Amplification of light in photonic waveguides and resonators modulated by a relatively slow travelling wave

The behaviour of electromagnetic waves in a medium modulated in time and space, largely investigated decades ago, has recently attracted emerging interest. Here, we address one of the thrilling questions of this research: can light be amplified in a realistic photonic circuit modulated by a travelling wave having a relatively small frequency (e.g., by an acoustic wave)? A positive answer to this question for an ideal broadband lossless and dispersionless waveguide, under the condition that the traveling wave phase velocity approaches the phase velocity of light, was given several decades ago. However, for realistic optical waveguides with relatively small transmission bandwidth, this amplification effect remains small. In contrast, we show that modulating a racetrack optical resonator by an acoustic wave with the phase velocity satisfying the Brillouin phase matching condition can significantly amplify light within a small transmission bandwidth.