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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Self-induced medium transparency and nutation echo in an ensemble of impurities in photonic crystals

Ashat M. Basharov

Published Mar 3, 2008• 0 citations
Publisher

Abstract

Nutation oscillations of an electromagnetic wave propagating through photonic crystal with resonant impurities are studied theoretically in case when one energy level of impurity is in a gap in photonic states. It is shown that this impurity energy level serves as a trap for excitation of impurity atom when two-photon relaxation processes are essential in the electromagnetic field. This effect causes self-induced medium transparency and peculiar attenuation of nutation oscillation which allow studying experimentally two-photon relaxation.

DOI
10.1117/12.801748

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Nutation oscillations of an electromagnetic wave propagating through photonic crystal with resonant impurities are studied theoretically in case when one energy level of impurity is in a gap in photonic states. It is shown that this impurity energy level serves as a trap for excitation of impurity atom when two-photon relaxation processes are essential in the electromagnetic field. This effect causes self-induced medium transparency and peculiar attenuation of nutation oscillation which allow studying experimentally two-photon relaxation.
Two-quantum relaxation transitions in an impurity atom that are activated by its resonance interaction with a monochromatic wave lead to hole burning in the distribution of atoms populating the lower energy level over detunings from the resonance. In this case, the levels of an impurity atom lying within the gap or the pseudogap in the density of photon states of a photonic crystal act as a trap. The impurity atoms change to these levels in the process of interaction of a monochromatic wave with the atomic transition that is not influenced by specific spectral features of a photonic crystal.
On the base of the concept of radiative interaction between atoms of two different species, a novel electric-dipole mechanism of spontaneous radiating relaxation of an impurity atom in a medium with a gap in the photonic density of states about the transition frequency has been suggested. A kinetic equation for an impurity atom has been derived, and polarizations of the photonic band-gap crystal and an induced electromagnetic wave at the spontaneous transition frequency due to the suggested mechanism have been investigated. The parameters of the induced wave are determined by those of the suggested mechanism, and this dependence can be used in experimental investigations of these parameters.
It is shown that resonant interaction of a coherent wave with impurity atoms leads to filling of levels of an impurity atom that lie in the gap in the photon density of states and do not belong to resonant transitions, while the interaction of impurity atoms with a nonresonant coherent wave results in effective deactivation of the indicated levels. The main mechanism determining the pumping and decay of an impurity level in a gap are two-photon radiative relaxation processes previously investigated by the present author (Zh. Éksp. Teor. Fiz. 102 , 1126 (1992) [Sov. Phys. JETP 75 , 611 (1992)]).
We consider a one-dimensional photonic crystal embedded in a two-level medium with various degrees of disorder, such that the tail of localized states in the forbidden gap is resonant with self-induced transparency pulses, which can propagate in the absorbing system. We theoretically and numerically predict that the SIT pulse not only is slowed down by the disorder, but, at high scattering strengths, it is trapped by coupling with Anderson states located in proximity of the cavity surface. We develop a perturbative analysis to address the role of the random perturbation on the propagation of a 2π pulse in a two level medium.
The phenomenon of electromagnetically induced transparency has been studied when a four-level atom is located in a photonic band gap material. Quantum interference is introduced by driving the two upper levels of the atom with a strong pump laser field. The top level and one of the ground levels are coupled by a weak probe laser field and absorption takes place between these two states. The susceptibility due to the absorption for this transition has been calculated by using the master equation method in linear response theory. Numerical simulations are performed for the real and imaginary parts of the susceptibility for a photonic band gap material whose gap-midgap ratio is 21%. It is found that when resonance frequencies lie within the band, the medium becomes transparent under the action of the strong pump laser field. More interesting results are found when one of the resonance frequencies lies at the band edge and within the band gap. When the resonance frequency lies at the band edge, the medium becomes nontransparent even under a strong pump laser field. On the other hand, when the resonance frequency lies within the band gap, the medium becomes transparent even under a weak pump laser field. In summary, we found that the medium can be transformed from the transparent state to the nontransparent state just by changing the location of the resonance frequency. We call these two effects anomalous electromagnetically induced transparency.