Stabilization of a Kerr frequency comb oscillator

Parametric interaction of laser cavity-solitons with an external CW pump

We study the interaction of a laser cavity-soliton microcomb with an externally coupled, co-propagating tunable CW pump, observing parametric Kerr interactions which lead to the formation of both a cross-phase modulation and a four-wave mixing replica of the laser cavity-soliton. We compare and explain the dependence of the microcomb spectra from both the cavity-soliton and pump parameters, demonstrating the ability to adjust the microcomb externally without breaking or interfering with the soliton state. The parametric nature of the process agrees with numerical simulations. The parametric extended state maintains the typical robustness of laser-cavity solitons.

Dynamics of cavity soliton driven by chirped optical pulses in Kerr resonators

Recent researches have demonstrated that pulsed driving is an effective method to increase the temporal overlap between cavity soliton (CS) and pump field, thereby increasing the pump-to-comb conversion efficiency. The amplitude-modulated inhomogeneity of the background wave causes the solitons to drift toward edges of the driving pulse. To eliminate the multiple temporal trapping positions, induced by the spontaneous symmetry breaking, we propose the chirped pulse driving for deterministic single soliton generation. We theoretically explain the physical mechanism of the chirp pulse driving, as the combination of amplitude and phase modulation. Our numerical simulations demonstrate the chirp is responsible for the single soliton generation. A detailed investigation for dynamics of CSs sustained by chirped pulses, shows the recovery of spontaneous symmetry breaking. In addition, the desynchronized chirped pulse driving is also considered here. Considering a weak chirp parameter, the desynchronization-dependent trapping position diagram is divided into multiple areas including two CSs, a single CS, two oscillating CSs, and no CS. With a sufficient chirp parameter considered, the trapping position curve becomes a monotonous function of the desynchronized drift velocity, which indicates deterministic single soliton generation.

Efficient Kerr soliton comb generation in micro-resonator with interferometric back-coupling

Nonlinear Kerr micro-resonators have enabled fundamental breakthroughs in the understanding of dissipative solitons, as well as in their application to optical frequency comb generation. However, the conversion efficiency of the pump power into a soliton frequency comb typically remains below a few percent. We fabricate and characterize a hybrid Mach-Zehnder ring resonator geometry, consisting of a micro-ring resonator embedded in an additional cavity with twice the optical path length of the ring. The resulting interferometric back coupling enables to achieve an unprecedented control of the pump depletion: pump-to-frequency comb conversion efficiencies of up to 55% of the input pump power is experimentally demonstrated with a soliton crystal comb. We assess the robustness of the proposed on-chip geometry by generating a large variety of dissipative Kerr soliton combs, which require a lower amount of pump power to be accessed, when compared with an isolated micro-ring resonator with identical parameters. Micro-resonators with feedback enable accessing new regimes of coherent soliton comb generation, and are well suited for comb applications in astronomy, spectroscopy and telecommunications.

Increasing the conversion efficiency of soliton crystals will enable further application of optical frequency comb. Here the authors engineer an hybrid Mach-Zehnder micro-ring resonator to achieve 80% pump-to-comb conversion efficiency based on dissipative Kerr solitons.

Probing 10 μK stability and residual drifts in the cross-polarized dual-mode stabilization of single-crystal ultrahigh-Q optical resonators

The thermal stability of monolithic optical microresonators is essential for many mesoscopic photonic applications such as ultrastable laser oscillators, photonic microwave clocks, and precision navigation and sensing. Their fundamental performance is largely bounded by thermal instability. Sensitive thermal monitoring can be achieved by utilizing cross-polarized dual-mode beat frequency metrology, determined by the polarization-dependent thermorefractivity of a single-crystal microresonator, wherein the heterodyne radio-frequency beat pins down the optical mode volume temperature for precision stabilization. Here, we investigate the correlation between the dual-mode beat frequency and the resonator temperature with time and the associated spectral noise of the dual-mode beat frequency in a single-crystal ultrahigh-Q MgF₂ resonator to illustrate that dual-mode frequency metrology can potentially be utilized for resonator temperature stabilization reaching the fundamental thermal noise limit in a realistic system. We show a resonator long-term temperature stability of 8.53 μK after stabilization and unveil various sources that hinder the stability from reaching sub-μK in the current system, an important step towards compact precision navigation, sensing, and frequency reference architectures.

Microresonator-based high-resolution gas spectroscopy

We report the first demonstration of a microresonator-based tunable mode-locked frequency comb source. We achieve a mode-hop-free tuning range of 16 GHz by simultaneously tuning both the pump laser and the cavity resonance while keeping the system in a multi-soliton mode-locked state. The optical spectrum spans 2520-4125  cm^-1 (2.425-3.970 μm) pumping at 3508  cm^-1 (2.850 μm) in a silicon microresonator with a comb line spacing of 4.23  cm^-1 (127 GHz). Our scanning technique can be used to increase the effective resolution of the microresonator-based comb spectroscopy. As a proof-of-principle demonstration, we record the absorption spectrum of the rovibrational transitions of the υ₃ and υ₂+(υ₄+υ₅)+0 bands of acetylene. We measure absorption features as narrow as 0.21  cm^-1 (6.4 GHz) full width at half-maximum at a frequency sampling step of 80 MHz.

Self-locking of the frequency comb repetition rate in microring resonators with higher order dispersions

We predict that the free spectral range (FSR) of the soliton combs in microring resonators can self-lock through the back-action of the Cherenkov dispersive radiation on its parent soliton under the conditions typical for recent experiments on the generation of the octave wide combs. The comb FSR in the self-locked state remains quasi-constant over sufficiently broad intervals of the pump frequencies, implying that this effect can be potentially used as the comb self-stabilisation technique. The intervals of self-locking form a sequence of the discrete plateaus reminiscent to other staircase-like structures known in the oscillator synchronisation research. We derive a version of the Adler equation for the self-locking regime and confirm that it is favoured by the strong overlap between the soliton and the dispersive radiation parts of the comb signal.

Soliton trapping and comb self-referencing in a single microresonator with χ(2) and χ(3) nonlinearities

A shaped doublet pump pulse is proposed for a simultaneous octave-spanning soliton Kerr frequency comb generation and second-harmonic conversion in a single microresonator. The temporal soliton in the cavity is trapped atop a doublet-pulse pedestal, resulting in a greatly expanded soliton region compared to that with a general Gaussian pulse pump. The possibility of single-microresonator comb self-referencing in a single silicon nitride microring that can facilitate compact on-chip optical clocks is demonstrated via simulation.

Optimization of primary Kerr optical frequency combs for tunable microwave generation

We analyze the condition under which Kerr combs generate the highest microwave output power after photodetection. These optimal comb states correspond to configurations in which the sidemode-to-pump ratio is the highest possible. For the case of primary combs, we show how the interplay between the power and frequency of the pump laser critically influences this ratio, which has a direct influence on the phase noise performance of the generated microwaves. We also experimentally demonstrate primary combs with a sidemode-to-pump ratio as high as -2  dB, thereby leading to efficient energy conversion from the lightwave to the microwave frequency range.

Chasing the thermodynamical noise limit in whispering-gallery-mode resonators for ultrastable laser frequency stabilization

Ultrastable high-spectral-purity lasers have served as the cornerstone behind optical atomic clocks, quantum measurements, precision optical microwave generation, high-resolution optical spectroscopy, and sensing. Hertz-level lasers stabilized to high-finesse Fabry-Pérot cavities are typically used for these studies, which are large and fragile and remain laboratory instruments. There is a clear demand for rugged miniaturized lasers with stabilities comparable to those of bulk lasers. Over the past decade, ultrahigh-Q optical whispering-gallery-mode resonators have served as a platform for low-noise microlasers but have not yet reached the stabilities defined by their fundamental noise. Here, we show the noise characteristics of whispering-gallery-mode resonators and demonstrate a resonator-stabilized laser at this limit by compensating the intrinsic thermal expansion, allowing a sub-25 Hz linewidth and a 32 Hz Allan deviation. We also reveal the environmental sensitivities of the resonator at the thermodynamical noise limit and long-term frequency drifts governed by random-walk-noise statistics.

High-quality optical resonators have the potential to provide a miniaturized frequency reference for metrology and sensing but they often lack stability. Here, Lim et al. experimentally characterize the stability of whispering-gallery resonators at their fundamental noise limits.

Transverse mode interaction via stimulated Raman scattering comb in a silica microcavity

Comb generation in different mode families via a stimulated Raman scattering (SRS) process is studied using a silica toroid microcavity. The broad gain bandwidth of SRS in silica allows us to excite longitudinal modes at long wavelengths belonging to mode families that are either the same as or different from the pump mode. We found through experiment and numerical analysis, that an SRS comb in a different mode family with a high quality factor (Q) is excited when we pump in a low-Q mode. No transverse mode interaction occurs when we excite in a high-Q mode resulting the generation of a single comb family. We studied the condition of the transverse mode interaction while varying the mode overlap and Q of the Raman mode. Our experimental results are in good agreement with the analysis and this enables us to control the generation of one- and two-mode combs.

Towards chip-scale optical frequency synthesis based on optical heterodyne phase-locked loop

An integrated heterodyne optical phase-locked loop was designed and demonstrated with an indium phosphide based photonic integrated circuit and commercial off-the-shelf electronic components. As an input reference, a stable microresonator-based optical frequency comb with a 50-dB span of 25 nm (~3 THz) around 1550 nm, having a spacing of ~26 GHz, was used. A widely-tunable on-chip sampled-grating distributed-Bragg-reflector laser is offset locked across multiple comb lines. An arbitrary frequency synthesis between the comb lines is demonstrated by tuning the RF offset source, and better than 100Hz tuning resolution with ± 5 Hz accuracy is obtained. Frequency switching of the on-chip laser to a point more than two dozen comb lines away (~5.6 nm) and simultaneous locking to the corresponding nearest comb line is also achieved in a time ~200 ns. A low residual phase noise of the optical phase-locking system is successfully achieved, as experimentally verified by the value of -80 dBc/Hz at an offset of as low as 200 Hz.

On the phase noise performance of microwave and millimeter-wave signals generated with versatile Kerr optical frequency combs

We investigate the phase noise performance of micro- and millimeter-wave signals generated using a ultra-high Q whispering gallery mode disk-resonator with Kerr nonlinearity. Our study focuses on the stability of the optical spectra and on the performances of the corresponding microwave and millimeter-wave beat notes in terms of power and phase noise. The blue slope of an optical mode of the resonator, allowing for the generation of optical frequency combs, is accurately explored in order to identify various comb patterns. Each of these patterns is characterized in the optical and radio-frequency domains. Phase noise levels below -100 dBc/Hz at 10 kHz offset have been achieved for beat notes in the radio-frequency spectrum at 12 GHz, 18 GHz, 24 GHz, 30 GHz, and 36 GHz with the same resonator.

Stabilized chip-scale Kerr frequency comb via a high-Q reference photonic microresonator

We stabilize a chip-scale Si₃N₄ phase-locked Kerr frequency comb via locking the pump laser to an independent stable high-Q reference microresonator and locking the comb spacing to an external microwave oscillator. In this comb, the pump laser shift induces negligible impact on the comb spacing change. This scheme is a step toward miniaturization of the stabilized Kerr comb system as the microresonator reference can potentially be integrated on-chip. Fractional instability of the optical harmonics of the stabilized comb is limited by the microwave oscillator used for a comb spacing lock below 1 s averaging time and coincides with the pump laser drift in the long term.

Chip Scale Atomic Resonator Frequency Stabilization System With Ultra-Low Power Consumption for Optoelectronic Oscillators

We present a long-term chip scale stabilization scheme for optoelectronic oscillators (OEOs) based on a rubidium coherent population trapping (CPT) atomic resonator. By locking a single mode of an OEO to the (85)Rb 3.035-GHz CPT resonance utilizing an improved phase-locked loop (PLL) with a PID regulator, we achieved a chip scale frequency stabilization system for the OEO. The fractional frequency stability of the stabilized OEO by overlapping Allan deviation reaches 6.2 ×10(-11) (1 s) and  ∼ 1.45 ×10 (-11) (1000 s). This scheme avoids a decrease in the extra phase noise performance induced by the electronic connection between the OEO and the microwave reference in common injection locking schemes. The total physical package of the stabilization system is [Formula: see text] and the total power consumption is 400 mW, which provides a chip scale and portable frequency stabilization approach with ultra-low power consumption for OEOs.

A broadband chip-scale optical frequency synthesizer at 2.7 × 10(-16) relative uncertainty

Optical frequency combs-coherent light sources that connect optical frequencies with microwave oscillations-have become the enabling tool for precision spectroscopy, optical clockwork, and attosecond physics over the past decades. Current benchmark systems are self-referenced femtosecond mode-locked lasers, but Kerr nonlinear dynamics in high-Q solid-state microresonators has recently demonstrated promising features as alternative platforms. The advance not only fosters studies of chip-scale frequency metrology but also extends the realm of optical frequency combs. We report the full stabilization of chip-scale optical frequency combs. The microcomb's two degrees of freedom, one of the comb lines and the native 18-GHz comb spacing, are simultaneously phase-locked to known optical and microwave references. Active comb spacing stabilization improves long-term stability by six orders of magnitude, reaching a record instrument-limited residual instability of [Formula: see text]. Comparing 46 nitride frequency comb lines with a fiber laser frequency comb, we demonstrate the unprecedented microcomb tooth-to-tooth relative frequency uncertainty down to 50 mHz and 2.7 × 10(-16), heralding novel solid-state applications in precision spectroscopy, coherent communications, and astronomical spectrography.

Dual-pumped degenerate Kerr oscillator in a silicon nitride microresonator

We demonstrate a degenerate parametric oscillator in a silicon nitride microresonator. We use two frequency-detuned pump waves to perform parametric four-wave mixing and operate in the normal group-velocity dispersion regime to produce signal and idler fields that are frequency degenerate. Our theoretical modeling shows that this regime enables generation of bimodal phase states, analogous to the χ(2)-based degenerate OPO. Our system offers potential for realization of CMOS-chip-based coherent optical computing and an all-optical quantum random number generator.

All-optical stabilization of a soliton frequency comb in a crystalline microresonator

We demonstrate the all-optical stabilization of a low-noise temporal soliton based microresonator based optical frequency comb in a crystalline resonator via a new technique to control the repetition rate. This is accomplished by thermally heating the microresonator with an additional probe laser coupled to an auxiliary optical resonator mode. The carrier-envelope offset frequency is controlled by stabilizing the pump laser frequency to a reference optical frequency comb. We analyze the stabilization by performing an out-of-loop comparison and measure the overlapping Allan deviation. This all-optical stabilization technique can prove useful as an actuator for self-referenced microresonator frequency combs.

Extended ultrahigh-Q-cavity diode laser

We report on a study of a 698 nm extended cavity semiconductor laser with intracavity narrowband optical feedback from a whispering gallery mode resonator. This laser comprises an ultrahigh-Q (>10(10)) resonator supporting stimulated Rayleigh scattering, a diffraction grating wavelength preselector, and a reflective semiconductor amplifier. Single longitudinal mode lasing is characterized with sub-kilohertz linewidth and a 9 nm coarse tuning range. The laser has a potential application for integration with the 1S0-3P0 strontium transition to create compact precision atomic clocks.

On the dispersion management of fluorite whispering-gallery mode resonators for Kerr optical frequency comb generation in the telecom and mid-infrared range

Optical whispering gallery mode (WGM) resonators have been very attracting platforms for versatile Kerr frequency comb generations. We report a systematic study on the material dispersion of various optical materials that are capable of supporting quality factors above 10⁹. Using an analytical approximation of WGM resonant frequencies in disk resonators, we investigate the effect of the geometry and transverse mode order on the total group-velocity dispersion (GVD). We demonstrate that the major radii and the radial mode indices play an important role in tailoring the GVD of WGM resonators. In particular, our study shows that in WGM disk-resonators, the polar families of modes have very similar GVD, while the radial families of modes feature dispersion values that can differ by up to several orders of magnitude. The effect of these giant dispersion shifts are experimentally evidenced in Kerr comb generation with magnesium fluoride. From a more general perspective, this critical feature enables to push the zero-dispersion wavelength of fluorite crystals towards the mid-infrared (mid-IR) range, thereby allowing for efficient Kerr comb generation in that spectral range. We show that barium fluoride is the most interesting crystal in this regard, due to its zero dispersion wavelength (ZDW) at 1.93 μm and an optimal dispersion profile in the mid-IR regime. We expect our results to facilitate the design of different platforms for Kerr frequency comb generations in both telecommunication and mid-IR spectral ranges.

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 10 GHz free spectral range and pumped either at 780 or 795 nm 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.

High-coherence mid-infrared frequency comb

We report on the generation of a frequency comb around 4330 nm with an unprecedented coherence of the single teeth. Generating the comb within a Ti:sapphire laser cavity by a difference-frequency process and using a phase-lock scheme based on direct digital synthesis, we achieve a tooth linewidth of 2.0 kHz in a 1-s timescale (750 Hz in 20 ms). The generated per-tooth power of 1 μW ranks this comb among the best ever realized in the mid-infrared in terms of power spectral density.