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Physical Review E

Recurrent scattering of spontaneous radiation from a randomly occupied optical lattice

Wei Guo

Published Mar 19, 2004• 3 citations
Publisher

Abstract

The problem of recurrent scattering of spontaneous radiation from a randomly occupied optical lattice is discussed herein theoretically. The intensity of the scattered radiation is calculated and averaged over the random distribution of atoms trapped inside the lattice. From the intensity of the scattered radiation, two properties of random lasing are derived. First, the random lasing's strongest oscillation has a wavelength comparable to the lattice constant and, second, its emission spectrum is discontinuous. In the present paper, a quantity, the number of multiple scattering channels based on the long-range regularity possessed by an optical lattice, is defined. This quantity is found to significantly determine the magnitudes of the mean intensity of the scattered radiation and the wave decay constant.

DOI
10.1103/physreve.69.036602

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•Jan 1, 2004•0 citations
The problem of recurrent scattering of spontaneous radiation from a randomly occupied optical lattice is discussed herein theoretically. The intensity of the scattered radiation is calculated and averaged over the random distribution of atoms trapped inside the lattice. From the intensity of the scattered radiation, two properties of random lasing are derived. First, the random lasing's strongest oscillation has a wavelength comparable to the lattice constant and, second, its emission spectrum is discontinuous. In the present paper, a quantity, the number of multiple scattering channels based on the long-range regularity possessed by an optical lattice, is defined. This quantity is found to significantly determine the magnitudes of the mean intensity of the scattered radiation and the wave decay constant.
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.
A theoretical study of the scattering of light from a randomly occupied optical lattice of resonant atoms is presented to reveal both the characteristics of the lattice and the properties of light scattered from the lattice. In the first-order Born approximation we discuss here, a number of interesting effects are established, including sideband Stokes scattering, a finite angular coherence of the scattered light, and spectral line narrowing. Specifically, the degree of angular coherence of the scattered light is calculated, and it is shown that such coherence is strongly influenced by the regularity and size of the underlying lattice structure. The previously observed phenomenon of the sideband spectral line narrowing is also explained in terms of the localization of atoms in the trapping potential wells. Important information about the lattice can thus be recovered by analyzing the scattered light in the Born approximation.
We derive the photon-number probability distribution and the resulting degree of second-order optical coherence for light emission from a uniformly distributed active species within a multiple-light-scattering medium. This is obtained from a master equation describing the probability distribution for photons in the vicinity of position r, traveling with a wave vector k, related, in turn, to a coarse-grained average of the optical Wigner coherence function. Using a simple model for isotropic, spatially uncorrelated scatterers, this reduces to a generalization of the master equation of a conventional laser in which the medium behaves like a random collection of low-quality factor cavities that are coupled by photon diffusion between a given cavity and its neighbors. Laserlike coherence, on average, is obtained in the random laser above a specific pumping threshold. Photon-number statistics above and below the lasing threshold are computed by first assuming that the atomic response to the local electromagnetic fields is nearly instantaneous. Corrections to this simple model, arising from nonadiabatic atomic dynamics, are then estimated. The dependence of the photon statistics on scatterer density, gain concentration, and position within a sample reveal that, on average, increase of the scattering strength (decrease of the photon transport mean free path) in the medium leads to a sharper peak in the local photon-number distribution, characteristic of increased local coherence in the optical field. We also evaluate the coherence of the output field at points outside the random-laser medium. This is a weighted average of radiation emitted at different positions in the sample, exhibiting varying degrees of coherence due to variations in the local pumping intensity.
In the first part of this thesis, a detailed analysis of lasing in random multiple-light-scattering media with gain is presented. Random laser emission is analyzed using a time-dependent diffusion model for light propagating in the medium containing active atoms. We demonstrate the effects of scatterers to narrow the emission spectral linewidth and to shorten the emitted pulse duration at a specific threshold pump intensity. This threshold pump intensity decreases with scatterer density and excitation spot diameter, in excellent agreement with experimental results. The coherence properties of the random laser are studied using a generalized master equation. The random laser medium is treated as a collection of low quality-factor cavities, coupled by random photon diffusion. Laser-like coherence, on average, is demonstrated above a specific pumping threshold. We demonstrate that with stronger scattering, the pumping threshold for the transition from chaotic to isotropic coherent light emission decreases and enhanced optical coherence for the emitted light is achieved above threshold. The second part of this thesis presents a study of lasing in photonic crystals (PCs). The emission from an incoherently pumped atomic system in interaction with the electro-magnetic reservoir of a PC is analyzed using a set of generalized semiclassical Maxwell-Bloch equations. We demonstrate that the photonic band edge facilitates the enhancement of stimulated emission and the reduction of internal losses, leading to an important lowering of the laser threshold. In addition, an increase of the laser output at a photonic band edge is demonstrated. We next develop a detailed quantum theory of a coherently pumped two-level atom in a photonic band gap material, coupled to both a multi-mode wave-guide channel and a high-quality micro-cavity embedded within the PC. The cavity field characteristics are highly distinct from that of a corresponding high-Q cavity in ordinary vacuum. We demonstrate enhanced, inversionless, and nearly coherent light generation when the photon density of states (DOS) jump between the Mollow spectral components of atomic resonance fluorescence is large. In the case of a vanishing photon DOS on the lower Mollow sideband and no dipolar dephasing, the emitted photon statistics is Poissonian and the cavity field exhibits quadrature coherence.