Monolithic optical resonator for ultrastable laser and photonic millimeter-wave synthesis.

Optical resonators are indispensable tools in optical metrology that usually benefit from an evacuated and highly-isolated environment to achieve peak performance. Even in the more sophisticated design of Fabry-Perot (FP) cavities, the material choice limits the achievable quality factors. For this reason, monolithic resonators are emerging as promising alternative to traditional designs, but their design is still at preliminary stage and far from being optimized. Here, we demonstrate a monolithic FP resonator with 4.5 cm3 volume and 2 × 105 finesse. In the ambient environment, we achieve 18 Hz integrated laser linewidth and 7 × 10-14 frequency stability measured from 0.08 s to 0.3 s averaging time, the highest spectral purity and stability demonstrated to date in the context of monolithic reference resonators. By locking two separate lasers to distinct modes of the same resonator, a 96 GHz microwave signals is generated with phase noise -100 dBc/Hz at 10 kHz frequency offset, achieving orders of magnitude improvement in the approach of photonic heterodyne synthesis. The compact monolithic FP resonator is promising for applications in spectrally-pure, high-frequency microwave photonic references as well as optical clocks and other metrological devices. ©2024. All rights reserved.

Photonic chip-based low-noise microwave oscillator.

Numerous modern technologies are reliant on the low-phase noise and exquisite timing stability of microwave signals. Substantial progress has been made in the field of microwave photonics, whereby low-noise microwave signals are generated by the down-conversion of ultrastable optical references using a frequency comb1-3. Such systems, however, are constructed with bulk or fibre optics and are difficult to further reduce in size and power consumption. In this work we address this challenge by leveraging advances in integrated photonics to demonstrate low-noise microwave generation via two-point optical frequency division4,5. Narrow-linewidth self-injection-locked integrated lasers6,7 are stabilized to a miniature Fabry-Pérot cavity8, and the frequency gap between the lasers is divided with an efficient dark soliton frequency comb9. The stabilized output of the microcomb is photodetected to produce a microwave signal at 20 GHz with phase noise of -96 dBc Hz-1 at 100 Hz offset frequency that decreases to -135 dBc Hz-1 at 10 kHz offset-values that are unprecedented for an integrated photonic system. All photonic components can be heterogeneously integrated on a single chip, providing a significant advance for the application of photonics to high-precision navigation, communication and timing systems.

Robust self-injection locking to a non-confocal monolithic Fabry-Perot cavity.

We demonstrate an efficient simultaneous self-injection locking of two semiconductor lasers to high-order modes of a standalone monolithic non-confocal Fabry-Perot cavity. The lasers are used to generate a low-noise microwave signal on a fast photodiode. The overall improvement of the laser spectral purity exceeds 80 dB. The observed single-sideband phase noise of X- to W-band signals is at the -110 dBc/Hz level and is limited by the fundamental thermorefractive noise of the cavity. The demonstrated cavity-laser configuration can be tightly packaged and is promising for the generation of high-frequency RF signals as well as for referencing optical frequency combs.

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.

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.

W-Band Photonic Receiver for Compact Cloud Radars.

We introduce an RF-photonics receiver concept enabling the next generation of ultra-compact millimeter wave radars suitable for cloud and precipitation profiling, planetary boundary layer observations, altimetry and surface scattering measurements. The RF-photonics receiver architecture offers some compelling advantages over traditional electronic implementations, including a reduced number of components and interfaces, leading to reduced size, weight and power (SWaP), as well as lower system noise, leading to improved sensitivity. Low instrument SWaP with increased sensitivity makes this approach particularly attractive for compact space-borne radars. We study the photonic receiver front-end both analytically and numerically and predict the feasibility of the greater than unity photonic gain and lower than ambient effective noise temperature of the device. The receiver design is optimized for W-band (94 GHz) radars, which are generally assessed to be the primary means for observing clouds in the free troposphere as well as planetary boundary layer from space.

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.

Stabilized photonic links for space applications.

We describe basic principles of operation and report on implementation of a standalone photonic link stabilized using the electronic phase conjugation technique. This method has been demonstrated to improve link stability by more than 2 orders while reducing its size and power consumption compared to other systems. We have demonstrated packaged robust links that achieve a relative frequency instability of 2×10-17 (5×10-17) at 10 h averaging while the temperature of the fiber was varied with 2°C (15°C) magnitude.

Application of a self-injection locked cyan laser for Barium ion cooling and spectroscopy.

Compact, high power lasers with narrow linewidth are important tools for the manipulation of quantum systems. We demonstrate a compact, self-injection locked, Fabry-Perot semiconductor laser diode with high output power at 493 nm. A high quality factor magnesium fluoride whispering gallery mode resonator enables both high passive stability and 1 kHz instantaneous linewidth. We use this laser for laser-cooling, in-situ isotope purifcation, and probing barium atomic ions confined in a radio-frequency ion trap. The results here demonstrate the suitability of these lasers in trapped ion quantum information processing and for probing weak coherent optical transitions.

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.

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.

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.

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.

Orthogonally polarized frequency comb generation from a Kerr comb via cross-phase modulation.

We experimentally demonstrate that a single microresonator can emit two orthogonally polarized individually coherent combs: (i) a strong polarized soliton comb and (ii) an orthogonally polarized continuous wave seeded weaker comb, generated from the first one via cross-phase modulation, sharing the repetition rate of the soliton comb. Experimental results show that the power of the transverse electric-polarized seed can be well below the threshold of comb generation (e.g., 0.1 mW). In addition, simulations show that a dark pulse could be generated in the anomalous dispersion regime by a bright soliton when the two orthogonally polarized modes have the same group velocity in the microresonator.

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.

On Sagnac frequency splitting in a solid-state ring Raman laser.

We report on an accurate measurement of the frequency splitting of an optical rotating ring microcavity made out of calcium fluoride. By measuring the frequencies of the clockwise and counter-clockwise coherent Raman emissions confined in the cavity modes, we show that the frequency splitting is inversely proportional to the refractive index of the cavity host material. The measurement has an accuracy of 1% and unambiguously confirms the classical theoretical prediction based on special theory of relativity. This Letter also demonstrates the usefulness of the ring Raman microlaser for rotation measurements.

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.

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.