We use theoretical analysis and numerical simulation to investigate the operation of a laser oscillating from gain supplied by stimulated Brillouin scattering (SBS) in a microresonator. The interaction of the forward, backward, and density waves with
in the microresonator results in a set of coupled-mode equations describing both the lasers phase and amplitude evolution over time. Using this coupled-mode formalism, we investigate the performance of the SBS laser under noise perturbation and identify the fundamental parameters and their optimization to enable low-noise SBS operation. The intrinsic laser linewidth, which is primarily limited by incoherent thermal occupation of the density wave, can be of order hertz or below. Our analysis also determines the SBS lasers relaxation oscillation, which results from the coupling between the optical and density waves, and appears as a resonance in both the phase and amplitude quadratures. We further explore contributions of the pump noise to the SBS lasers performance, which we find under most circumstances to increase the SBS laser noise beyond its fundamental limits. By tightly stabilizing the pump laser onto the microcavity resonance, the transfer of pump noise is significantly reduced. Our analysis is both supported and extended through numerical simulations of the SBS laser.
Optical-frequency combs enable measurement precision at the 20th digit, and accuracy entirely commensurate with their reference oscillator. A new direction in experiments is the creation of ultracompact frequency combs by way of nonlinear parametric
optics in microresonators. We refer to these as microcombs, and here we report a silicon-chip-based microcomb optical clock that phase-coherently converts an optical-frequency reference to a microwave signal. A low-noise comb spectrum with 25 THz span is generated with a 2 mm diameter silica disk and broadening in nonlinear fiber. This spectrum is stabilized to rubidium frequency references separated by 3.5 THz by controlling two teeth 108 modes apart. The optical clocks output is the electronically countable 33 GHz microcomb line spacing, which features an absolute stability better than the rubidium transitions by the expected factor of 108. Our work demonstrates the comprehensive set of tools needed for interfacing microcombs to state-of-the-art optical clocks.
Microresonator-based optical frequency combs have been a topic of extensive research during the last few years. Several theoretical models for the comb generation have been proposed; however, they do not comprehensively address experimental results t
hat show a variety of independent comb generation mechanisms. Here, we present frequency-domain experiments that illuminate the transition of microcombs into phase-locked states, which show characteristics of injection locking between ensembles of comb modes. In addition, we demonstrate the existence of equidistant optical frequency combs that are phase stable but with non-deterministic phase relationships between individual comb modes.
Optical whispering-gallery microresonators are useful tools in microphotonics, and nonlinear optics at very low threshold powers. Here, we present details about the fabrication of ultra-high-Q whispering-gallery-mode resonators made by CO2-laser lath
e machining of fused-quartz rods. The resonators can be fabricated in less than one minute and the obtained optical quality factors exceed Q = 10^9. Demonstrated resonator diameters are in the range between 170 {mu}m and 8 mm (free spectral ranges between 390 GHz and 8 GHz). Using these microresonators, a variety of optical nonlinearities are observed, including Raman scattering, Brillouin scattering and four-wave mixing.
We have investigated parametric seeding of a microresonator frequency comb (microcomb) by way of a pump laser with two electro-optic-modulation sidebands. We show that the pump-sideband spacing is precisely replicated throughout the microcombs optica
l spectrum, and we demonstrate a record absolute line-spacing stability for microcombs of $1.6times10^{-13}$ at 1 s. The spectrum of a parametric comb is complex, and often non-equidistant subcombs are observed. Our results demonstrate that parametric seeding can not only control the subcombs, but can lead to the generation of a strictly equidistant microcomb spectrum.
Optical frequency combs based on mode-locked lasers have proven to be invaluable tools for a wide range of applications in precision spectroscopy and metrology. A novel principle of optical frequency comb generation in whispering-gallery mode microre
sonators (microcombs) has been developed recently, which represents a promising route towards chip-level integration and out-of-the-lab use of these devices. Presently, two families of microcombs have been demonstrated: combs with electronically detectable mode spacing that can be directly stabilized, and broadband combs with up to octave-spanning spectra but mode spacings beyond electronic detection limits. However, it has not yet been possible to achieve these two key requirements simultaneously, as will be critical for most microcomb applications. Here we present a key step to overcome this problem by interleaving an electro-optic comb with the spectrum from a parametric microcomb. This allows, for the first time, direct control and stabilization of a microcomb spectrum with large mode spacing (>140 GHz) with no need for an additional mode-locked laser frequency comb. The attained residual 1-second-instability of the microcomb comb spacing is 10^-15, with a microwave reference limited absolute instability of 10^-12 at a 140 GHz mode spacing.
Robust control and stabilization of optical frequency combs enables an extraordinary range of scientific and technological applications, including frequency metrology at extreme levels of precision, novel spectroscopy of quantum gases and of molecule
s from visible wavelengths to the far infrared, searches for exoplanets, and photonic waveform synthesis. Here we report on the stabilization of a microresonator-based optical comb (microcomb) by way of mechanical actuation. This represents an important step in the development of microcomb technology, which offers a pathway toward fully-integrated comb systems. Residual fluctuations of our 32.6 GHz microcomb line spacing reach a record stability level of $5times10^{-15}$ for 1 s averaging, thereby highlighting the potential of microcombs to support modern optical frequency standards. Furthermore, measurements of the line spacing with respect to an independent frequency reference reveal the effective stabilization of different spectral slices of the comb with a $<$0.5 mHz variation among 140 comb lines spanning 4.5 THz. These experiments were performed with newly-developed microrod resonators, which were fabricated using a CO$_2$-laser-machining technique.
We report on the fabrication of high-Q, fused-quartz microresonators and the parametric generation of a frequency comb with 36 GHz line spacing using them. We have characterized the intrinsic stability of the comb in both the time and frequency domai
ns to assess its suitability for future precision metrology applications. Intensity autocorrelation measurements and line-by-line comb control reveal near-transform-limited picosecond pulse trains that are associated with good relative phase and amplitude stability of the comb lines. The combs 36 GHz line spacing can be readily photodetected, which enables measurements of its intrinsic and absolute phase fluctuations.
