Amplification and attenuation of light in a waveguide modulated by a travelling wave

Light propagating in an optical waveguide can gain or lose power through interaction with a travelling acoustic wave or radio-frequency modulation of permittivity. Here, we model this propagation by considering an optical wave interacting with a weak travelling-wave permittivity perturbation whose frequency is much smaller than the optical frequency and whose amplitude decays exponentially along the propagation direction. Four modulation cases are analyzed: instantaneous modulation, synchronous modulation, and the Stokes and anti-Stokes resonances. For these cases, simple expressions are obtained for the carrier and sideband transmission and reflection powers as well as for the total gain and loss powers. Although the achievable total gain remains small for realistic modulation and waveguide parameters, the anti-Stokes resonance is identified as the most promising condition for observing modulation-induced light amplification.