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physica status solidi (b)

Enhancement Mechanisms of Radiation-Matter Interaction in Various Arrangements of Resonant Objects

K. Cho, Tomoe Ikawa

Published Sep 1, 1999• 4 citations
Publisher

Abstract

A systematic study is made by means of a microscopic nonlocal response theory about the enhancement mechanisms of the optical signals of resonant matter units in various arrangements, where the lattice constant in one direction allows Bragg scattering. Considering that the radiative decay width is a general measure of the coupling strength, we study (a) its size-enhancement and saturation, (b) its speed-up effect due to Bragg scattering, and (c) a super-enhancement effect due to the combination of (a) and (b).

DOI
10.1002/(sici)1521-3951(199909)215:1<281::aid-pssb281>3.0.co;2-o

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A systematic study is made by means of a microscopic nonlocal response theory about the enhancement mechanisms of the optical signals of resonant matter units in various arrangements, where the lattice constant in one direction allows Bragg scattering. Considering that the radiative decay width is a general measure of the coupling strength, we study (a) its size-enhancement and saturation, (b) its speed-up effect due to Bragg scattering, and (c) a super-enhancement effect due to the combination of (a) and (b).
Combining the two enhancement mechanisms of radiation-matter interaction, one in long wavelength regime (LWR) and the other via resonant Bragg reflection, we systematically studied the coupling strengths of various arrays of resonant units. As a general measure of the coupling strength, the radiative width of each resonance was calculated according to the first-principles theory of microscopic nonlocal response of matter. A numerical study was carried out for three resonant Bragg arrangements of (A) N atoms, (B) N chains of atoms, and (C) N planes of atoms. Different aspects of enhancement are clarified as the size-linear increase in LWR and its dimensionality dependence, the speed-up effect of decay, and the super-enhancement effect due to all these mechanisms in case (C) with its saturation behavior for large N.
The subject of the review is the diffraction of an electromagnetic wave on a periodic condensed matter where the Bragg condition is satisfied at the frequency of resonance excited in this medium. The Bragg systems known as resonant photonic crystals in general have been considered, and the propagation, reflection, transmission, and diffraction of electromagnetic radiation in different objects—(I) periodic quantum-well structures near the exciton resonance, (II) optical lattices of atoms cooled in a laser field, and (III) bulk crystals and multilayers with gamma-ray resonance intranuclear transitions—have been described in a unified context. The main attention has been paid to the steady-state linear diffraction, including resonant reflection and transmission, which is the best studied and allows a comparison of the three aforementioned systems with the aim of revealing specific characteristics and common features. A characteristic common property of the considered systems is the suppression of non-radiative channels and an inhomogeneous broadening of the resonance frequency. The second fundamental property of resonant photonic crystals is that the interaction of light with resonant excitation can occur in two regimes depending on the thickness of the sample. In the superradiant regime realized for a small number of resonant layers N (fine structures), the height of the peak and half-width of the reflection spectrum monotonically increase with increasing value of N. With a further increase in N, there occurs a transition to a photonic-crystal regime where the half-width of the reflection spectrum is saturated, which manifests itself in the form of an optical stop band. The theoretical description is illustrated by experimental spectra measured for all three resonant Bragg systems.
We observe coherently enhanced reflection (Bragg scattering) of a near resonant laser beam from cesium atoms ordered by a periodic array of optical potential wells known as an optical lattice. The reflected light is enhanced by a factor of $\ensuremath{\sim}{10}^{5}$ over scattering from a disordered atomic sample. We measure the magnitude of the reflectivity and its detuning dependence as functions of the density and the degree of localization of the atoms. The change in lattice constant due to the frequency-dependent effective index of refraction seen by the lattice light field is observed.
In this paper, we study the problem of multiple scattering of light from a randomly occupied optical lattice, thereby extending the first-order Born analysis of the previous paper. A full multiple-scattering analysis is essential to a complete understanding of the nature of light propagation inside a medium. Our calculations show that the incident wave, when resonant with the atomic medium, is rapidly extinguished due to multiple scattering. The decay constant depends critically on the incident wavelength, the lattice constant, the average number density of atoms, and their polarizability. Both the Bragg scattering amplitudes and directions are modified as a result of multiple scattering. Because of the random site occupation of an otherwise regular lattice structure, a coherent enhancement of the scattering cross section is also predicted to occur along a discrete set of directions that are related to the strictly backward direction by reciprocal lattice vectors.
In nanostructures with a high excitonic coherence, the interplay between the spatial structure of the excitonic wavefunction and that of the radiation field plays an essential role, causing drastic size effects in the optical response, such as size-resonant enhancement of the radiative decay rate and the nonlinear response and the interchange of quantized levels. This article discusses such peculiar optical effects based on the theoretical treatment beyond the long-wavelength approximation and demonstrates the possibility of designing novel photofunctions with the explicit use of the spatial structures of the radiation field.