Ultranarrow resonance peaks in the transmission and reflection spectra of a photonic crystal cavity with Raman gain

Abstract

The Raman gain of a probe light in a three-state $\ensuremath{\Lambda}$ scheme placed into a defect of a one-dimensional photonic crystal is studied theoretically. We show that there exists a pump intensity range, where the transmission and reflection spectra of the probe field exhibit simultaneously occurring narrow peaks (resonances) whose position is determined by the Raman resonance. Transmission and reflection coefficients can be larger than unity at pump intensities on the order of tens of $\ensuremath{\mu}\text{W}/{\text{cm}}^{2}$. When the pump intensity is outside this region, the peak in the transmission spectrum turns into a narrow dip. The nature of narrow resonances is attributed to a drastic dispersion of the nonlinear refractive index in the vicinity of the Raman transition, which leads to a significant reduction in the group velocity of the probe wave.