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Physical Review A

Behavior of spectral lines and degree of spatial coherence in the presence of refraction

G. Hazak, O. Zahavi

Published Oct 1, 1992• 2 citations
Publisher

Abstract

The propagation of radiation from a source embedded in an inhomogeneous refractive medium is studied, using both mode-analysis and ray-tracing methods. Scaling laws for excitation strengths of the modes, the degree of spatial coherence, and the shift of the spectral line are derived.
DOI
10.1103/physreva.46.4167

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It is generally taken for granted that the spectrum of light does not change on propagation. This belief is implicit in all spectroscopy. In the last few years it was discovered that while such spectral invariance holds for radiation from commonly used sources it does not hold, in general, because the spectrum of emitted radiation depends not only on the source spectrum but also on the coherence properties of the source. It was found that in some cases the induced changes may be appreciable, possibly resulting in frequency shifts of spectral lines. It has also been demonstrated that similar spectral changes may be produced by scattering on media whose dielectric susceptibility is appropriately correlated.
Methods of integrals of motion, coherent states, dynamical symmetry group, and density matrix formalism are used to describe the propagation of light in weakly inhomogeneous media, in particular, in a two-dimensional medium having a quadratic transverse distribution of the refractive index and an arbitrarily inhomogeneous longitudinal distribution. Expressions are obtained for the trajectories and widths of the modes and rays. The coefficients of coupling between the modes and rays due to the longitudinal inhomogeneity of the medium and distortion of the axis are discussed. It is shown that, for certain laws of longitudinal inhomogeneity, matching occurs when no energy redistribution takes place between the modes and mismatch is found when all the energy is coupled out of the medium. On the basis of these effects, methods of matched joining of two different graded-index optical waveguides and of coupling light out of a graded-index waveguide are proposed. It is shown that each initial mode of the medium is strongly coupled to three final modes. These results may be used in fiber-optic communication lines.
The steady-state wave equation, used in the literature for the description of amplified spontaneous emission (ASE) in a refractive medium with inverted atoms, focuses on a narrow frequency band at the atomic line center. In the present work, the effect of this approximation was studied by comparison to an alternative procedure that accounts for the full line shape. The three-dimensional time-dependent Maxwell-Bloch equations for ASE in a refraction guided system were solved as an initial-value problem by using transverse-mode expansion. The steady-state limit was approached only for quantities that are bilinear in the field (autorcorrelation function, complex degree of coherence, and radiation intensity). It was found that, except for a gain narrowing factor, the inclusion of the full line shape (or equivalently the detailed dynamics of atomic polarization) does not change the theoretical prediction for the amplification of mode intensities. However, it drastically changes the prediction for the behavior of cross correlations of mode amplitudes. In the high-gain limit the steady-state wave equation predicts that these cross correlations, normalized to the intensity of the involved modes, are independent of the system length and of the excitation strength of the modes. The solution of the Maxwell-Bloch equations predicts that the normalized cross correlations are exponentially decreasing functions of the system length and of the difference between the excitation strengths of the modes. It is therefore argued that the inclusion of the detailed atomic line shape is essential to the analysis of spatial coherence in ASE systems.
We propose a scheme to generate coherent radiation with a tunable frequency spectrum based on the excitation of an inhomogeneous thin layer of a resonant medium by an ultrashort pulse. The Cherenkov-type radiation emitted in a transient stage, i.e., while the excitation wavefront is still propagating over the medium, is shown to contain additional frequency components, which are determined by the spatial frequency components of the medium's density distribution and the excitation geometry. We demonstrate that the spectral content of this transient radiation can be adjusted in wide limits by controlling the spatial density distribution of the resonant medium and the shape of the excitation wavefront. Our theoretical results pave the way towards simple and compact swept-frequency or frequency-tunable optical oscillators as well as sources of the frequency-modulated optical radiation.