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We frequency stabilize the output of a miniature stimulated Brillouin scattering (SBS) laser to rubidium atoms in a microfabricated cell to realize a laser system with frequency stability at the $10^{-11}$ level over seven decades in averaging time. In addition, our system has the advantages of robustness, low cost and the potential for integration that would lead to still further miniaturization. The SBS laser operating at 1560 nm exhibits a spectral linewidth of 820 Hz, but its frequency drifts over a few MHz on the 1 hour timescale. By locking the second harmonic of the SBS laser to the Rb reference, we reduce this drift by a factor of $10^3$ to the level of a few kHz over the course of an hour. For our combined SBS and Rb laser system, we measure a frequency noise of $4times10^4$ $Hz^2/Hz$ at 10 Hz offset frequency which rapidly rolls off to a level of 0.2 $Hz^2/Hz$ at 100 kHz offset. The corresponding Allan deviation is $leq2times10^{-11}$ for averaging times spanning $10^{-4}$ to $10^3$ s. By optically dividing the signal of the laser down to microwave frequencies, we generate an RF signal at 2 GHz with phase noise at the level of -76 dBc/Hz and -140 dBc/Hz at offset frequencies of 10 Hz and 10 kHz, respectively.
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Self-injection locking is a dynamic phenomenon representing stabilization of the emission frequency of an oscillator with a passive cavity enabling frequency filtered coherent feedback to the oscillator cavity. For instance, self-injection locking of a semiconductor laser to a high-quality-factor (high-Q) whispering gallery mode (WGM) microresonator can result in multiple orders of magnitude reduction of the laser linewidth. The phenomenon was broadly studied in experiments, but its detailed theoretical model allowing improving the stabilization performance does not exist. In this paper we develop such a theory. We introduce five parameters identifying efficiency of the self-injection locking in an experiment, comprising back-scattering efficiency, phase delay between the laser and the high-Q cavities, frequency detuning between the laser and the high-Q cavities, the pump coupling efficiency, the optical path length between the laser and the microresonator. Our calculations show that the laser linewidth can be improved by two orders of magnitude compared with the case of not optimal self-injection locking. We present recommendations on the experimental realization of the optimal self-injection locking regime. The theoretical model provides deeper understanding of the self-injection locking and benefits multiple practical applications of self-injection locked oscillators.
Brillouin laser oscillators offer powerful and flexible dynamics as the basis for mode-locked lasers, microwave oscillators, and optical gyroscopes in a variety of optical systems. However, Brillouin interactions are exceedingly weak in conventional silicon photonic waveguides, stifling progress towards silicon-based Brillouin lasers. The recent advent of hybrid photonic-phononic waveguides has revealed Brillouin interactions to be one of the strongest and most tailorable nonlinearities in silicon. Here, we harness these engineered nonlinearities to demonstrate Brillouin lasing in silicon. Moreover, we show that this silicon-based Brillouin laser enters an intriguing regime of dynamics, in which optical self-oscillation produces phonon linewidth narrowing. Our results provide a platform to develop a range of applications for monolithic integration within silicon photonic circuits.
We demonstrate control and stabilization of an optical frequency comb generated by four-wave mixing in a monolithic microresonator with a mode spacing in the microwave regime (86 GHz). The comb parameters (mode spacing and offset frequency) are controlled via the power and the frequency of the pump laser, which constitutes one of the comb modes. Furthermore, generation of a microwave beat note at the combs mode spacing frequency is presented, enabling direct stabilization to a microwave frequency standard.
Over the last decade, optical atomic clocks have surpassed their microwave counterparts and now offer the ability to measure time with an increase in precision of two orders of magnitude or more. This performance increase is compelling not only for enabling new science, such as geodetic measurements of the earth, searches for dark matter, and investigations into possible long-term variations of fundamental physics constants but also for revolutionizing existing technology, such as the global positioning system (GPS). A significant remaining challenge is to transition these optical clocks to non-laboratory environments, which requires the ruggedization and miniaturization of the atomic reference and clock laser along with their supporting lasers and electronics. Here, using a compact stimulated Brillouin scattering (SBS) laser to interrogate a $^8$$^8$Sr$^+$ ion, we demonstrate a promising component of a portable optical atomic clock architecture. In order to bring the stability of the SBS laser to a level suitable for clock operation, we utilize a self-referencing technique to compensate for temperature drift of the laser to within $170$ nK. Our SBS optical clock achieves a short-term stability of $3.9 times 10^{-14}$ at $1$ s---an order of magnitude improvement over state-of-the-art microwave clocks. Based on this technology, a future GPS employing portable SBS clocks offers the potential for distance measurements with a 100-fold increase in resolution.
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 within 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.
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