Chaotic dynamics of frequency combs generated with continuously pumped nonlinear microresonators.

We theoretically and experimentally investigate the chaotic regime of optical frequency combs generated in nonlinear ring microresonators pumped with continuous wave light. We show that the chaotic regime reveals itself by a flat top symmetric envelope of the frequency spectrum, when observed by means of an optical spectrum analyzer. The comb, demodulated on a fast photodiode, produces a noisy radio frequency signal with spectral width significantly exceeding the linear bandwidth of the microresonator mode. We discuss practical ways of excitation of a coherent frequency comb and avoiding the chaotic regime.

Whispering gallery mode diamond resonator.

We demonstrate a nearly spherical diamond whispering gallery mode resonator with quality factor (Q factor) Q=2.4×10(7) limited by material loss approaching α=4×10(-3) cm(-1). The Q factor does not depend on the wavelength: it is approximately the same at 1319 and 1550 nm. Resonators with this range of Q (<10 MHz at 1550 nm wavelength) are attractive for laser locking and stabilization. Applications such as stable compact optical comb generators as well as Raman optical frequency shifters will be feasible with further improvement of the material.

Stabilization of a Kerr frequency comb oscillator.

We study stability and spectral purity of a microresonator-based Kerr frequency comb oscillator experimentally and observe a correlation between the frequency of the continuous wave laser pumping the nonlinear resonator and the repetition frequency of the comb. This correlation is used in a proof-of-principle demonstration of a Kerr frequency comb stabilized with an optical transition of 87Rb.

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.

Normal group-velocity dispersion Kerr frequency comb.

We show via numerical simulation that Kerr frequency combs can be generated in a nonlinear resonator characterized with normal group-velocity dispersion. We find the spectral shape of the comb and temporal envelope of the corresponding optical pulses formed in the resonator.

On excitation of breather solitons in an optical microresonator.

We theoretically investigate mode-locked regimes of optical-frequency combs generated in a nonlinear ring microresonator pumped with continuous-wave light. We find that breather solitons can be formed in the resonator for certain values of frequency and power of the pump. We argue that relatively slow modulation of the comb-frequency harmonics observed in several recent experiments can be attributed to soliton formation.

Generation of near-infrared frequency combs from a MgF2 whispering gallery mode resonator.

We report on generation of a 20 nm wide, 35 GHz repetition rate optical frequency comb in a magnesium fluoride whispering gallery mode resonator pumped with 2 mW of 1543 nm light. The high efficiency of comb generation is associated with the small anomalous group velocity dispersion of the resonator. Growth dynamics of the comb is studied and compared with earlier theoretical predictions.

Optical-RF frequency stability transformer.

An optical technique based on stability transfer among modes of a monolithic optical microresonator is proposed for long term frequency stabilization of a radio frequency (RF) oscillator. We show that locking the frequency difference of two microresonator modes with dissimilar sensitivity to an applied forcing function to a master RF oscillator improves the long term stability of a slave RF oscillator locked to the frequency difference of another pair of modes with nearly identical sensitivity to the same forcing function. For instance, the stability of a 10 MHz master oscillator with Allan deviation of 10(-7) at 10(3) s can be improved and transferred to a slave oscillator with identical free running stability performance, so that the resultant Allan deviation of the slave oscillator becomes equal to 10(-13) at 10(3) s. The suggested method does not require absolute frequency references.

Surface acoustic wave opto-mechanical oscillator and frequency comb generator.

We report on realization of an efficient triply resonant coupling between two long lived optical modes and a high frequency surface acoustic wave (SAW) mode of the same monolithic crystalline whispering gallery mode resonator. The coupling results in an opto-mechanical oscillation and generation of a monochromatic SAW. A strong nonlinear interaction of this mechanical mode with other equidistant SAW modes leads to mechanical hyperparametric oscillation and generation of a SAW pulse train and associated frequency comb in the resonator. We visualized the comb by observing the modulation of the light escaping the resonator.

Mode-locked Kerr frequency combs.

We analyze a mode-locked regime in Kerr frequency combs generated in nonlinear microresonators. Using damped driven nonlinear Schrödinger equations we show that the combs can produce subpicosecond optical pulses when the resonators are characterized with a small enough anomalous group velocity dispersion. We provide an analytical solution of the problem for the case of small damping.

Second-order optical filter based on a mirrored gradient index lens.

We demonstrate a second-order bandpass filter using a single gradient index lens (GRIN) coated with mirrors. The filter becomes possible because of the residual and externally introduced small birefringence of the GRIN lens material. We show that the filter function can be trimmed by mechanical strain of the lens. Applications of the filter in microwave photonics are discussed.

Whispering-gallery-mode-resonator-based ultranarrow linewidth external-cavity semiconductor laser.

We demonstrate a miniature self-injection locked distributed-feedback laser using resonant optical feedback from a high-Q crystalline whispering-gallery-mode resonator. The linewidth reduction factor is greater than 10,000, with resultant instantaneous linewidth of less than 200 Hz. The minimal value of the Allan deviation for the laser-frequency stability is 3 x 10(-12) at the integration time of 20 micros. The laser possesses excellent spectral purity and good long-term stability.

Voltage-controlled photonic oscillator.

We report the development and demonstration of an X-band voltage-controlled photonic oscillator based on a whispering gallery mode resonator made of an electro-optic crystalline material. The oscillator has good spectral purity and wide, agile, linear tunability. We have modified the existing theoretical model of the opto-electronic oscillator to describe the performance of our tunable oscillator and have found a good agreement between the theoretical predictions and the measurement results. We show that the device is promising for higher-frequency applications where high-performance tunable oscillators with wide tunability do not exist.

Passively mode-locked Raman laser.

We report on the observation of a mode-locked laser generated with a crystalline whispering gallery mode resonator pumped with a continuous wave laser. Optical pumping of the resonator generates an optical frequency comb with phase locked components at the Raman offset of the resonator host material. Phase locking of the modes is confirmed via measurement of the radio-frequency beat note produced by the comb on a fast photodiode. Neither the conventional Kerr comb nor hyperparametric oscillation is observed when the comb is present. We present a theoretical explanation of the effect.

Collective emission and absorption in a linear resonator chain.

We show that a linear chain of circular macroscopic resonators coupled in parallel demonstrates the phenomena of "superabsorption" and superradiance. Both the frequency spectrum of the transmitted light through the resonator chain and the decay rate of the resonator chain being prepared in a proper initial state are proportional to the number of resonators in the chain, N, and the intensity of the emitted radiation grows as N(2). The spectral bandwidth, the growth of the decay rate, and the intensity are restricted by the dispersion of the waveguides connecting the resonators.

Optomechanics with surface-acoustic-wave whispering-gallery modes.

A surface-acoustic wave (SAW) creates its own high-Q ultrasmall-volume whispering-gallery mode (WGM), different from the usual bulk acoustic WGMs, in an optical dielectric WGM resonator. We show that it is possible to realize an externally controllable, efficient triply resonant optomechanical interaction between two optical WGMs and the SAW WGM and to use such an interaction in various sensor applications.

Ultralow noise miniature external cavity semiconductor laser.

Advanced applications in optical metrology demand improved lasers with high spectral purity, in form factors that are small and insensitive to environmental perturbations. While laboratory-scale lasers with extraordinarily high stability and low noise have been reported, all-integrated chip-scale devices with sub-100 Hz linewidth have not been previously demonstrated. Lasers integrated with optical microresonators as external cavities have the potential for substantial reduction of noise. However, stability and spectral purity improvements of these lasers have only been validated with rack-mounted support equipment, assembled with fibre lasers to marginally improve their noise performance. In this work we report on a realization of a heterogeneously integrated, chip-scale semiconductor laser featuring 30-Hz integral linewidth as well as sub-Hz instantaneous linewidth.

High spectral purity Kerr frequency comb radio frequency photonic oscillator.

Femtosecond laser-based generation of radio frequency signals has produced astonishing improvements in achievable spectral purity, one of the basic features characterizing the performance of an radio frequency oscillator. Kerr frequency combs hold promise for transforming these lab-scale oscillators to chip-scale level. In this work we demonstrate a miniature 10 GHz radio frequency photonic oscillator characterized with phase noise better than -60 dBc Hz(-1) at 10 Hz, -90 dBc Hz(-1) at 100 Hz and -170 dBc Hz(-1) at 10 MHz. The frequency stability of this device, as represented by Allan deviation measurements, is at the level of 10(-10) at 1-100 s integration time-orders of magnitude better than existing radio frequency photonic devices of similar size, weight and power consumption.

Efficient upconversion of subterahertz radiation in a high-Q whispering gallery resonator.

We demonstrate efficient upconversion of subterahertz radiation into the optical domain in a high-Q whispering gallery mode resonator with quadratic optical nonlinearity. The 5x10(-3) power conversion efficiency of a cw 100 GHz signal is achieved with only 16 mW of optical pump.

Tunable optical single-sideband modulator with complete sideband suppression.

We report on the development of a new class of widely tunable resonant single-sideband electro-optical modulators based on interaction of different mode families of a crystalline whispering gallery mode resonator with an externally applied rf field. The tunability comes from the different response of mode families to either the temperature change or the voltage applied to the resonator.