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Optics Express

Enhanced light amplification due to group-velocity anomaly peculiar to two- and three-dimensional photonic crystals

Kazuaki Sakoda

Published Mar 1, 1999• 184 citations
Publisher

Abstract

An analytical expression was derived for light amplification by stimulated emission in arbitrary photonic crystals, which showed and enhancement due to small group velocity. This enhancement was evaluated quantitatively for a two-dimensional crystal with a finite thickness, and an extremely large enhancement due to group-velocity anomaly peculiar to two- and three-dimensional crystals was found even for quite a thin crystal.

DOI
10.1364/oe.4.000167

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Enhanced light amplification due to group-velocity anomaly in two-dimensional photonic crystals

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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.

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Journal of the Optical Society of America B•Feb 10, 2010•6 citations
An analytical expression was derived for light amplification by stimulated emission in arbitrary photonic crystals, which showed and enhancement due to small group velocity. This enhancement was evaluated quantitatively for a two-dimensional crystal with a finite thickness, and an extremely large enhancement due to group-velocity anomaly peculiar to two- and three-dimensional crystals was found even for quite a thin crystal.
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.
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. In photonic crystals with spatially periodic dielectric constants, a variety of novel optical and quantum optical phenomena are expected to be realized. One of their peculiar features is the presence of those electromagnetic eigenmodes with extremely small group velocities (group-velocity anomaly) that leads to the enhancement of various optical processes. The phase-matching condition is relaxed in photonic crystals compared with uniform materials. Therefore nonlinear optics of the photonic crystals is a promising field for future experimental studies. In this paper, we believe we will report the first theoretical prediction of the enhancement of quadrature-phase squeezing due to optical parametric amplification by means of a perturbation theory based on a Green's function formalism.
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.