Spontaneous Brillouin Scattering in a Few-Mode Optical Fiber

TL;DR

The paper investigates spontaneous Brillouin scattering in a two-mode optical fiber (LP$_{01}$ and LP$_{11}$), resolving forward and backward scattering for intra- and inter-modal interactions using heterodyne detection. It derives and tests dispersion-based phase matching, Brillouin shifts, and gain coefficients, including a calibrated Brillouin gain $G_B$ and linewidths for multiple acoustic modes, with backward scattering dominated by longitudinal core-guided modes ($L_{lm}$) and forward scattering by torsional-radial modes ($TR_{lm}$). The authors observe Stokes and anti-Stokes components without external acoustic drive, report maximum backward gains up to $G_B \approx 160$ W$^{-1}$ km$^{-1}$ and forward gains up to $G_B \approx 2.0$ W$^{-1}$ km$^{-1}$, and demonstrate excellent agreement with theory across intra- and inter-modal configurations. The results provide calibrated benchmarks for Brillouin interactions in few-mode fibers and enable insights for phonon-based quantum applications and mode-selective optomechanics, including potential OAM-based acoustic quantum memories.

Abstract

We report a comprehensive experimental study of spontaneous Brillouin scattering in a few-mode optical fiber, resolving both forward and backward scattering processes for intra- and inter-modal interactions. Using heterodyne detection, Stokes and anti-Stokes components without external acoustic excitation are observed and quantitatively extracted Brillouin shifts, linewidths, and gain coefficients. Forward scattering is mediated by guided torsional-radial acoustic modes with frequencies ranging from MHz to GHz, while backward scattering involves longitudinal core-guided modes at frequencies of tens of GHz. These results provide calibrated benchmarks for Brillouin interactions in few-mode fibers, offering insights relevant to phonon-based quantum applications and mode-selective optomechanics.

Figures (5)

• Figure 1: Optical and acoustic dispersion relations for various Brillouin scattering configurations. (a) Forward scattering within a single optical mode (intra-modal scattering). An initial optical state (green) with frequency $\omega_0$ and wavenumber $k_0$ is scattered to generate an anti-Stokes signal (blue) and a Stokes signal (magenta). (b) Forward scattering involving two optical modes with refractive indices $n_1$ and $n_2$. (c) Backward scattering within a single optical mode, where a large momentum transfer is required, in contrast to forward scattering. (d) Backward scattering between two optical modes with refractive indices $n_1$ and $n_2$. (e) Acoustic dispersion relation for a bulk acoustic mode. (f) Acoustic dispersion relations in an optical fiber, showing multiple guided acoustic branches.
• Figure 2: (a) Schematic illustration of the optical fiber used in the experiment. A pump beam is launched into a few-mode fiber. (b) Optical modes supported in the fiber core, namely the $LP_{01}$ and $LP_{11}$ modes. (c) Dominant acoustic mode in forward Brillouin scattering, corresponding to a torsional–radial mode $TR_{lm}$ with a large transversal wavevector $q_r, q_\theta \gg q_z$. (d) Dominant acoustic mode in backward Brillouin scattering, corresponding to a longitudinal mode $L_{lm}$ with a large axial wavevector $q_z \gg q_r, q_\theta$.
• Figure 3: (a) Experimental setup for measuring backward Brillouin scattering. The laser beam is split into two paths. (Top) One path is used to generate the local oscillator (LO) with a frequency shift introduced by an acousto-optic modulator (AOM) and an electro-optic modulator (EOM). A filter cavity removes unwanted sideband signals, followed by polarization control and optical amplification. (Bottom) The other path is shaped by a spatial light modulator (SLM) to generate the desired spatial profile of the pump beam. The backward-scattered light is separated using a non-polarizing beam splitter (NPBS) and coupled into a single-mode fiber to suppress non-$LP_{01}$ components. The spatially filtered signal is then mixed with the LO beam. The resulting heterodyne signal is detected by a photodetector and analyzed using a spectrum analyzer. (b) Experimental setup for detecting intra-modal forward Brillouin scattering. Polarization-controlling waveplates and a polarizing beam splitter (PBS) are used to suppress the pump beam and extract only the orthogonally polarized component of the scattered light. This signal is subsequently coupled into a single-mode fiber (SMF) for heterodyne detection. (c) Experimental setup for detecting inter-modal forward Brillouin scattering. A Laguerre--Gaussian beam is used to excite the $LP_{11}$ mode in an SMF-28 fiber. The scattered signal is collected via free-space coupling and filtered by a single-mode fiber to isolate the $LP_{01}$ component.
• Figure 4: Backward scattering spectra obtained from heterodyne measurements. (a) Intra-modal scattering spectrum ($LP_{01}\rightarrow LP_{01}$). Three Stokes resonances corresponding to distinct acoustic modes, $L_{01}$, $L_{02}$, and $L_{03}$, are observed around $\Omega/2\pi \approx 16$ GHz. The reference level of the vertical axis (0.0 dB) is set to the electrical noise floor. (b) Inter-modal scattering spectrum ($LP_{11}\rightarrow LP_{01}$). Three resonances associated with acoustic modes of azimuthal order $l=1$, namely $L_{11}$, $L_{12}$, and $L_{13}$, are observed. Slight shifts in the resonance frequencies originate from differences in the acoustic phase velocities. In both spectra, weaker anti-Stokes (AS) signals are also observed, as indicated in the figure.
• Figure 5: Forward scattering spectra for (a-d) intra-modal and (e-h) inter-modal scattering. For both scattering processes [see (a) and (e)], nearly identical series of resonances for Stokes and anti-Stokes processes are observed, ranging from a few MHz to a GHz. (b) and (f) show a comparison of the Brillouin gain calculated from data (solid line) and from calculation (dots) for shear acoustic waves. The orange shade shows the variation of the calculated gain. (c) and (g) show the gain comparison described above for the longitudinal acoustic waves. The blue shaded area shows the calculated gain. (d) and (h) show the variation of the Brillouin linewidth $\Gamma$ for shear (red triangle) and longitudinal (blue circle) acoustic modes observed.