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Journal of Physics Condensed Matter

The enhancement of stimulated emission near a photonic band edge

Xingsheng Xu, Bingying Cheng, Daozhong Zhang

Published Oct 24, 2003• 3 citations
Publisher

Abstract

We have derived an analytical expression for light amplification for stimulated emission in arbitrary two-dimensional photonic crystals (PHCs) using the response formula of the PHCs and the Bloch equations. This shows that the gain is proportional to the population inversion, and is inversely proportional to the group velocity and the relaxation coefficient of the phase, which indicates that the gain can be induced by population inversion and enhanced dramatically by small group velocity or anomalous group velocity.

DOI
10.1088/0953-8984/15/44/001

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We have derived an analytical expression for light amplification for stimulated emission in arbitrary two-dimensional photonic crystals (PHCs) using the response formula of the PHCs and the Bloch equations. This shows that the gain is proportional to the population inversion, and is inversely proportional to the group velocity and the relaxation coefficient of the phase, which indicates that the gain can be induced by population inversion and enhanced dramatically by small group velocity or anomalous group velocity.
Summary form only given. Photonic crystals can control the nature of radiation field. In addition to their peculiar optical properties such as suppression of spontaneous emission due to photonic band gaps, the small group velocity at band edges, which will be called group-velocity anomaly, brings about the enhancement of sum-frequency generation and stimulated emission. In this paper, we will derive an analytical expression for the enhancement of light amplification and evaluate it numerically for two-dimensional crystals with finite thickness to show that an extremely large enhancement can be observed even for very thin samples.
Summary form only given. Photonic crystals can control the nature of radiation field. In addition to their peculiar optical properties such as suppression of spontaneous emission due to photonic band gaps, the small group velocity at band edges and so on, which will be called group-velocity anomaly hereafter, brings about the enhancement of sum-frequency generation and stimulated emission. In this paper, we will derive an analytical expression for the enhancement of light amplification and evaluate it numerically for two-dimensional crystals with finite thickness to show that an extremely large enhancement can be observed even for very thin samples.
Using the response formula of photonic crystals and Bloch equations, we analyzed the coherent emission in a two-level atom embedded in an arbitrary photonic crystal. We derived a formula for the transient emission expressed by the photon density of states (DOS), the Rabi frequency, and the background decay. Near the band edge, when the ratio of the Rabi frequency to the decay rate is a proper value, a transient gain occurs and the sharp structures of the DOS near the band edge lead to a drastic enhancement of the emission and the oscillation of the emission.
We demonstrate both theoretically and numerically that slow light can enhance the stimulated emission of four-level atomic systems in photonic crystals. By applying the Bloch-Floquet formalism and the semiclassical physical model of harmonic oscillators coupled to electromagnetic fields, we develop a formalism that relates the group velocity of slow light to the conversion rate between the electric field and atomic potential energy. From our numerical study of the stimulated emission in fiber Bragg gratings (FBGs) and nongrating fiber, a ninefold enhancement of stimulated emission is observed in a FBG over the nongrating fiber when pumping at the band edge, while a 20-fold enhancement of is observed when the frequency of the stimulated emission approaches the band edge.
We study the stimulated Raman scattering (SRS) of light from an atomic system embedded in a photonic crystal and coherently pumped by a laser field. In our study, the electromagnetic field is treated classically and the atomic system is described quantum mechanically. Considering a decomposition of the pump and Stokes fields into the Bloch modes of the photonic crystals and using a multiscale analysis, we derive the Maxwell-Bloch equations for SRS in photonic crystals. These equations contain effective parameters that characterize the SRS gain, the nonlinear atomic response to the electromagnetic field, and the group velocity and that can be calculated in terms of the Bloch modes of the unperturbed photonic crystal. We show that if the pump laser frequency is tuned near a photonic band edge and the atomic system is carefully chosen such that the Stokes mode matches another photonic band edge, low-threshold, enhanced Raman amplification is possible. Possible physical realizations of SRS in photonic crystals are also discussed.