On-chip Frequency Comb Generation at Visible Wavelengths via Simultaneous Second-and Third-order Optical Nonlinearities References and Links

Microresonator-based frequency comb generation at or near visible wavelengths would enable applications in precise optical clocks, frequency metrology, and biomedical imaging. Comb generation in the visible has been limited by strong material dispersion and loss at short wavelengths, and only very narrowband comb generation has reached below 800 nm. We use the second-order optical nonlinearity in an integrated high-Q silicon nitride ring resonator cavity to convert a near-infrared frequency comb into the visible range. We simultaneously demonstrate parametric frequency comb generation in the near-infrared, second-harmonic generation, and sum-frequency generation. We measure 17 comb lines converted to visible wavelengths extending to 765 nm. Towards an accurate frequency standard at 778 nm using a laser diode stabilized on a hyperfine component of the doppler-free two-photon transitions in rubidium, " Opt. Tailored anomalous group-velocity dispersion in silicon channel waveguides, " Opt.

Microresonator-based optical frequency combs at visible wavelengths enable various applications including precise optical clocks, frequency metrology, and biomedical imaging [1][2][3].However, visible comb generation has been limited by strong material dispersion and scattering losses at short wavelengths.Frequency comb lines generated near visible wavelengths would enable locking of combs to atomic transitions, which is critical for metrology.Several atomic transitions commonly used for stabilization of optical clocks, including rubidium and cesium, are located in the near-visible to visible range [4][5][6].Additionally, comb lines in the visible range are of particular interest for biological applications.The red to near-infrared (near-IR) wavelength range is a target region for biological imaging, falling between the increased absorption of water at longer wavelengths and the increased Rayleigh scattering in tissue at shorter wavelengths.The availability of multiple comb line sources in this range could enhance the resolution in biological tissue imaging using optical coherence tomography (OCT) [3,7].One of the main challenges in achieving comb generation at visible wavelengths is the strong normal material dispersion that is characteristic of the dielectric materials used in microresonator devices (silica, silicon nitride, calcium fluoride, etc) as well as the high degree of scattering in this spectral range.For microresonator-based comb generation, low anomalous group-velocity dispersion (GVD) is necessary for phase-matching and efficient four-wave mixing (FWM) and parametric oscillation [8].At near-IR wavelengths, the normal material dispersion is compensated by waveguide dispersion, which is dependent on the waveguide dimensions, to allow for the requisite dispersion profile for efficient comb generation [8,9].However, at shorter wavelengths approaching the band gap of the dielectric material, the material dispersion becomes too strong to be compensated by waveguide dispersion, which results in poor phase matching conditions.Additionally, Rayleigh scattering at the waveguide sidewalls increases inversely as λ 4 , which inherently lowers the quality factor (Q) of resonators at shorter wavelengths.This decreases the cavity enhancement of the pump and further reduces the efficiency of nonlinear processes required for comb generation.
Previous demonstrations of broadband combs pumped in the near-infrared have not been able to extend into the visible range, and only narrowband comb generation has been achieved below 800 nm.Octave-spanning combs pumped at 1.55 µm have generated lines beyond 2 µm wavelength on the long-wavelength side but fail to extend beyond 900 nm at shorter wavelengths [10,11].Microring resonators have also been pumped closer to the visible range at 1064 nm, resulting in broad combs with lines extending below 1 µm [12] and as low as 830 nm [13].There has been one demonstration to date of frequency comb lines below 800 nm, which employed a higher-order whispering gallery mode in a crystalline calcium fluoride resonator, but was able to generate only a 2 nm wide comb at 794 nm [14].
In this work, we circumvent the traditional challenges in achieving microcombs in the visible range and instead simultaneously employ the second-and third-order nonlinearity of silicon nitride (Si 3 N 4 ) to generate frequency comb lines at visible wavelengths.Silicon-based materials have traditionally been limited to third-order (χ (3) ) nonlinear interactions as they are inherently centrosymmetric in either crystalline (c-Si) or amorphous (a-Si or SiN x ) forms.Second-order nonlinear optical processes require breaking the symmetry of the material.The recent demonstrations of both Si 3 N 4 and silicon as second-order nonlinear (χ (2) ) materials [15][16][17][18][19][20][21][22][23] has expanded the range of possible applications for this CMOS-compatible platform.The symmetrybreaking in these otherwise-centrosymmetric materials has been attributed to 1) high levels of strain in the waveguide material [15], 2) surface effects from waveguide-cladding interfaces, which removes the bulk symmetry of the amorphous film [17][18][19][20], and 3) embedded silicon defects or nanoclusters [21,22].The χ (2) coefficient has been estimated to be as high as 5.9 pm/V in Si 3 N 4 [22], and 190 pm/V in silicon [23].Second-order nonlinear processes such as second-harmonic or sum-frequency generation inherently involve wide, octave-spanning frequency conversion away from the pump frequency, as opposed to third-order processes such as FWM, which typically involve narrow conversion near the pump frequency.Here we use this wide-band attribute of χ (2) nonlinearity to achieve wide frequency conversion from near-IR into visible wavelengths.We generate a parametric frequency comb in the near-IR using χ (3) and frequency-translate it into the visible range (Fig. 1(a)) using χ (2) in an integrated ring resonator cavity.A singlefrequency, continuous-wave (CW) pump laser in the near-IR is coupled into a high-Q Si 3 N 4 ring resonator [24,25], which acts to enhance the pump power and serves as the nonlinear medium.The pump laser first undergoes χ (2) second-harmonic generation (SHG), producing one line in the visible range.As the cavity circulating power increases, the pump undergoes χ (3) FWM optical parametric oscillation, which produces a frequency comb in the near-IR range (Fig. 1(b)).The comb lines then mix with the strong near-IR pump through a χ (2) sum-frequency generation (SFG) process (Fig. 1(c)), which produces a set of comb lines in the visible range that are generated simultaneously with the near-IR comb.The generated comb lines therefore simultaneously address two widely different wavelength bands.Additionally, all processes are achieved in a single integrated device using a single CW laser source.
We engineer the waveguide dispersion to simultaneously phase-match near-IR frequency comb generation, second-harmonic generation, and sum-frequency generation.The high finesse of the Si 3 N 4 cavity enhances the efficiency of nonlinear processes.The use of high-index contrast waveguides provides the ability to readily control the waveguide dispersion, and using Si 3 N 4 eliminates the negative effects of free carriers and two photon absorption at the operating wavelengths [26].Through dispersion engineering, we simultaneously satisfy the phasematching conditions for each nonlinear process.For efficient SHG, the effective indices of the fundamental and second harmonic (SH) modes must match.This phase-matching is achieved by using a higher-order waveguide mode for the SH light, as in [17].The third-order TE mode at twice the fundamental frequency is designed to have the same effective mode index as the fundamental TE mode of the pump.We use a finite-element mode solver to calculate effective indices of each mode by taking into consideration material dispersion, a 4 • sidewall angle introduced during fabrication, and the waveguide bending radius of 104 µm.As shown in Fig. 2(a), this phase-matching condition is satisfied at a fundamental wavelength of 1540 nm for a waveguide with dimensions 700-nm tall by 1400-nm wide.This waveguide dimension is also chosen to optimize optical parametric oscillation.The phase-matching condition for optical parametric oscillation is largely dependent on group-velocity dispersion (GVD).The optimal condition for oscillation is a low level of anomalous GVD at the pump frequency [9].This dispersion is then compensated by the χ (3) nonlinear phase shift in order to achieve the proper phase-matching for degenerate FWM.As shown in Fig. 2(b), the waveguide dimensions that satisfy SHG phase-matching also exhibit a sufficiently low level of anomalous GVD for efficient parametric oscillation.  (2SHG and SFG processes, estimated using Eq.(1).Phase-matching bandwidth for SFG is wider than for SHG, allowing for multiple comb lines to be converted into the visible range.
Once phase-matching is ensured for both FWM and SHG processes, the final SFG process is automatically phase-matched, resulting in simultaneous phase-matching for all desired processes.The phase-matching of the SFG process involves one photon from a comb line mixing with one photon from the strong pump.The phase-mismatch ∆k is given by: ∆k = n 1 ω 1 /c + n 2 ω 2 /c -n 3 ω 3 /c, where n i are the effective mode indices of the pump, comb line, and sumfrequency line, respectively.The corresponding photon angular frequencies, ω i , satisfy energy conservation (ω 1 + ω 2 = ω 3 ).For a waveguide of equivalent length, in the limit of low singlepass conversion, the converted power for SFG in a cavity is given by: where d eff = χ (2) /2, C i P i is the cavity circulating power, where C i is the cavity enhancement factor, A i is the effective mode area, and L eff is the effective cavity length [27].The effective cavity length L eff is equal to the product of the group velocity and the cavity lifetime of the mode τ i where τ i = Q i /ω i .The overlap between the spatial modes of the interacting spectral lines is taken into account by the function f 1,2,3 [17].Figure 2(c) shows normalized conversion efficiency versus wavelength for SFG and SHG, in which the latter follows the same conversion efficiency as SFG but with two photons allocated for the pump.The phase-matching requirement for SFG is less stringent than that of SHG, which provides the opportunity to convert a wider bandwidth of near-IR comb lines into the visible range.Intuitively, this property arises from keeping the pump stationary as the comb line varies in the SFG process, which reduces the phase-mismatch compared to SHG, in which both source photons contribute to the phasemismatch.This bandwidth is determined primarily by the slope of the phase-mismatch ∆k with respect to wavelength, which in turn is determined by the group index mismatch of the fundamental and higher-order modes.The choice of a different higher-order mode with a group index closer to that of the fundamental mode could further increase the conversion bandwidth.Overall, these three nonlinear processes are simultaneously phase-matched and are able to occur together in the same cavity structure.Comb spacing is preserved by the SFG process for all states of the frequency comb shown.
Inset micrograph shows the visible light generated by the device.These wavelengths fall just outside the normal range of the CCD camera, so the red color that is seen by the naked eye is distorted.A microheater was fabricated on this device for thermal tuning but was not used in this experiment.
We measure up to 17 comb lines frequency-translated from near-IR into visible wavelengths extending from 765-775 nm.We use a Si 3 N 4 ring resonator with radius 104 µm, waveguide dimensions 700 nm × 1400 nm and a coupling gap of 560 nm.The fabrication methods are the same as those outlined in previous work [24].The resonator has a Q = 1.5×10 6 .All nonlinear processes occur inside the resonator cavity, and are enhanced by this high Q.The pump is produced by a single-frequency tunable diode laser amplified with an erbium-doped fiber amplifier (EDFA).The amplified spontaneous emission (ASE) noise from the EDFA is filtered using a 1-nm tunable bandpass filter, and a polarization controller is used to couple to the fundamental quasi-TE mode of the waveguide using a single-mode lensed fiber.The pump is tuned into a cavity resonance near 1540 nm (Fig. 3(a), black curve), with approximately 700mW in the bus waveguide.At low circulating power in the cavity, the second-harmonic is generated at the expected wavelength of 770.3 nm, as shown in the black curve of Fig. 3(b).The maximum second harmonic conversion efficiency we measure is -29 dB, in which ∼1 mW of the second harmonic has been generated.As the pump is tuned into the resonance, the circulating power in the cavity builds up, which leads to the onset of near-IR frequency comb generation as well as frequency conversion of the comb lines into the visible range.A micrograph inset shows the generated visible light.Several states [28,29] of the generated comb are shown, with comb lines generated every 5, 3, and 1 free-spectral ranges (FSRs).In the filled-in comb state (red), we observe a visible comb bandwidth of nearly 10 nm, covering 17 FSRs.There is equal frequency spacing of 217 GHz among the near-IR comb lines and the visible comb lines.The SFG conversion efficiency is approximately -20 dB.We believe this conversion efficiency is higher than the SHG conversion of the pump due to a lack of precise pump phase-matching for this resonator.This is evident in the blue curve in Fig. 3(b) where we see that the converted comb line five FSRs away has a higher power than the second-harmonic of the pump.We also observe significant variations across different comb lines, which we attribute to higher-order group index mismatch, resulting in a detuning of the generated light from the cavity resonances.We perform a seeded SFG experiment in order to characterize and confirm this conversion process.Nonlinear frequency conversion processes can be characterized by the conversion efficiency with varying pump powers.For SFG, the nonlinear process involves one pump photon, so the converted power is proportional to the pump power.For a χ (3) process such as degenerate FWM, the nonlinear process involves two pump photons, so the converted power is proportional to the square of the pump power.Therefore, in a plot of conversion versus pump power, the slope reflects the nature of the nonlinear process.In this experiment, we use a fiber wavelength-division multiplexing (WDM) coupler in order to combine the near-IR pump laser with another near-IR tunable diode laser to send into the resonator cavity.This second tunable laser allows us to have experimental control of the signal being converted into the visible range rather than for the case above, in which the generated comb lines are being converted.For this experiment, we use a ring resonator cavity with the same cross-sectional dimensions as above but with lower Q, yielding a higher parametric oscillation threshold.This ensures that there are no near-IR comb lines that can be converted into the visible range.We begin by tuning the pump laser far enough into resonance to generate a second harmonic line while remaining below the oscillation threshold.This ensures that we are operating at the proper phase-matching position for the SFG process, consistent with the above results.Next, the signal laser is tuned into a neighboring resonance.We observe seeded FWM surrounding the pump (Fig. 4(a)), which is not desired but is unavoidable in this situation as this process is well phase-matched.Additionally, we observe the desired conversion into the visible range for both lines surrounding the pump (Fig. 4(b)).We measure the conversion efficiency versus pump power, as shown in Figs.4(c) and 4(d).Our conversion here is low because we are using lower power values to ensure we remain below the parametric oscillation threshold.Some small error in the slope for the signal conversion is due to instabilities in the measurement setup.As shown, we observe a slope of approximately 1, confirming that this is indeed a χ (2) SFG process.
We analyze the phase-matching conditions for several nonlinear interactions and confirm that the nonlinear process translating the comb into visible wavelengths is the SFG process.The presence of lines at all FSR resonances rules out SHG as the overall dominant process.If the entire near-IR comb were to undergo SHG, the frequency spacing of the visible comb would be doubled, resulting in a comb line at every-other FSR resonance.We also consider other χ (3) processes as an alternative comb generation mechanism.FWM optical parametric oscillation of the second-harmonic frequency would generate a visible comb with lines at every FSR.However, according to [30], the parametric oscillation threshold is given by, where n eff is the linear mode index, V is the resonator mode volume, n 2 = 2×10 −19 m 2 /W is the nonlinear refractive index, λ 0 is the pump wavelength, Q C and Q L are coupling and loaded quality factors of the resonator mode, respectively, and, where Q i is the intrinsic quality factor [30].At visible frequencies, P th increases due to increase of scattering losses from Rayleigh scattering (decreasing Q i ) and due to the frequency dependence of the waveguide-ring coupling condition (decreasing Q C ).We estimate that Q i at visible wavelengths is less than 10 5 and the ratio Q C /Q L is at least 10, yielding an under-coupled resonance condition.Thus, assuming a mode volume of 400 µm 3 , P th ≥ 10 W, which is at least four orders of magnitude above the ∼1 mW of power in our second-harmonic line.Finally, we also rule out non-degenerate FWM for generating the visible comb lines.Non-degenerate FWM would involve the near-IR pump mixing with the second-harmonic and the near-IR comb lines to generate the visible comb lines.The phase-matching requirements for this process stipulate that the group velocities (v g ) of the near-IR light and the visible light must match.As shown in Fig. 2(a), the slope of the effective index curve for each mode is different, and this slope determines the v g of the circulating light.While the nonlinear phase shift due to cross-phase modulation can be used to compensate for this v g mismatch, this phase shift would require ∼2 W of pump power to minimize the phase mismatch for lines even only one FSR away.Here, we only supply 700 mW in the bus waveguide and generate ten FSRs away from the pump, so this non-degenerate FWM process is not suitably phase-matched.As outlined above, χ (2) SFG is phase-matched and takes advantage of direct interaction with the strong pump, and thus it is left as the most plausible process for generating these comb lines.
In conclusion, we demonstrate on-chip frequency conversion of up to 17 frequency comb lines from the near-IR to visible wavelengths, extending down to 765 nm.This is achieved by simultaneously phase-matching χ (2) and χ (3) nonlinear processes in an integrated high-Q silicon nitride ring resonator cavity.We utilize infrared SHG, frequency comb generation, and SFG to simultaneously generate two combs separated one octave apart in frequency.We envision this result as a potential platform for an on-chip optical atomic clock and the creation of a coherent link between visible and near-IR wavelengths.Recent studies have shown the operation of microresonator-based combs in a phase-locked state in which all comb lines are phase-correlated with each other and all comb frequencies have a precisely equal spacing [29,[31][32][33][34][35][36].We predict that phase correlations will be preserved in the SFG process, so the visible comb lines would be correlated with the near-IR comb as well.Additionally, the ability to produce SHG on-chip could also be applied to f-2f self-referencing by frequencydoubling the long wavelength edge of an octave-spanning comb.Off-chip χ (2) crystals used for f-2f self-referencing of octave spanning combs are not always available for the desired wavelength ranges and are not integrated, but by tailoring phase-matching conditions, this selfreferencing could potentially be integrated on-chip.Additionally, by integrating the on-chip microresonator devices with atomic vapor systems [37,38], this process can enable a compact platform for microresonator-based frequency comb stabilization, leading to applications in biomedical imaging, frequency metrology, and on-chip optical clocks.

Fig. 1 .
Fig. 1.(a) A single near-IR pump is coupled into a microring cavity and undergoes secondharmonic generation, near-IR frequency comb generation, and sum-frequency generation to generate simultaneous near-IR and visible wavelength frequency comb lines.(b) Nonlinear photon interaction energy conservation for degenerate four-wave mixing optical parametric oscillation taking place in the near-IR.(c) Nonlinear photon interaction energy conservation for sum-frequency generation between one pump photon and one comb line photon generating a comb line in the visible.This process is identical for corresponding comb lines colored red in (a).

Fig. 2 .
Fig. 2. (a)The effective mode index dispersion of the fundamental TE mode in near IR spectral range and the third-order TE mode in the visible spectral range.One can see that around the pump wavelength of 1540 nm (red X), phase-matching occurs.(b) The group velocity dispersion (GVD) of the fundamental TE mode shown in (a).The low level of anomalous GVD at the pump wavelength of 1540 nm allows for efficient frequency comb generation.(c) Conversion efficiency vs. wavelength for χ(2) SHG and SFG processes, estimated using Eq.(1).Phase-matching bandwidth for SFG is wider than for SHG, allowing for multiple comb lines to be converted into the visible range.

Fig. 3 .
Fig. 3. (a) Near-IR CW pump laser and frequency comb generation.Several different states of the frequency comb are shown.(b) Visible second-harmonic generation and frequency comb lines for corresponding spectra in (a).The vertical scales have been offset for clarity.Comb spacing is preserved by the SFG process for all states of the frequency comb shown.Inset micrograph shows the visible light generated by the device.These wavelengths fall just outside the normal range of the CCD camera, so the red color that is seen by the naked eye is distorted.A microheater was fabricated on this device for thermal tuning but was not used in this experiment.

Fig. 4 .
Fig. 4. Seeded SFG experiment.(a) Near-IR pump and signal lasers are coupled into the ring resonator.An additional line is seen symmetric about the pump, resulting from FWM.(b) The visible spectrum shows SHG of the pump wavelength and SFG of pump wavelength mixing with both the signal and FWM idler lines.(c) Conversion efficiency vs. pump power for SFG signal , showing conversion proportional to the pump power.(d) Conversion efficiency vs. pump power for SFG idler , showing conversion proportional to pump power.