Spontaneous forward Brillouin scattering in carbon disulfide

In recent years, guided acoustic wave Brillouin scattering has become an important tool in photonics, serving as the basis for everything from new forms of information processing to silicon lasers. Due to low losses and long interaction lengths, fiber optic systems offer an intriguing platform to harness these guided-wave light-sound interactions. However, within typical fiber optic systems these interactions are exceedingly weak—requiring complex microstucturing to yield appreciable light-sound coupling. Here, we enhance this light-sound coupling by using a ${\mathrm{CS}}_2$-filled liquid core optical fiber. Owing to tight confinement of the optical and acoustic modes within the fiber core, as well as the large electrostrictive response of ${\mathrm{CS}}_2$, this system yields an unprecedented forward Brillouin gain for a fiber optic system. To demonstrate this physics, we measure multipeaked spontaneous forward Brillouin scattering power spectra, yielding information about the fiber geometry, material properties, and acousto-optic coupling strength. To interpret these data, we simulate the spontaneous Brillouin scattering power spectrum for this fiber system. These results reveal that hybridized acoustic excitations within the fiber core and cladding produce this characteristic multipeaked power spectrum. In the future, the large forward Brillouin coupling, long interaction lengths, and low losses of liquid-core fibers may enable new forms of distributed sensing, lasers with customizable emission, and physics including continuum optomechanical cooling.

Figure 1

(a) Phenomenology of spontaneous forward Brillouin scattering. (b) A laser scatters from thermally populated guided acoustic waves, (c) producing Stokes and anti-Stokes sidebands.

Figure 2

Phase-matching conditions for forward Brillouin scattering. (a) Dispersion relations (green) for a collection of guided-acoustic waves near $q=0$; the intersection of the depicted light line with each dispersion curve gives the frequency and wave vector for each Brillouin-active acoustic mode. (b) Dispersion relation for light. The frequency and wave vector of a forward Brillouin-active phonon mode can couple two distinct (pump and Stokes) optical modes.

Figure 3

(a) Illustration of LCOF system. Cross section of liquid-core fiber system (not to scale) showing (b) layout of materials, (c) electric-field norm for a guided electromagnetic mode, (d) labels for the geometry ${\mathrm{R}}_{\mathrm{core}}=0.9\mu \mathrm{m}$ and ${\mathrm{R}}_{\mathrm{clad}}\approx 64.5\mu \mathrm{m}$, and (e) one example of an acoustic mode that is tightly trapped within the core.

Figure 4

Apparatus for heterodyne spectroscopy of spontaneous forward Brillouin scattering. A pump laser, amplified by an erbium-doped fiber amplifier (EDFA), is passed through the liquid-core fiber and filtered. The filtered output of the LCOF, comprising the transmitted pump (local oscillator) and scattered light, is photomixed and detected on a radio-frequency spectrum analyzer (RFSA).

Figure 5

Spontaneous forward Brillouin Stokes power spectra vs intrafiber pump power. Power spectra are offset 0.3 pW with increasing power for clarity. Inset: estimated Brillouin gain obtained for peak located at 827 MHz (see vertical line). Horizontal line is given by best fit to data, yielding $G_{\mathrm{B}}=5.8\pm 1{\left(\mathrm{W}\mathrm{m}\right)}^{-1}$.

Figure 6

Spontaneous forward Brillouin scattering spectrum. Open red circles are measurements and solid line is simulated spectrum. Both measured and simulated spectra have been normalized to peak gain. For this comparison, a small contribution from the scattered power background is subtracted and the resulting power spectrum is scaled to have a max value of unity. The insets (a), (b), and (c), show the magnitude of the acoustic displacement along fiber cross section—illustrating that the spectra subpeaks [e.g., see (a)] represent motion spanning the fiber cladding and that the large peaks near $800\mathrm{MHz}$ [see points (b) and (c)] comprise acoustic motion that is tightly trapped within the fiber core.