Acoustic coefficients of P₂O₅-doped silica fiber: Acoustic velocity, acoustic attenuation, and thermo-acoustic coefficient

We present measurements and modeling of the effect of P₂O₅ doping on the acoustic damping and temperature sensitivity coefficients of silica fibers. In particular, the Brillouin gain spectrum of a highly P-doped fiber is measured and investigated at different temperatures. It is found that the acoustic damping coefficient (proportional to the Brillouin spectral width) of phosphorus pentoxide (1.41 × 10⁵ m^-1 for bulk P₂O₅ at 11 GHz) is similar to, but larger than, that of germanium dioxide. Additionally, the acoustic velocity (and thereby the Stokes' shift) is found to be much less dependent on temperature in P₂O₅ (+ 0.12 m/s/°C) than in SiO₂ (+ 0.56 m/s/°C). Using these coefficients (the thermo-acoustic coefficients), the modeled and unique slopes of the Stoke'-shift-versus-temperature curves for the four observed acoustic modes each lie within 3% of the measured values. Finally, utilizing both the thermo-optic and thermo-acoustic coefficients, a design example is presented where a composition is determined for which the dependence of the Brillouin frequency shift on temperature is minimized. In this example, the calculated temperature sensitivity is less than 5 kHz/°C over the temperature range -100 °C < T < 100 °C for the molar composition 0.54P₂O₅:0.46SiO₂.