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The remarkable frequency stability of resonant systems in the optical domain (optical cavities and atomic transitions) can be harnessed at frequency scales accessible by electronics using optical frequency division. This capability is revolutionizing technologies spanning time keeping to high-performance electrical signal sources. A version of the technique called 2-point optical frequency division (2P-OFD) is proving advantageous for application to high-performance signal sources. In 2P-OFD, an optical cavity anchors two spectral endpoints defined by lines of a frequency comb. The comb need not be self-referenced, which greatly simplifies the system architecture and reduces power requirements. Here, a 2P-OFD microwave signal source is demonstrated with record-low phase noise using a microcomb. Key to this advance is a spectral endpoint defined by a frequency agile single-mode dispersive wave that is emitted by the microcomb soliton. Moreover, the system frequency reference is a compact all-solid-state optical cavity with a record Q-factor. The results advance integrable microcomb-based signal sources into the performance realm of much larger microwave sources.

Normal group velocity dispersion (GVD) microcombs offer high comb line power and high pumping efficiency compared to bright pulse microcombs. The recent demonstration of normal GVD microcombs using CMOS-foundry-produced microresonators is an important step towards scalable production. However, the chromatic dispersion of CMOS devices is large and impairs generation of broadband microcombs. Here, we report the development of a microresonator in which GVD is reduced due to a couple-ring resonator configuration. Operating in the turnkey self-injection-locking mode, the resonator is hybridly integrated with a semiconductor laser pump to produce high-power-efficiency combs spanning a bandwidth of 9.9 nm (1.22 THz) centered at 1560 nm, corresponding to 62 comb lines. Fast, linear optical sampling of the comb waveform is used to observe the rich set of near-zero GVD comb behaviors, including soliton molecules, switching waves (platicons) and their hybrids. Tuning of the 20 GHz repetition rate by electrical actuation enables servo locking to a microwave reference, which simultaneously stabilizes the comb repetition rate, offset frequency and temporal waveform. This hybridly integrated system could be used in coherent communications or for ultra-stable microwave signal generation by two-point optical frequency division., Comment: 8 pages, 4 figures

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-P\'erot mirror cavities are typically used for these studies but are large and fragile such that they have remained laboratory instruments. There is a clear demand in rugged miniaturized lasers operating potentially at comparable stabilities to those bulk lasers. Over the past decade, ultrahigh-Q optical whispering-gallery-mode (WGM) resonators have served as a platform for low-noise microlasers but have not yet reached the ultimate stabilities defined by their fundamental noise. Here, we show the noise characteristics of WGM resonators and demonstrate a resonator-stabilized laser at the fundamental limit by compensating the intrinsic thermal expansion of a WGM resonator, allowing a sub-25 Hz linewidth and a 32 Hz Allan deviation on the 191 THz carrier in 100 ms integration. 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.

We report on the generation of mid-infrared Kerr frequency combs in high-finesse CaF$_2$ and MgF$_2$ whispering-gallery mode resonators pumped with continuous wave room temperature quantum cascade lasers. The combs were centered at 4.5$\mu$m, the longest wavelength to date. A frequency comb wider than a half of an octave was demonstrated when approximately 20mW of pump power was coupled to an MgF2 resonator characterized with quality factor exceeding 10$^8$., Comment: 5 pages, 5 figures

We demonstrate experimentally, and explain theoretically, generation of a wide, fundamentally phase locked Kerr frequency comb in a nonlinear resonator with a normal group velocity dispersion. A magnesium fluoride whispering gallery resonator characterized with 10 GHz free spectral range and pumped either at 780 nm 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 phases of the generated harmonics are fixed., Comment: 5 pages, 5 figures, to appear in Optics Letters

An optical technique based on stability transfer among modes of a monolithic optical microresonator is proposed for long therm frequency stabilization of a radiofrequency (RF) oscillator. We show that locking two resonator modes, characterized with dissimilar sensitivity in responding to an applied forcing function, to a master RF oscillator allows enhancing the long term stability of a slave RF oscillator locked to two resonator modes having nearly identical sensitivity. For instance, the stability of a 10 MHz master oscillator characterized with Allan deviation of 10^-7 at 10^4s can be increased and transferred to a slave oscillator with identical stability performance, so that the resultant Allan deviation of the slave oscillator becomes equal to 10-13 at 10^4s. The method does not require absolute frequency references to achieve such a performance., Comment: 3 pages, 1 figure, to appear in Optics Letters

We theoretically study the stability conditions and excitation regimes of hyper-parametric oscillation and Kerr frequency comb generation in continuously pumped nonlinear optical resonators possessing anomalous group velocity dispersion. We show that both hard and soft excitation regimes are possible in the resonators. Selection between the regimes is achieved via change in the parameters of the pumping light., Comment: 4 pages, 7 figures

Temporal growth of an optical Kerr frequency comb generated in a microresonator is studied both experimentally and numerically. We find that the comb emerges from vacuum fluctuations of the electromagnetic field on timescales significantly exceeding the ringdown time of the resonator modes. The frequency harmonics of the comb spread starting from the optically pumped mode if the microresonator is characterized with anomalous group velocity dispersion. The harmonics have different growth rates resulting from sequential four-wave mixing process that explains intrinsic modelocking of the comb., Comment: 4 pages, 5 figures

We propose theoretically and demonstrate experimentally a coherent microwave photonic receiver operating at 35 GHz carrier frequency. The device is based on a lithium niobate or lithium tantalate optical whispering gallery mode resonator coupled to a microwave strip line resonator. Microwave local oscillator is fed into the microwave resonator along with the microwave signal. We show that the sensitivity of this receiver significantly exceeds the sensitivity of the incoherent quadratic receiver based on the same technology. The coherent receiver can possess a dynamic range in excess of 100 dB in 5 MHz band if a low noise laser is utilized.

We report on the experimental demonstration of a tunable monolithic optical frequency comb generator. The device is based on the four-wave mixing in a crystalline calcium fluoride whispering gallery mode resonator. The frequency spacing of the comb is given by an integer number of the free spectral range of the resonator. We select the desired number by tuning the pumping laser frequency with respect to the corresponding resonator mode. We also observe interacting optical combs and high-frequency hyperparametric oscillation, depending on the experimental conditions. A potential application of the comb for generating narrowband frequency microwave signals is demonstrated.

We have tuned the whispering gallery modes of a fused silica micro- resonator over nearly 1 nm at 800 nm, i.e.over half of a free spectral range or the equivalent of 10^6 linewidths of the resonator.This has been achieved by a new method based on the stretching of a two-stem microsphere.The devices described below will permit new Cavity-QED experiments with this ultra high .nesse optical resonator when it is desirable to optimise its coupling to emitters with given transition frequencies. The tuning capability demonstrated is compatible with both UHV and low temperature operation which should be useful for future experiments with laser cooled atoms or single quantum dots.A general overview of the current state of the art in microspheres is given as well as a more general introduction., Comment: ReVTeX, 16 pages, 9 color figures

We have demonstrated a 165 micron oblate spheroidal microcavity with free spectral range 383.7 GHz (3.06nm), resonance bandwidth 25 MHz (Q ~ 10^7) at 1550nm, and finesse F > 10^4. The highly oblate spheroidal dielectric microcavity combines very high Q-factor, typical of microspheres, with vastly reduced number of excited whispering-gallery (WG) modes (by two orders of magnitude). The very large free spectral range in the novel microcavity - few hundred instead of few GigaHertz in typical microspheres - is desirable for applications in spectral analysis, narrow-linewidth optical and RF oscillators, and cavity QED., Comment: 11 pages, 3 figures

We have tuned the whispering gallery modes of a fused silica microresonator over nearly 1 nm at 800 nm, i.e. over 0.5 FSR or 10^6 linewidths of the resonator. This has been achieved by a new method based on the stretching of a two-stem microsphere. The devices described below will permit new Cavity-QED experiments with this high-Q optical resonator when it is desirable to optimize its coupling to emitters with given transition frequencies. The tuning capability demonstrated here is compatible with both UHV and low temperature operation, which should be useful for future experiments with laser cooled atoms or single quantum dots., Comment: ReVTeX, 4 pages, 3 figures

A general model is presented for coupling of high-$Q$ whispering-gallery modes in optical microsphere resonators with coupler devices possessing discrete and continuous spectrum of propagating modes. By contrast to conventional high-Q optical cavities, in microspheres independence of high intrinsic quality-factor and controllable parameters of coupling via evanescent field offer variety of regimes earlier available in RF devices. The theory is applied to the earlier-reported data on different types of couplers to microsphere resonators and complemented by experimental demonstration of enhanced coupling efficiency (about 80%) and variable loading regimes with Q>10^8 fused silica microspheres., Comment: 14 pages, 4 figures

Techniques and devices that stabilize optical resonators.