Measurement of the frequency response of the electrostrictive nonlinearity in optical fibers

Abstract

The electrostrictive contribution to the nonlinear refractive index is investigated by use of frequency-dependent cross-phase modulation with a weak unpolarized cw probe wave and a harmonically modulated pump copropagating in optical fibers. Self-delayed homodyne detection is used to measure the amplitude of the sidebands imposed upon the probe wave as a function of pump intensity for pump modulation frequencies from 10 MHz to 1 GHz. The ratio of the electrostrictive nonlinear coefficient to the cross-phase-modulation Kerr coefficient for unpolarized light is measured to be 1.58:1 for a standard step-index single-mode fiber and 0.41:1 for dispersion-shifted fibers, indicating a larger electrostrictive response in silica fibers than previously expected.

Sudden spontaneous acceleration and deceleration of gap-acoustic solitons

“…(3a) and (3b)]. Reference [39] found electrostriction to be equal to 19% of the fast (mainly electronic) contribution to the Kerr effect ͓2͑ 0 / c͒ 2 / k 0 ͔ s [39], or 16% of the total Kerr effect, and [40] found different values for different fibers, using unpolarized light, including electrostrictive Kerr contributions a few times larger. By comparison, for bulk fused silica and linear polarized light at the wavelength of 0 = 0.8 m, using the (typical) material coefficients above, the electrostrictive contribution to the Kerr coefficient is es es / ␤ s 2 Ϸ 0.46ϫ 10 −8 s 2 /g, and the fast contribution to the Kerr coefficient is ͓2͑ 0 / c͒ 2 / k 0 ͔ s = 1.53ϫ 10 −8 s 2 / g, giving an electrostrictive contribution of 30% of the fast nonlinearity or 23% of the total Kerr effect.…”

“…Waveguides can have significantly different optical and acoustic properties than the bulk [35,36,[38][39][40][41][42][43][44][45]. This is partly due to variations in the transverse cross-section of the light intensity and partly due to the composite nature of fibers-interfaces between the core and cladding are especially sensitive to opto-mechanical affects and can also absorb acoustic energy.…”

“…This is partly due to variations in the transverse cross-section of the light intensity and partly due to the composite nature of fibers-interfaces between the core and cladding are especially sensitive to opto-mechanical affects and can also absorb acoustic energy. For example, [39,40] measured the contribution of electrostriction to the Kerr effect for linear light in an optical fiber at low frequencies ͑ es es / ␤ s 2 ͒. This factor is obtained by eliminating the time derivatives in Eq.…”

Nonlinear Scattering Effects in Optical Fibers

“…The disorder is time dependent so the scattered light is shifted (Brillouin shift) in frequency by the frequency of sound wave. For pulses shorter than 500 ps, there is no spatial overlap between the pulse and acoustic wave, which results in negligible electrostrictive nonlinearity [5].…”

“…There are two nonlinear scattering phenomenon in fibers and both are related to vibrational excitation modes of silica [2][3][4][5][6][31][32][33]. These phenomenon are known as stimulated Raman scattering (SRS) and stimulated Brillouin scattering (SBS).…”