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Technical Physics Letters

Self-induced suppression of Bragg scattering of a resonant radiation pulse in a periodic medium

Boris I. Mantsyzov, R. N. Kuzmin

Published Jul 1, 1984• 1 citation
OpenAlex

Abstract

The kinetics of interaction of a coherent electromagnetic field with a periodic medium is considered for a two-wave case. Numerical solution of the generalized system of Maxwell-Bloch equations is obtained. It is noted that the self-induced selective suppression of Bragg reflection at a boundary and the suppression of the scattering of a field pulse in a medium could be observed experimentally while studying the interaction of a laser beam with resonant atoms or molecules in layered crystals.

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The kinetics of interaction of a coherent electromagnetic field with a periodic medium is considered for a two-wave case. Numerical solution of the generalized system of Maxwell-Bloch equations is obtained. It is noted that the self-induced selective suppression of Bragg reflection at a boundary and the suppression of the scattering of a field pulse in a medium could be observed experimentally while studying the interaction of a laser beam with resonant atoms or molecules in layered crystals.
Summary form only given. In recent years, there has been considerable interest in nonlinear and quantum optics of photonic bandgap structures. Some of this attention has centered on the properties of gap solitary waves, which are light pulses tuned at a Bragg frequency within a forbidden bandgap of the periodic structure. These solitary waves may occur in a periodically modulated medium with a Kerr-like nonlinearity, and in the resonance grating as a two-wave soliton of self-induced transparency. In the later case, the coupled-mode Maxwell-Bloch equations which describe the on-resonance coherent interaction of the intense field with a periodic structure of thin layers of two-level atoms in the ground state, lead to an integrable sine-Gordon equation. In our study, we concentrate on the nonintegrable case, that is, amplification in a resonant Bragg structure by means of a comprehensive analysis that includes and numerical modelling of Dicke superradiance and coherent amplification.
The nonlinear interaction of high-intensity coherent optical radiation and a continuous resonant photonic crystal is analytically and numerically studied in the framework of the semiclassical approximation using the two-wave Maxwell-Bloch equations at various initial excitations of resonant atoms. It is demonstrated that the initially unexcited resonant photonic crystal with an arbitrary concentration function of resonant atoms allows the propagation of the Bragg soliton of the self-induced transparency. The Bragg reflection is suppressed at zero initial inversion when the number of atoms in the excited state is equal to the number of atoms in the stationary state.
The gap 2\ensuremath{\pi} pulse or gap solitary wave of self-induced transparency at an inhomogeneously broadened line of a resonant Bragg periodical structure has been found theoretically as an exact solution of the coupled-mode Maxwell-Bloch equations. In the case of a slight violation of the Bragg condition at exact two-level resonance, the analytical solution for the gap 2\ensuremath{\pi} pulse with phase modulation has been obtained. Furthermore, the existence of an oscillating pulse that periodically changes in amplitude and in the sign of its velocity has been numerically shown.
We investigate the reflected field for few-cycle ultra-short laser pulses propagating through resonant media embedded within wavelength-scale structures.Full-wave Maxwell-Bloch equations are solved numerically by using the finite-difference time-domain method.The results show that the spectral feature of the reflected spectrum is determined by the Bragg reflection condition, and that the periodic structure of a dense atomic system can be regarded as a one-dimensional photonic crystal and even as a highly reflective multilayer film.Our study explains the suppression of the frequency shifts in the reflected spectrum based on the Bragg reflection theory and provides a method to control the frequency and frequency intervals of the spectral spikes in the reflected spectrum.
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.
A linear response of a resonant medium to a weak electromagnetic field is studied in the case when a medium is a gas of three-level atoms subjected to a strong saturating pulse. A noncoherent intense pulse and a coherent 2π pulse (of the kind encountered in the theory of self-induced transparency) are considered. The expressions obtained are used to study the problem of the spectrum of the reflection of light by a pulse moving in a medium. An analysis is made of the possibility of using the Doppler effect, which occurs when light is reflected by a moving pulse, in an investigation of the characteristics of pulse propagation, determination of its parameters, and study of the nonlinear characteristics of the medium itself. Possibilities of experimental observation of the predicted effects are discussed, particularly the possibility of conversion of an electromagnetic radiation spectrum.