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Journal of Experimental and Theoretical Physics

Transmission and reflection spectra of a photonic crystal with a Raman defects

Vasily G. Arkhipkin, S. A. Myslivets

Published Jan 1, 2010• 4 citations
Publisher

Abstract

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.

DOI
10.1134/s1063776110120022

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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 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.
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.
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.
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.
A possible switching mechanism has been investigated for nonlinear photonic crystals doped with an ensemble of non-interacting three-level nanoparticles. In this scheme, an intense pump laser field is used to change the refractive index of the nonlinear photonic crystal while a weaker probe field monitors an absorption transition in the nanoparticles. In the absence of the strong laser field the system transmits the probe field when the resonance energy of the nanoparticles lies near the edge of the photonic band gap due to strong coupling between the photonic crystal and the nanoparticles. However, upon application of an intense pump laser field the system becomes absorbing due to a band edge frequency shift that arises due to a nonlinear Kerr effect which changes the refractive index of the crystal. It is anticipated that the optical switching mechanism described in this work can be used to make new types of photonic devices.