Noise dynamics in large mode volume Brillouin lasers

TL;DR

This work develops a coupled-mode theory for large mode volume Brillouin lasers in which many cavity resonances reside within a broad Brillouin gain bandwidth. By modeling pump-cavity-phonon interactions with a multimode Hamiltonian and performing phonon adiabatic elimination, the authors derive steady-state, spontaneous-scattering, and noise properties, showing that the mode with the highest gain lases while others remain off, and that frequency pulling and linewidth modifications arise from phase mismatch across multiple phonon modes. The analysis reveals distinctive noise signatures in the RIN and frequency noise spectra at high offsets, and demonstrates how transferred pump RIN can degrade linewidth in non-ideal phase-matching scenarios, while also offering a potential tool for phonon spectroscopy and effective high-Q mode engineering. Overall, the model provides a comprehensive framework to optimize LMV Brillouin lasers for watt-level output and sub-mHz linewidths, with practical implications for precision sensing and communications.

Abstract

Photonic integrated Brillouin lasers have emerged as an important tool to realize a wide range of precision applications, including atomic time-keeping, low-noise microwave signal generation, fiber and quantum sensing, and ultra-high capacity coherent communications. While Brillouin lasers routinely achieve sub-Hz instantaneous linewidths, many of these applications also require exceptional frequency stability and high-power single-mode emission. A recent demonstration showed that extending the resonator length increases the laser power while also improving the frequency stability through suppression of thermorefractive noise. However, as the resonator scales to larger lengths, multiple optical resonances can be found within the Brillouin gain bandwidth, greatly complicating the laser dynamics compared to existing coupled-mode Brillouin laser models. Given the potential to scale lasers of this type to watt-level output powers at sub-mHz linewidths, a theoretical model describing this physics is needed to provide key insights into their performance. Here, we develop a coupled-mode theory of integrated large mode volume Brillouin lasers, accounting for multiple cavity modes with potential to lase within the gain bandwidth. We obtain expressions for the steady-state dynamics, spontaneous spectrum, relative intensity noise, and frequency noise. Our analysis reveals that the broad gain bandwidth results in atypical Brillouin dynamics, giving rise to distinct features in the noise spectra, and consequently modifications of the standard, single-mode fundamental linewidth of Brillouin lasers. Additionally, these features may be used for a variety of tangential applications, such as phonon spectroscopy or quality factor enhancement. Furthermore, we find that the linewidth can be significantly impacted by transferred RIN from the external pump in Brillouin lasers that lack ideal phase matching.

Figures (4)

• Figure 1: (a) Illustration of large mode volume Brillouin laser dynamics, where the pump mode $a_p$, is coupled (denoted by the sum and mixer symbol) to multiple cavity modes $a_j$, with each $a_p\rightarrow a_j$ coupling mediated by a distinct set of phonon modes $b_{jk}$. (b) Brillouin gain spectrum for a given cavity mode $j$. (c) Contrasting cascaded control in standard Brillouin lasers (top) vs. a large mode volume Brillouin laser (bottom), where removal of the lasing mode from the supported cavity modes will not cancel cascading.
• Figure 2: (a) Spontaneous power spectrum below threshold with increasing input power from gray to orange. The gain spectrum shape is shown as the dotted line, with no relation to the y-axis. (b) Frequency pulling of each mode from cavity resonance vs. increasing input power. The vertical, dashed gray line represents $P^P_{th}$, where the frequency drift clamps with the pump. Inset: zoomed in power spectrum of the $j=0$ mode as power increases, where frequency pulling is contrasted with the cavity resonance, given by the gray vertical line.
• Figure 3: Theoretical RIN for the large mode volume Brillouin laser (solid red line) vs. a single mode laser involving overlap between one phonon and one cavity mode (dashed) with 314 mW of input power ($P_{th}^{S1}$). The vertical gray lines represent $\Delta\Omega_{lk}$'s, highlighting the source of additional noise at high-offset frequencies. Inset: Increasing input power from blue to red. Solid lines represent no transferred RIN, (i.e., $S_{ext}^{\rm RIN}=0$) and dotted lines show the inclusion of constant white noise, where $S_{ext}^{\rm RIN}=-140$ dBc/Hz.
• Figure 4: (a) Theoretical frequency noise spectrum for a large mode volume Brillouin laser (solid red line) vs. a single mode laser involving overlap between one phonon and one cavity mode (dashed) with an input power of 314 mW ($P_{th}^{S1}$). Inset: increasing input power from blue to red, and $S_{ext}^{\rm RIN}=0$ (solid) and $-140$ dBc/Hz (dotted). (b) Plotting $S_\Delta[\omega]$ and the second term of Eq. \ref{['eq:freqnoise']} separated for $S_{ext}^{\rm RIN}=0$ (solid) and $-140$ dBc/Hz (dashed). Inset: Effect of $0\rightarrow-140$ dBc/Hz (solid $\rightarrow$ dashed) transferred external RIN on linewidth in the low-frequency limit (i.e., contents in the brackets of Eq. \ref{['eq:STLW']}). The vertical line represents $P_{th}^{\rm S1}$.