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arXiv:0909.0092 · Physical Review A

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

Vasily G. Arkhipkin, S. A. Myslivets

Published Dec 7, 2009• 7 citations
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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.

DOI
10.1103/physreva.80.061802

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The Raman gain of a probe light in a three-state \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ 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 \ensuremathμW/cm2\ensuremath{\mu}\text{W}/{\text{cm}}^{2}\ensuremathμW/cm2. 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.
Features of Raman gain of probe radiation in three-level atoms placed in a defect of a one-dimensional photonic crystal in the presence of laser radiation (pump) at an adjacent high-frequency transition have been theoretically investigated. It has been shown that there is a pump intensity range where narrow peaks (resonances) simultaneously appear in the transmission and reflection spectra of the probe field. Beyond this region, the peak in the transmission spectrum is transformed to a narrow dip. The spectral position of these peaks is determined by the Raman resonance and the transmittance and reflectance can be larger than unity at pump intensities from several microwatts per square centimeter to several tens of milliwatts per square centimeter. The nature of narrow peaks is due to a sharp dispersion of a nonlinear refractive index near the Raman resonance; this dispersion is responsible for a strong decrease in the group velocity of probe radiation. The proposed scheme makes it possible to obtain controlled ultranarrow resonances in the transmission and reflection spectra of the photonic crystal.
The dispersion and transmission in one-dimensional photonic crystals with a defect containing three-level system with two closely placed Raman gain peaks is discussed, there is a steep curve with negative slop between the two gain peaks, two resonant transmissions with transmissivities larger than 1 are found in photonic band gap. The two resonant transmissions depends on the position of the defects and structure parameters. There is a steep curve with negative slop at the left resonant frequency and positive slop at right resonant frequency, a negative group velocity and a very slow speed is found.
The spectral properties of an electromagnetically induced grating that is based on the spatial modulation of the Raman gain in the field of a standing pump wave in a three-level homogeneous medium have been discussed. It has been shown that, by varying the intensity or the frequency of the pump field, one can control the transmission and reflection spectra, while the transmission and reflection coefficients of the probe (Raman) wave can simultaneously be greater than unity. The influence of the nonideality of the standing wave on the spectral characteristics of the grating has been studied.
We study the transmission spectra of a one-dimensional photonic crystal with a defect containing a four-level atomic medium that exhibits a greatly enhanced third-order susceptibility while having a vanishing linear susceptibility dependent on the electromagnetically induced transparency. Two ways of controlling the transmission of a photonic crystal are discussed: via absorption, i.e., nonlinear (two-photon) absorption of the probe field enhanced by constructive quantum interference, and via dispersion, which comes down to shifting the resonance frequency of the defect mode for the probe field by varying the refractive index based on the giant Kerr nonlinearity (cross-phase modulation). We demonstrate that such systems enable nonlinear all-optical switching at ultralow intensities of the coupling and switching laser fields.
We propose a design of an all-optical transistor based on a one-dimensional photonic-crystal cavity doped with a four-level N\mathsf{N}N-type active Raman gain medium. The calculated results show that in a photonic-crystal cavity of this kind transmission and reflection of the probe (Raman) beam are strongly dependent on the optical switching power. Transmission and reflection of the probe beam can be greatly amplified or attenuated. Therefore the optical switching field can serve as a gate field of the transistor to effectively control propagation of the weak probe field. It is shown that the group velocity of the probe pulse can be controlled in the range from subluminal (slow light) to superluminal (fast light).