Low threshold Kerr solitons.

Pumping a nonlinear optical cavity with continuous wave coherent light can result in generation of a stable train of short optical pulses. Pumping the cavity with a non-degenerate resonant coherent dichromatic pump usually does not produce a stable mode-locked regime due to competition of the oscillations at the pump frequencies. We show that generation of stable optical pulses is feasible in a dichromatically pumped cavity characterized with group velocity dispersion optimized in a way that the group velocity value becomes identical for the generated pulses and the beat note of the pump harmonics. The power threshold of the process drops nearly four times in this case and the produced pulses become sub-harmonically locked to the dichromatic pump harmonics. The process is useful for generation of broadband optical frequency combs and optical time crystals.

Coupler-induced phase matching of resonant hyperparametric scattering.

We show that an evanescent field coupler can break the symmetry of a high quality factor monolithic ring microcavity, enabling generation of strongly nondegenerate frequency harmonics involving a few mode families that are orthogonal in an unperturbed microcavity. Using this property, we explain observed experimental generation of frequency combs in magnesium fluoride whispering gallery mode resonators characterized with strong normal group velocity dispersion.

Quartic dissipative solitons in optical Kerr cavities.

Solitons, ubiquitous in nonlinear sciences, are wavepackets which maintain their characteristic shape upon propagation. In optics, they have been observed and extensively studied in optical fibers. The spontaneous generation of a dissipative Kerr soliton (DKS) train in an optical microresonator pumped with continuous wave (CW) coherent light has placed solitons at the heart of optical frequency comb research in recent years. The commonly observed soliton has a "sech"-shaped envelope resulting from resonator cubic nonlinearity balanced by its quadratic anomalous group velocity dispersion (GVD). Here we exploit the Lagrangian variational method to show that CW pumping of a Kerr resonator featuring quartic GVD forms a pure quartic soliton (PQS) with Gaussian envelope. We find analytical expressions for pulse parameters in terms of experimentally relevant quantities and derive an area theorem. Analytical predictions are validated with extensive numerical simulations and apply also to fiber-based and spatial Kerr resonators. Broader bandwidth with flatter spectral envelope of a PQS, compared to a DKS of the same pulse width and peak power, make it superior for applications requiring small frequency comb line-to-line power variation.

Self-injection locking efficiency of a UV Fabry-Perot laser diode.

In this Letter, we have studied the performance of a gallium nitride 370 nm Fabry-Perot laser diode self-injection locked via a high quality (Q-) factor magnesium fluoride whispering gallery mode (WGM) resonator and show that the state of locking strongly depends on frequency detuning between the internal laser cavity and the resonator modes. Optimizing the detuning, we were able to observe monochromatic laser emission with a sub-100 kHz linewidth. The Q-factor of the resonator measured in this regime exceeded 109.

On acceleration sensitivity of 2 µm whispering gallery mode-based semiconductor self-injection locked laser.

While whispering gallery mode resonators are well known for their low acceleration sensitivity, there has not been much published experimental research on the subject. We performed environmental sensitivity tests of a 2 µm semiconductor distributed feedback (DFB) laser, self-injection locked to a high-Q crystalline whispering gallery mode resonator. Measured acceleration sensitivity of the laser is below 5×10-11 g-1 in the 1-200 Hz frequency bandwidth and thermal sensitivity does not exceed 12 MHz/°C. The laser's frequency noise is below 50 Hz/Hz1/2 at 10 Hz, reaching 0.4 Hz/Hz1/2 at 400 kHz. The instantaneous linewidth of the laser is improved by nearly 4 orders of magnitude compared to the free-running DFB laser and is measured to be 50 Hz at 0.1 ms measurement time. The Allan deviation of the laser frequency is on the order of 10-9 from 1 to 1000 s. All these features make the laser attractive for metrology applications involving low-noise 2 µm seed lasers.

Bose-Hubbard hopping due to resonant Rayleigh scattering.

We show theoretically that dynamic behavior of light confined in the modes of a nonlinear optical ring cavity characterized by resonant Rayleigh scattering can be described using the Bose-Hubbard model. Nonlinear interaction between clockwise and counterclockwise optical modes results in instability and intermode hopping occurring at a rate defined by the frequency separation of the Rayleigh doublet harmonics. Hopping may lead to an instability and breathing behavior of a Kerr frequency comb observed in the cavity.

Microresonator-stabilized extended-cavity diode laser for supercavity frequency stabilization.

We demonstrate a simple, compact, and cost-effective laser noise reduction method for stabilizing an extended-cavity diode laser to a 3×105 finesse mirror Fabry-Perot (F-P) cavity, corresponding to a resonance linewidth of 10 kHz, by using a crystalline MgF2 whispering gallery mode microresonator. The laser linewidth is reduced to sub-kilohertz such that a stable Pound-Drever-Hall error signal is built up. The wavelength of the pre-stabilized laser is tunable within a large bandwidth covering the high-reflection mirror coating of an F-P supercavity.

Optical Cherenkov radiation in overmoded microresonators.

We show that an optical analog of Cherenkov radiation (dispersive wave) is observable in a nonlinear microring resonator generating Kerr frequency comb and containing linearly interacting families of equidistant modes. The radiation results from disruptions in the frequency dependent group velocity dispersion of the pumped cavity modes and is emitted into different mode families of the resonator. This effect reveals itself as a dispersive shaped structure in the spectral envelope of the frequency comb. We found that the dips in the comb spectrum correspond to peaks of the emission of the power in the other mode families of the resonator. The spectrum of the combs that includes both mode families does not have any dips, but peaks and resembles the Cherenkov radiation spectra frequently observed in Kerr comb systems. This Letter shows that a correct description of the Kerr comb in presence of mode anti-crossings should take into account not only the pumped mode family with modified dispersion parameter, but also the modes of the interacting families.

Clustered frequency comb.

We show theoretically that it is feasible to generate a spectrally broad Kerr frequency comb consisting of several spectral clusters phase matched due to interplay among second- and higher-order group velocity dispersion contributions. We validate the theoretical analysis experimentally by driving a magnesium fluoride resonator, characterized with 110 GHz free spectral range, with a continuous wave light at 1.55 µm and observing two comb clusters separated by nearly two-thirds of an octave.

Microresonator stabilized 2 µm distributed-feedback GaSb-based diode laser.

We report on the stabilization of a high-power distributed feedback (DFB) semiconductor laser operating at 2.05 µm wavelength, using a crystalline whispering gallery mode microresonator. The laser's frequency noise is measured to be below 100 Hz/Hz1/2 at Fourier frequencies ranging from 10 Hz to 1 MHz. The instantaneous linewidth of the laser is improved by four orders of magnitude compared with the free-running DFB laser, and is measured to be 15 Hz at 0.1 ms measurement time. The integral linewidth approaches 100 Hz. The stabilized DFB laser is integrated with a polarization maintaining output fiber and an integrated optical isolator.

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.

Trapping light into high orbital momentum modes of fiber tapers.

A tapered cylindrical dielectric optical waveguide acts as a high quality factor white-light cavity providing high field concentration as well as long optical group delay. It is possible to optimize shape of a lossless taper to suppress reflection of the input light and to achieve infinitely high field concentration. These tapers can be used in sensing and optoelectronics applications instead of conventional microcavities.

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.

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).

Compact stabilized semiconductor laser for frequency metrology.

We report on the development of a frequency modulatable 795 nm semiconductor laser based on self-injection locking to a high-quality-factor whispering-gallery-mode microresonator. The laser is characterized by residual amplitude modulation below -80 dB and frequency noise better than 300 Hz/Hz(1/2) at offset frequencies ranging from 100 Hz to 10 MHz. The frequency modulation speed and span of the laser exceed 1 MHz and 4 GHz, respectively. Locking of the laser to the Doppler-free saturated absorption resonance of the (87)Rb D1 line is demonstrated and relative frequency stability better than 10(-12) is measured for integration time spanning from 1 s to 1 day. The architecture demonstrated in this study is suitable for the realization of frequency modulatable lasers at any wavelength.

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.

On timing jitter of mode locked Kerr frequency combs.

We study fundamental timing jitter in repetition rate of a mode locked Kerr frequency comb generated in an externally pumped nonlinear ring resonator. We show that the increase in the integrated power of the comb harmonics, and the corresponding decrease of the duration of the associated pulse, results in the increase of low frequency noise, and a decrease in high frequency noise.

Application of kernel principal component analysis for optical vector atomic magnetometry.

Vector atomic magnetometers that incorporate electromagnetically induced transparency (EIT) allow for precision measurements of magnetic fields that are sensitive to the directionality of the observed field by virtue of fundamental physics. However, a practical methodology of accurately recovering the longitudinal angle of the local field through observations of EIT spectra has not been established. In this work, we address this problem of angle determination with an unsupervised machine learning algorithm utilizing nonlinear dimensionality reduction. The proposed algorithm was developed to interface with spectroscopic measurements from an EIT-based atomic rubidium magnetometer and uses kernel principal component analysis (KPCA) as an unsupervised feature extraction tool. The resulting KPCA features allow each EIT spectrum measurement to be represented by a single coordinate in a new reduced dimensional feature space, thereby streamlining the process of angle determination. A supervised support vector regression (SVR) machine was implemented to model the resulting relationship between the KPCA projections and field direction. If the magnetometer is configured so that the azimuthal angle of the field is defined with a polarization lock, the KPCA-SVR algorithm is capable of predicting the longitudinal angle of the local magnetic field within 1 degree of accuracy and the magnitude of the absolute field with a resolution of 70 nT. The combined scalar and angular sensitivity of this method make the KPCA-enabled EIT magnetometer competitive with conventional vector magnetometry methods.

All-optical dissipative discrete time crystals.

Time crystals are periodic states exhibiting spontaneous symmetry breaking in either time-independent or periodically-driven quantum many-body systems. Spontaneous modification of discrete time-translation symmetry in periodically-forced physical systems can create a discrete time crystal (DTC) constituting a state of matter possessing properties like temporal rigid long-range order and coherence, which are inherently desirable for quantum computing and information processing. Despite their appeal, experimental demonstrations of DTCs are scarce and significant aspects of their behavior remain unexplored. Here, we report the experimental observation and theoretical investigation of DTCs in a Kerr-nonlinear optical microcavity. Empowered by the self-injection locking of two independent lasers with arbitrarily large frequency separation simultaneously to two same-family cavity modes and a dissipative Kerr soliton, this versatile platform enables realizing long-awaited phenomena such as defect-carrying DTCs and phase transitions. Combined with monolithic microfabrication, this room-temperature system paves the way for chip-scale time crystals supporting real-world applications outside sophisticated laboratories.

A low-noise photonic heterodyne synthesizer and its application to millimeter-wave radar.

Microwave photonics offers transformative capabilities for ultra-wideband electronic signal processing and frequency synthesis with record-low phase noise levels. Despite the intrinsic bandwidth of optical systems operating at ~200 THz carrier frequencies, many schemes for high-performance photonics-based microwave generation lack broadband tunability, and experience tradeoffs between noise level, complexity, and frequency. An alternative approach uses direct frequency down-mixing of two tunable semiconductor lasers on a fast photodiode. This form of optical heterodyning is frequency-agile, but experimental realizations have been hindered by the relatively high noise of free-running lasers. Here, we demonstrate a heterodyne synthesizer based on ultralow-noise self-injection-locked lasers, enabling highly-coherent, photonics-based microwave and millimeter-wave generation. Continuously-tunable operation is realized from 1-104 GHz, with constant phase noise of -109 dBc/Hz at 100 kHz offset from carrier. To explore its practical utility, we leverage this photonic source as the local oscillator within a 95-GHz frequency-modulated continuous wave (FMCW) radar. Through field testing, we observe dramatic reduction in phase-noise-related Doppler and ranging artifacts as compared to the radar's existing electronic synthesizer. These results establish strong potential for coherent heterodyne millimeter-wave generation, opening the door to a variety of future applications including high-dynamic range remote sensing, wideband wireless communications, and THz spectroscopy.