Engineering & Science
Brillouin Scattering Acoustic Phonon Frequency Shift (nu_B) in Optical Fiber
Calculate the Léon Brillouin inelastic acoustic-phonon frequency shift nu_B = ((2 * n * v_a) / lambda_0) * SIN(RADIANS(theta / 2)) in GHz for distributed fiber-optic BOTDR strain/temperature sensors and SBS power limits.
Why 1,550 nm telecom fibers reflect an ~11.15 GHz downshifted Stimulated Brillouin wave!
Léon Brillouin (1922) predicted that light propagating through a solid or liquid scatters inelastically off thermally excited (or electrostrictively driven) longitudinal acoustic phonons moving at sound speed v_a (m/s). Phase-matching photon and phonon wavevectors yields the Doppler-like Brillouin Frequency Shift: nu_B = ((2 * n * v_a) / lambda_0) * sin(theta / 2), where n is refractive index, lambda_0 is vacuum laser wavelength, and theta is scattering angle!
In single-mode fused-silica telecom fiber (n = 1.45, longitudinal sound speed v_a = 5,960 m/s, lambda_0 = 1,550 nm), backward scattering along the fiber core (theta = 180° -> sin(90°) = 1) produces the famous nu_B = 11.151 GHz Stokes shift—used by 50-km pipeline and subsea-cable BOTDR distributed strain/temperature sensors! At right-angle 90° bulk crystal light-scattering spectroscopy (theta = 90°), nu_B drops by sin(45°) to 7.885 GHz, and vanishes at forward theta = 0°!
| Scattering Geometry (Silica n = 1.45, va = 5,960 m/s, lambda0 = 1,550 nm) | sin(theta / 2) | Brillouin Shift nuB (GHz) | Photonics Application |
|---|---|---|---|
| Backward Fiber Core (theta = 180°) | 1.0000 | 11.151 GHz | SBS Threshold & BOTDR Fiber Sensing |
| Right-Angle Bulk Cell (theta = 90°) | 0.7071 | 7.885 GHz | Elastic-Modulus Brillouin Spectroscopy |
| Forward Beam (theta = 0°) | 0.0000 | 0.000 GHz | Zero Acoustic Momentum Transfer |
Brillouin Acoustic Frequency Shift nu_B (GHz)
Since wavelength lambda_0 is entered in nanometers (10^-9 m) and frequency output is in gigahertz (10^9 Hz), the 10^-9 and 10^9 scale factors cancel cleanly: nu_B (GHz) = ((2 * n * v_a) / lambda_nm) * SIN(RADIANS(theta / 2)).
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B5 < 0, B5 > 180), "Invalid Brillouin Inputs", ROUND(((2 * B2 * B3) / B4) * SIN(RADIANS(B5 / 2)), 3))Matched Acoustic Phonon Grating Period Lambda_a (nm) = lambda_0 / (2 * n * sin(theta / 2))
Calculates the spatial period of the Bragg-matched hypersonic acoustic wave inside the medium.
=IF(OR(B2 <= 0, B4 <= 0, B5 <= 0, B5 > 180), "Invalid Brillouin Inputs", ROUND(B4 / (2 * B2 * SIN(RADIANS(B5 / 2))), 2))Try the example
Use the original values or change them to test your understanding.