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

摘要

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