Transformation and amplification of light modulated by a traveling wave with a relatively low frequency

Abstract

The behavior of electromagnetic waves in media modulated in both time and space, extensively studied decades ago, has recently attracted renewed attention. In this work, we address a central question of this research: can light at an initial frequency $\omega_{0}$ be amplified solely by pumping with a traveling wave of much lower frequency $\omega_{p} \ll \omega_{0}$? In general, the bandwidth of the modulation-induced optical frequency-comb spectrum increases substantially when the phase velocity of the traveling wave, $v_{p}$, approaches the phase velocity of light, $v_{0}$. However, in realistic photonic waveguides, the resulting amplification remains negligible due to the unfeasible modulation strengths and waveguide parameters required. In contrast, we demonstrate that modulating an optical resonator with a traveling wave of frequency $\omega_{p}$ and phase velocity $v_{p}$ much smaller than the frequency $\omega_{0}$ and phase velocity $v_{0}$ of light can produce strong amplification. This effect is accompanied by conversion into multiple comb lines within a relatively narrow frequency band.