Kerr Frequency Comb Generation Research Articles

Thermal tuning of Kerr frequency combs in silicon nitride microring resonators.

Microresonator based Kerr frequency comb generation has many attractive features, including ultrabroad spectra, chip-level integration, and low power consumption. Achieving precise tuning control over the comb frequencies will be important for a number of practical applications, but has been little explored for microresonator combs. In this paper, we characterize the thermal tuning of a coherent Kerr frequency comb generated from an on-chip silicon nitride microring. When the microring temperature is changed by ~70 °C with an integrated microheater, the line spacing and center frequency of the comb are tuned respectively by -253 MHz (-3.57 MHz/°C) and by -175 GHz (-2.63 GHz/°C); the latter constitutes 75% of the comb line spacing. From these results we obtain a shift of 25 GHz (362.07 MHz/°C) in the comb carrier-envelope offset frequency. Numerical simulations are performed by taking into account the thermo-optic effects in the waveguide core and cladding. The temperature variation of the comb line spacing predicted from simulations is close to that observed in experiments. The time-dependent thermal response of the microheater based tuning scheme is characterized; time constants of 30.9 μs and 0.71 ms are observed.

Enabling arbitrary wavelength frequency combs on chip

AbstractA necessary condition for generation of bright soliton Kerr frequency combs in microresonators is to achieve anomalous group velocity dispersion (GVD) for the resonator modes. This condition is hard to implement in the visible as well as ultraviolet since the majority of optical materials are characterized with large normal GVD in these wavelength regions. We overcome this challenge by borrowing ideas from strongly dispersive coupled systems in solid state physics and optics. We show that photonic compound ring resonators can possess large anomalous GVD at any desirable wavelength, even if each individual resonator is characterized with normal GVD. Based on this concept, we design a mode‐locked frequency comb with thin‐film silicon nitride compound ring resonators in the vicinity of the rubidium D1 line (794.6 nm) and propose to use this optical comb as a flywheel for chip‐scale optical clocks. image

Spatiotemporal evolution of a cosine-modulated stationary field and Kerr frequency comb generation in a microresonator.

Based on the normalized spatiotemporal Lugiato-Lefever equation, the evolutions of cosine-modulated stationary fields relating to the generation of single-free spectral range (FSR) or multi-FSR Kerr frequency combs in a microresonator with anomalous dispersion are studied numerically. The research results show that a single-FSR comb arises when a dissipative soliton pulse or multiple nonequidistant soliton pulses form in the cavity. Compared with the smooth and regular spectral structure of a single soliton pulse, the comb corresponding to the uneven distribution of multiple soliton pulses exhibits a complex and irregular profile. When the stable intracavity field consists of a "roll" Turing pattern or N(N>1) evenly distributed soliton pulses separated by 2π/N, multi-FSR combs can be generated. In the case of the "roll" Turing pattern solution, it is found that third-order dispersion could modify the comb mode spacing and decrease the intensity of high-order comb modes. For the situation of multiple soliton pulse generation, the simulation results indicate that both the number and locations of the soliton pulses can be actively controlled through the careful selection of modulation frequency. In addition, for the selected cosine-modulated initial field profile, only those modes with the mode numbers being equal to an integer multiple of N can be greatly amplified by the parametric gain during propagation in the microresonator. This process eventually leads to the formation of a N-FSR frequency comb.

Generation of Kerr combs centered at 4.5 μm in crystalline microresonators pumped with quantum-cascade lasers.

We report on the generation of mid-infrared Kerr frequency combs in high-finesse CaF2 and MgF2 whispering-gallery-mode resonators pumped with continuous-wave room-temperature quantum cascade lasers. The combs were centered at 4.5 μm, the longest wavelength to date. A frequency comb wider than one half of an octave was demonstrated when approximately 20 mW of pump power was coupled to an MgF2 resonator characterized with quality factor exceeding 10(8).

Soliton breathing induced by stimulated Raman scattering and self-steepening in octave-spanning Kerr frequency comb generation.

We investigate the impact of stimulated Raman scattering (SRS) and self-steepening (SS) on breather soliton dynamics in octave-spanning Kerr frequency comb generation. SRS and SS can transform chaotic fluctuations in cavity solitons into periodic breathing. Furthermore, with SRS and SS considered, bandwidth of the soliton breathes more than two times stronger. The simultaneous presence of SRS and SS also make the soliton breathe slower and degrades the coherence of the soliton.

Normal‐dispersion microcombs enabled by controllable mode interactions

AbstractWe demonstrate a scheme incorporating dual‐coupled microresonators through which mode interactions are intentionally introduced and controlled for Kerr frequency comb (microcomb) generation in the normal‐dispersion region. Microcomb generation, repetition rate selection, and mode locking are achieved with coupled silicon nitride microrings controlled via an on‐chip microheater. The proposed scheme shows for the first time a reliable design strategy for normal‐dispersion microcombs and may make it possible to generate microcombs in an extended wavelength range (e.g. in the visible) where normal material dispersion is likely to dominate. image

Mode-pulling and phase-matching in broadband Kerr frequency comb generation

We present a quantitative analysis of Kerr effect induced cavity resonance pulling and phase-matching in broadband Kerr frequency comb generation based on the Lugiato–Lefever equation. Unevenly spaced cavity modes are pulled to be evenly spaced by the Kerr effect when cavity solitons are formed. Phase-matching in the cascaded four-wave mixing is achieved simultaneously, giving the cavity solitons strong stability. The number of modes that can be pulled into alignment in the cavity soliton regime depends on the pump condition and decreases exponentially with linearly increasing anomalous dispersion. However, in the chaotic modulation instability and breather soliton regimes, well-aligned cavity modes and phase-matching are not achieved. Compared to intracavity pulse dynamics, the mode-pulling effect and phase-matching are less sensitive to high-order dispersion as long as the cavity solitons stay stable.

Nonlinear conversion efficiency in Kerr frequency comb generation.

We analytically and numerically investigate the nonlinear conversion efficiency in ring microresonator-based mode-locked frequency combs under different dispersion conditions. Efficiency is defined as the ratio of the average round trip energy values for the generated pulse(s) to the input pump light. We find that the efficiency degrades with growth of the comb spectral width and is inversely proportional to the number of comb lines. It depends on the cold-cavity properties of a microresonator only and can be improved by increasing the coupling coefficient. Also, it can be increased in the multi-soliton state.

Investigation of mode coupling in normal-dispersion silicon nitride microresonators for Kerr frequency comb generation

Kerr frequency combs generated from microresonators are the subject of intense study. Most research employs microresonators with anomalous dispersion, for which modulation instability is believed to play a key role in initiation of the comb. Comb generation in normal dispersion microresonators has also been reported but is less well understood. Here we report a detailed investigation of few-moded, normal dispersion silicon nitride microresonators, showing that mode coupling can strongly modify the local dispersion, even changing its sign. We demonstrate a link between mode coupling and initiation of comb generation by showing experimentally, for the first time to our knowledge, pinning of one of the initial comb sidebands near a mode crossing frequency. Associated with this route to comb formation, we observe direct generation of coherent, bandwidth-limited pulses at repetition rates down to 75 GHz, without the need to first pass through a chaotic state.

Generation of Kerr frequency combs in a sapphire whispering gallery mode microresonator

We study theoretically and demonstrate experimentally generation of coherent optical frequency combs in a sapphire whispering gallery mode resonator. We verify phase locking of the comb harmonics by demodulating the comb on a fast photodiode and by observing the production of a spectrally pure radio frequency signal. Because of excellent optical and superior mechanical properties of the material, the sapphire resonator is an excellent candidate for the on-chip device integration of the comb oscillator.

Intra-Cavity Dispersion of Microresonators and its Engineering for Octave-Spanning Kerr Frequency Comb Generation

We present an analysis on intra-cavity dispersion of a micro-resonator. As an example, different dispersion sources of a silicon nitride microring resonator are identified and evaluated over a wide wavelength range. We also show the dispersion flattening technique based on a strip/slot hybrid waveguide structure can be used to tailor the intra-cavity dispersions. Octave-spanning Kerr frequency combs are numerically simulated using 2-D-FDTD. It is shown that 7.5-fs two-cycle cavity solitons can be generated, enabling ultrawide mode-locked Kerr combs, with improved comb spectral flatness.

Generation of a coherent near-infrared Kerr frequency comb in a monolithic microresonator with normal GVD.

We demonstrate experimentally, and describe theoretically, generation of a wide, fundamentally phase-locked Kerr frequency comb in a nonlinear resonator with a normal group velocity dispersion (GVD). A magnesium fluoride whispering-gallery mode resonator characterized with 10GHz free spectral range and pumped either at 780 or 795nm is used in the experiment. The envelope of the observed frequency comb differs significantly from the Kerr frequency comb spectra reported previously. We show via numerical simulation that, while the frequency comb does not correspond to generation of short optical pulses, the relative phase of the generated harmonics are fixed.

Analytical approach to the design of microring resonators for nonlinear four-wave mixing applications

An analytical approach for obtaining linear and nonlinear design parameters of microresonators is presented. The eigenmode/eigenfrequency problem of planar resonators is considered in detail, with an analytical closed-form approximation derived for resonators possessing a large radius to width ratio. The analysis permits the resonant frequencies and mode profiles to be determined together with the dispersion properties. The dependence of the effective nonlinear Kerr coefficient on the mode volume is further considered, and also the waveguide coupling together with estimates of the Q-value. Examples, which are in good agreement with numerical simulations, are presented for silicon resonators. The approach can be used for designing planar microring resonators for nonlinear four-wave mixing applications, such as optical Kerr frequency comb generation.

Nonlinear Group IV photonics based on silicon and germanium: from near-infrared to mid-infrared

AbstractGroup IV photonics hold great potential for nonlinear applications in the near- and mid-infrared (IR) wavelength ranges, exhibiting strong nonlinearities in bulk materials, high index contrast, CMOS compatibility, and cost-effectiveness. In this paper, we review our recent numerical work on various types of silicon and germanium waveguides for octave-spanning ultrafast nonlinear applications. We discuss the material properties of silicon, silicon nitride, silicon nano-crystals, silica, germanium, and chalcogenide glasses including arsenic sulfide and arsenic selenide to use them for waveguide core, cladding and slot layer. The waveguides are analyzed and improved for four spectrum ranges from visible, near-IR to mid-IR, with material dispersion given by Sellmeier equations and wavelength-dependent nonlinear Kerr index taken into account. Broadband dispersion engineering is emphasized as a critical approach to achieving on-chip octave-spanning nonlinear functions. These include octave-wide supercontinuum generation, ultrashort pulse compression to sub-cycle level, and mode-locked Kerr frequency comb generation based on few-cycle cavity solitons, which are potentially useful for next-generation optical communications, signal processing, imaging and sensing applications.

On the numerical simulation of Kerr frequency combs using coupled mode equations

It is demonstrated that Kerr frequency comb generation described by coupled mode equations can be numerically simulated using Fast Fourier Transform methods. This allows broadband frequency combs spanning a full octave to be efficiently simulated using standard algorithms, resulting in orders of magnitude improvements in the computation time.

Kerr parametric oscillations and frequency comb generation from dispersion compensated silica micro-bubble resonators

Silica micro-bubble resonators (MBRs) with cavity quality factor as high as Q = 5 × 10(7) are fabricated. The total dispersion of MBRs is analyzed. The thin-wall structure opens a new anomalous dispersion window and thus supports the dispersion compensation for hyper-parametric frequency conversion processes. Experimentally, Kerr parametric oscillation is observed in a 136 μm diameter MBR, frequency comb generation is also realized. Meanwhile the same nonlinear process is not allowed in solid silica spheres with size smaller than 150 μm.

Kerr frequency comb generation in overmoded resonators

We show that scattering-based interaction among nearly degenerate optical modes is the key factor in low threshold generation of Kerr frequency combs in nonlinear optical resonators with small group velocity dispersion (GVD). Mode interaction is capable of producing drastic changes in the local GVD, resulting in either a significant reduction, or an increase, in the oscillation threshold. Furthermore, we show that mode interaction is also responsible for majority of observed optical frequency combs in resonators characterized with large normal GVD. We present results of our numerical simulations together with supporting experimental data.

Hard and soft excitation regimes of Kerr frequency combs

We theoretically study the stability conditions and excitation regimes of hyperparametric oscillation and Kerr frequency comb generation in continuously pumped nonlinear optical microresonators possessing an anomalous group velocity dispersion. We show that both hard and soft excitation regimes are possible in the microresonators. Selection between the regimes is achieved via change in the parameters of the pumping light.