Discrete Cavity Dynamics in Free-Space Brillouin Laser

Abstract

Highly coherent lasers are central to modern photonics. To date, high-coherence operation has been achieved predominantly in microcavity and fiber-based platforms. More recently, free-space Brillouin-laser experiments have revealed unusually strong noise suppression whose physical origin cannot be explained by conventional continuous-medium models developed for those platforms. In conventional continuous-medium models, the optical and acoustic fields are assumed to remain continuously coupled throughout the cavity evolution, whereas in free-space implementations the coupling is confined to the nonlinear medium and interrupted by passive propagation over the rest of the round trip. To describe this interaction-propagation separation, we develop a discrete-cavity model in which the short Brillouin interaction inside the gain medium and the subsequent free-space propagation are treated as two separate stages of the round-trip evolution. This separation introduces a temporal asymmetry between optical storage and acoustic relaxation, which effectively enhances acoustic damping at the cavity level and strongly reduces pump-noise transfer to the Stokes field. If the cavity round-trip time is much longer than the interaction time in the nonlinear medium, the noise-suppression ratio scales with the ratio of the total cavity length to the nonlinear-medium length. Our discrete-cavity model further provides quantitative predictions for the lasing threshold, output power, phase-noise transfer, and fundamental linewidth, in good agreement with experiment. These results identify the discrete interaction-propagation structure as the physical origin of the unusually strong noise suppression in free-space Brillouin lasers systems.

Figures (5)

• Figure 1: Comparison of the conventional continuous-medium scheme and the free-space Brillouin laser configuration. (a) Microresonator Brillouin laser with continuous opto-acoustic interaction in a co-localized nonlinear medium. (b) Free-space Brillouin laser with localized interaction in the gain crystal and passive propagation over the remainder of the cavity round trip.
• Figure 2: Steady-state output Stokes power as a function of input pump power. The solid curve represents the analytical steady-state solution of Eq. (\ref{['ss:Stokes_intensity']}), while circles denote numerical solutions of the discrete cavity map. The threshold is $P_{\mathrm{th}}\approx 12~\mathrm{W}$, above which the Stokes power increases linearly due to pump clamping. At an input pump power of $45~\mathrm{W}$, the Stokes output power reaches approximately $17~\mathrm{W}$.
• Figure 3: (a) Simulated phase evolution versus round-trip index.The blue curve represents the pump phase, while the red curve denotes the Stokes phase. (b) Frequency-noise spectra from numerical simulation. Pump noise (blue), Stokes noise (red), and analytical prediction (black dashed).
• Figure 4: Simulated fundamental frequency-noise spectrum of the Stokes field (red). The black dashed curve shows the theoretical prediction.
• Figure 5: Relative intensity noise (RIN) spectrum of the Stokes field. The red solid line denotes the simulated Stokes RIN, while the black dashed line indicates the theoretical prediction.