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Acta Sinica Quantum Optica

Dispersive Effect in One-dimensional Photonic Crystals with a Defect Containing Three-level System with Two Closely Placed Raman Gain Peaks

Nian-Hua Liu

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

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.

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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.
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.
Localized fields in the defect mode of one-dimensional photonic crystals with active impurity are studied with the help of the theory of spontaneous emission from two-level atoms embedded in photonic crystals. Numerical simulations demonstrate that the enhancement of stimulated radiation, as well as the phenomena of transmissivity larger than unity and the abnormality of group velocity close to the edges of photonic band gap, are related to the negative imaginary part of the complex effective refractive index of doped layers. This means that the complex effective refractive index has a negative imaginary part, and that the impurity state with very high quality factor and great state density will occur in the photonic forbidden band if active impurity is introduced into the defect layer properly. Therefore, the spontaneous emission can be enhanced, the amplitude of stimulated emission will be very large and it occurs most probably close to the edges of photonic band gap with the fundamental reason, the group velocity close to the edges of band gap is very small or abnormal. OCIS codes: 130.3120, 120.7000, 160.4670, 120.4570, 160.5690, 230.4170. More and more importance has been attached to the unique behaviors of electromagnetic wave propagating in photonic crystals, a novel and artificial photonic mate-
Localized fields in the defect mode of one-dimensional photonic crystals with active impurity are studied with the help of the theory of spontaneous emission from two-level atoms embedded in photonic crystals. Numerical simulations demonstrate that the enhancement of stimulated radiation,as well as the phenomena of transmissivity larger than unity and the abnormality of group velocity close to the edges of photonic band gap,are related to the negative imaginary part of the complex effective refractive index of doped layers.This means that the complex effective refractive index has a negative imaginary part,and that the impurity state with very high quality factor and great state density will occur in the photonic forbidden band if active impurity is introduced into the defect layer properly.Therefore,the spontaneous emission can be enhanced,the amplitude of stimulated emission will be very large and it occurs most probably close to the edges of photonic band gap with the fundamental reason,the group velocity close to the edges of band gap is very small or abnormal.
The propagation of a pulse through one-dimensional photonic crystals that contain a dispersive and absorptive defect layer doped with two-level atoms is discussed. The dynamical evolution of the pulse inside the photonic crystal is presented. Superluminal negative group velocity (the peak appears at the exit end before it reaches the input end) is discovered. Although the group velocity is larger than c and even negative, the velocity of energy propagation never exceeds the vacuum light speed. The appearance of the superluminal advance or subluminal delay of the pulse peak inside the photonic crystal or at the exit end is due to the wave interference from Bragg reflections.