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Quantum Electronics and Laser Science Conference

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

K. Sakoda

Published Jan 20, 2003• 0 citations
Publisher

Abstract

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.

DOI
10.1109/qels.1999.807636

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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.
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.
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.
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-
We have proved the inevitability of the existence of localized field with a defect mode as well as its basic properties with the help of the theory of spontaneous emission from two-level atoms in photonic crystals,which provide a theoretical proof for studying the inherent laws of spontaneous radiation from the doped medium in the paper.On this basis,the inherent laws between the characteristics of localized field,the enhancement of stimulated emission,the phenomenon of transmissivity greater than 1,the abnormality of the group velocity close to the edge of photonic band gap and the negative imaginary component of the complex active refractive index of doped layers in one-dimensional photonic crystals with active impurities or without active impurities were studied by using the method of numerical simulation,which illustrated that the complex active refractive index has a negative imaginary component,and that the dope modes with very high quality factors and great mode density will occur in the photonic forbidden band if an active impurity is introduced into the defect medium in the photonic crystals.Therefore,the enhancement of spontaneous emission can be realized,and the amplification of stimulated emission will be very great and it most probably occurs close to the edge of photonic band gap with the fundamental reason and the group velocity close to the edge of band gap being very small or abnormal.