Photonics (3)

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2010).
[Crossref]

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Kerr combs with selectable central frequency,” Nat. Photonics 5, 293–296 (2011).
[Crossref]

X. Lu, G. Moille, Q. Li, D. A. Westly, A. Singh, A. Rao, S. P. Yu, T. C. Briles, S. B. Papp, and K. Srinivasan, “Efficient telecom-to-visible spectral translation through ultralow power nonlinear nanophotonics,” Nat. Photonics 13, 593–601 (2019).
[Crossref]

Nature (1)

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

Opt. Express (5)

Opt. Lett. (10)

K. Luke, Y. Okawachi, M. R. Lamont, A. L. Gaeta, and M. Lipson, “Broadband mid-infrared frequency comb generation in a Si3N4 microresonator,” Opt. Lett. 40, 4823–4826 (2015).
[Crossref]

S. Ramelow, A. Farsi, S. Clemmen, J. S. Levy, A. R. Johnson, Y. Okawachi, M. R. E. Lamont, M. Lipson, and A. L. Gaeta, “Strong polarization mode coupling in microresonators,” Opt. Lett. 39, 5134–5137 (2014).
[Crossref]

J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. Knight, W. J. Wadsworth, and P. St.J. Russell, “Scalar modulation instability in the normal dispersion regime by use of a photonic crystal fiber,” Opt. Lett. 28, 2225–2227 (2003).
[Crossref]

M. Haelterman, S. Trillo, and S. Wabnitz, “Additive-modulation-instability ring laser in the normal dispersion regime of a fiber,” Opt. Lett. 17, 745–747 (1992).
[Crossref]

A. S. Koligy, D. D. Hickstein, A. Lind, D. R. Carlson, H. Timmers, N. Nader, D. L. Maser, D. Westly, K. Srinivasan, S. B. Papp, and S. A. Diddams, “Tunable mid-infrared generation via wide-band four-wave mixing in silicon nitride waveguides,” Opt. Lett. 43, 4220–4223 (2018).
[Crossref]

Y. Tang, Z. Gong, X. Liu, and H. X. Tang, “Widely separated optical Kerr parametric oscillation in AlN microrings,” Opt. Lett. 45, 1124–1127 (2020).
[Crossref]

Y. Okawachi, M. R. E. Lamont, K. Luke, D. O. Carvalho, M. Yu, M. Lipson, and A. L. Gaeta, “Bandwidth shaping of microresonator-based frequency combs via dispersion engineering,” Opt. Lett. 39, 3535–3538 (2014).
[Crossref]

S. J. Garth and C. Pask, “Four-photon mixing and dispersion in single-mode fibers,” Opt. Lett. 11, 380–382 (1986).
[Crossref]

A. B. Matsko, A. A. Savchenkov, S.-W. Huang, and L. Maleki, “Clustered frequency comb,” Opt. Lett. 41, 5102–5105 (2016).
[Crossref]

C. González-Arciniegas, N. Treps, and P. Nussenzveig, “Third-order nonlinearity OPO: Schmidt mode decomposition and tripartite entanglement,” Opt. Lett. 42, 4865–4868 (2017).
[Crossref]

Optica (7)

Y. Zhao, X. Ji, B. Y. Kim, P. S. Donvalkar, J. K. Jang, C. Joshi, M. Yu, C. Joshi, R. R. Domeneguetti, F. A. S. Barbosa, P. Nussenzveig, Y. Okawachi, M. Lipson, and A. L. Gaeta, “Visible nonlinear photonics via high-order-mode dispersion engineering,” Optica 7, 135–141 (2020).
[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, 707–712 (2017).
[Crossref]

X. Ji, F. A. S. 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, 619–624 (2017).
[Crossref]

X. Lu, G. Moille, A. Rao, D. A. Westly, and K. Srinivasan, “On-chip optical parametric oscillation into the visible: generating red, orange, yellow, and green from a near-infrared pump,” Optica 7, 1417–1425 (2020).
[Crossref]

X. Lu, G. Moille, A. Singh, Q. Li, D. A. Westly, A. Rao, S.-P. Yu, T. C. Briles, S. B. Papp, and K. Srinivasan, “Milliwatt-threshold visible–telecom optical parametric oscillation using silicon nanophotonics,” Optica 6, 1535–1541 (2019).
[Crossref]

W. Liang, A. A. Savchenkov, Z. Xie, J. F. McMillan, J. Burkhart, V. S. Ilchenko, C. W. Wong, A. B. Matsko, and L. Maleki, “Miniature multioctave light source based on a monolithic microcavity,” Optica 2, 40–47 (2015).
[Crossref]

H. Jung, R. Stoll, X. Guo, D. Fischer, and H. X. Tang, “Green, red, and IR frequency comb line generation from single IR pump in AlN microring resonator,” Optica 1, 396–399 (2014).
[Crossref]

Phys. Rev. Appl. (1)

A. Dutt, K. Luke, S. Manipatruni, A. L. Gaeta, P. Nussenzveig, and M. Lipson, “On-chip optical squeezing,” Phys. Rev. Appl. 3, 044005 (2015).
[Crossref]

Phys. Rev. Lett. (3)

S. Coen and M. Haelterman, “Modulational instability induced by cavity boundary conditions in a normally dispersive optical fiber,” Phys. Rev. Lett. 79, 4139–4142 (1997).
[Crossref]

S. W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D. L. Kwong, L. Maleki, and C. W. Wong, “Mode-locked ultrashort pulse generation from on-chip normal dispersion microresonators,” Phys. Rev. Lett. 114, 053901 (2015).
[Crossref]

T. Carmon, H. G. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100, 103905 (2008).
[Crossref]

Science (1)

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).
[Crossref]

Other (1)

N. L. B. Sayson, H. Pham, K. E. Webb, L. S. Trainor, H. G. Schwefel, S. Coen, M. Erkintalo, and S. G. Murdoch, “Widely-tunable optical parametric oscillation in MgF2 microresonators,” in Conference on Lasers and Electro-Optics (2018).

Supplementary Material (1)

NameDescription
Supplement 1       Output power of the widely separated sidebands as a function of the pump power.

Cited By

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

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1. Simulation of the dispersion coefficients: (a) second- and fourth-order terms of the Taylor expansion of the propagation constant for the ${{\rm TM}_1}$ mode in a microresonator with the cross section of ${730} \times {2000}\;{\rm nm}$. (b) Phase mismatching calculation for the simulated values of ${\beta _2}$ and ${\beta _4}$, evaluated for pump wavelength of 795 nm, zero detuning, and power close to the measured oscillation threshold of 150 mW.
Fig. 2.
Fig. 2. (a) Schematic description of the experimental setup, a cw laser is used as the pump. (b) Spectral measurement of microcavity resonances by microheater sweeping. The inset shows a measurement of the cavity bandwidth by laser scanning. (c) Concept of the mode conversion at the bus waveguide and microring coupling.
Fig. 3.
Fig. 3. Parametric oscillation at visible and telecom wavelengths in a microring using the high-order mode ${{\rm TM}_1}$. (a) The data at shorter wavelengths ($\lt 600\,\,{\rm nm}$) were taken with a low-resolution spectrometer, (b) whereas the data from 600 to ${\sim}\;{1560}\;{\rm nm}$ were detected directly from the chip output by an OSA. The peak at 1092.3 nm is an artifice of the OSA, showing the second-order diffraction signal of the 546 nm mode. The corresponding idler pair is observed at 1465.3 nm. For the spectrum in (a) and (b), the estimated pump power in the bus waveguide was 175 mW (17% above the oscillation threshold). (c) Measured (markers) and theoretical (solid lines) FSRs and (d) measured loaded ${Q}$-factor of the three coupled modes ${{\rm TM}_0}$, ${{\rm TM}_1}$, and ${{\rm TM}_2}$. The dashed lines are a guide to the eyes. (e) Measured (blue marker) and FDTD simulation (red line) of the total dispersion. The inset compares the shape of the curve with the experimental tendency.
Fig. 4.
Fig. 4. Experimentally measured spectra for different pump wavelengths: (a) ${\lambda _p} = 799.5\;{\rm nm} $, (b) ${\lambda _p} = 797.2\;{\rm nm} $, and (c) ${\lambda _p} = 795.6\;{\rm nm} $. For all of these measurements, we used the same TM polarization and maximum pump power of 1 W, which corresponds to approximately 500 mW in the bus waveguide.
Fig. 5.
Fig. 5. Measured OPO spectra of widely separated sidebands with and without clustered frequency combs. For all measurements, we pumped the same cavity mode at TM polarization while changing the pump power. With 180 mW of pump power, the device produces only a single bright field at 1465.3 nm. The weak and strong signals at 1092.3 and ${\sim}{1591}\;{\rm nm}$ are second-order responses from the signal (546.2 nm) and pump (795.6 nm) in the OSA grating, respectively.

Equations (2)

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

Δ κ = δ 0 L n = 2 , 4 , β n n ! Ω n 2 γ L P 0 ,
P 0 t h = α γ L ( 1 Ω p m 2 ω 0 2 ) 1 ,

Metrics