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Optics and Spectroscopy

Specific features of the resonance interaction of a coherent wave with an ensemble of impurity atoms of a photonic crystal

Ashat M. Basharov

Published Mar 1, 2001• 1 citation
Publisher

Abstract

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.

DOI
10.1134/1.1358456

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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.
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)]).
It is shown that when an optically allowed transition is coherently excited in an impurity atom in a photonic crystal under conditions where one of the normal relaxation channels is suppressed by the spectral characteristics of the photonic crystal, new relaxation mechanisms are activated involving a coherent field quantum. These mechanisms substantially alter the dynamics of the atomic system, leading to filling of levels of the impurity atom which do not belong to the coherently excited atomic transition. Under certain conditions this leads to population inversion as a result of an optically allowed transition which does not interact with the coherent pump and at a frequency where no photonic band gaps can exist.
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.
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.
We studied the effects of a coherent monochromatic resonant laser field driving the transition of a two-level atom embedded in a photonic band gap (PBG) material on the emission dynamics of the atom. When the transition frequency of the atom lies outside a PBG and sufficiently far from the band edge that the emission dynamics of the atom is not normally affected by the gap, the dynamic stark splitting of the upper level of the atom into two dressed states by a sufficiently strong resonant driving field can bring the lower dressed state close enough to the band edge or even inside the gap so as to be affected by the gap, providing a switchable means of extending the novel effects of atom–photon interaction near the edge of a PBG for atomic transitions outside the gap and far from the band edge. The net effect is as if a sufficiently strong resonant field driving a transition of an atom embedded in a PBG actively shifts the PBG close enough to the transition so that the gap affects the emission dynamics associated with the transition.
A theory of photon trapping has been developed in photonic band-gap (PBG) and dispersive polaritonic band-gap (DPBG) materials doped with an ensemble of five-level atoms. These materials have gaps in their photon energy spectra. The atoms are prepared as coherent superpositions of the two lower states and interact with a reservoir and two photon fields. They also interact with each other by dipole-dipole interaction. The Schrödinger equation and the Laplace transform method are used to calculate the expressions for the number densities of the atomic states. Numerical simulations for a PBG material reveal that when the resonance energies lie away from the band edges and within the lower or upper bands, trapping is observed at certain values of the relative Rabi frequency associated with the two fields, which vary depending on the strength of the dipole-dipole interaction between the atoms. Also, if the photon fields are held constant, the population densities of the excited states of the atoms increase with increasing dipole-dipole interaction. These are very interesting phenomena. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)