Noise and dynamics of stimulated-Brillouin-scattering microresonator lasers

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 laser's 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 laser's 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 laser's 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.

Figure 1

Schematic of setup for SBS generation via a microresonator oscillator. The cw laser pumps the microresonator to generate SBS oscillation in the reverse direction.

Figure 2

Illustration of forward, backward, and density wave translations due to pump detuning. $\mathrm{\Omega }={\mathrm{\Omega }}_b$ in this example. Note that although the shifts are in general different for each of the waves, the combined shift must satisfy ${\sigma }_F={\sigma }_B+{\sigma }_{\rho }$.

Figure 3

Illustration of a density wave amplitude and phase perturbation due to a single noise event.

Figure 4

Illustration of noise propagating into a perturbation of the total SBS wave.

Figure 5

Simulated SBS laser (a) normalized transmission past the cavity, (b) outcoupled power, (c) normalized intracavity forward wave power, and (d) gain phase as a function of pump detuning (in units of cavity linewidths). The simulations of (b), (c), and (d) correspond to a pump power of 1 mW.

Figure 6

SBS laser outcoupled power as a function of the total input power supplied into the cavity.

Figure 7

Simulated (blue solid line) and analytical (black dashed line) SBS laser (a) frequency noise and (b) RIN for a pump power of 1 mW and pump detuning of 0 Hz.

Figure 8

Simulated pump to SBS laser (a) frequency noise and (b) RIN transfer for a pump power of 1 mW and zero pump detuning.

Figure 9

Simulated (a) pump frequency noise to SBS RIN, (b) pump RIN to SBS frequency noise, (c) pump frequency noise to SBS frequency noise, and (d) pump RIN to SBS RIN transfer for a pump power of 2 mW, a pump detuning of $1/{\tau }_B$ (1 cavity linewidth), and a SBS gain detuning of ${\mathrm{\Gamma }}_b$ (one SBS gain linewidth).