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IEEE photonics journal

Spectrum Changes Produced by Scattering of Light With Tunable Spectral Degree of Coherence from a Spatially Deterministic Medium

Jia Li, Pinghui Wu, Yali Qin, Shuqin Guo

Published Mar 23, 2016• 8 citations

Abstract

Within the validity of the first-order Born approximation, we study the spectrum changes generated by the scattering of light with a tunable spectral degree of coherence (SDOC) from a spatially deterministic medium. Before interacting with the medium, a scalar plane wave is incident upon Young's pinholes, which are employed to produce the incident wave with a tunable SDOC. By assuming that both the scattering potential of the medium and the spectrum of incident plane waves obey Gaussian profiles, the spectrum of the scattered field is derived as a linear combination of Fourier transforms of the scattering potentials. Changes in the spectrum of the scattered field are strongly dependent on the scattering angle, the effective radius of the medium, and Young's pinhole parameter. Moreover, red shifts occurring in the scattered field can be enhanced by either reducing the scattering angle or increasing the effective radius. The results presented here generalize the previous reports, where the light with prescribed functions of the SDOC scattered from a deterministic medium was considered.

DOI: 10.1109/jphot.2016.2546060

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Within the validity of the first-order Born approximation, we study the spectrum changes generated by the scattering of light with a tunable spectral degree of coherence (SDOC) from a spatially deterministic medium. Before interacting with the medium, a scalar plane wave is incident upon Young's pinholes, which are employed to produce the incident wave with a tunable SDOC. By assuming that both the scattering potential of the medium and the spectrum of incident plane waves obey Gaussian profiles, the spectrum of the scattered field is derived as a linear combination of Fourier transforms of the scattering potentials. Changes in the spectrum of the scattered field are strongly dependent on the scattering angle, the effective radius of the medium, and Young's pinhole parameter. Moreover, red shifts occurring in the scattered field can be enhanced by either reducing the scattering angle or increasing the effective radius. The results presented here generalize the previous reports, where the light with prescribed functions of the SDOC scattered from a deterministic medium was considered.

Within the accuracy of the Born approximation, it is shown that the light, which is generated by the scattering of an arbitrary coherent polychromatic wave from a quasi-homogeneous (QH) media can, display both spectral shifts and spectral switches. In our study, a pair of Young's pinholes is utilized to modulate spatial coherence of the incident plane wave before it interacts with the scatterer. The spectral shifts are found to be highly dependent of the scattering angle, the correlation length of scatterer and the Young's configuration parameter. Moreover, the spectral shifts can be converted from the red shift to blue one provided that the correlation length of scatterer is small enough. Derived results are confirmed by numerical simulations where influences of various factors on the spectrum are analyzed in detail.

Scattering of polychromatic light by a medium whose dielectric susceptibility is a random function of position is considered within the accuracy of the first Born approximation. It is shown, in particular, that if the two-point spatial correlation function of the dielectric susceptibility has Gaussian form and the spectrum of the incident light has a Gaussian profile, the spectrum of the scattered light may be shifted toward the shorter or the longer wavelengths, depending on the angle of scattering. The results are analogous to those derived recently in connection with radiation from partially coherent sources [ Nature (London)326, 363 ( 1987)].

The effect of the statistical properties of fluctuating light sources on the spectrum of the emitted radiation has been the subject of intense research over the last few years. It was first shown that due to spatial correlations, the spectrum of light was not, in general, invariant on propagation, even in free space.1 It was also shown that these effects can lead to shifts of spectral lines, a result which is of interest particularly for astrophysics.2 In view of the intimate connection between radiation from localized sources and scattering from media of finite extent, similar spectral changes may also be produced by scattering. In this paper a model scatterer is introduced, whose dielectric response function is a random function of space and time and whose space-time correlation function is a Gaussian function in all its variables. Using the first-order Born approximation, such scattering media are shown to generate frequency shifts of spectral lines that imitate the Doppler effect in its main features. The shifts may be arbitrarily large. Some numerical simulations of such shifts are presented and compared with Doppler shifts.

A theory is developed, valid within the accuracy of the first-order Born approximation, of the scattering of electromagnetic fields that applies under much more general conditions than do the current theories. The incident field is assumed to be statistically homogeneous and stationary, of arbitrary state of coherence, of arbitrary state of polarization, and to have arbitrary spectrum. The medium is assumed to be linear and spatially and temporally random, with the randomness being characterized by an ensemble that is statistically homogeneous, isotropic, and stationary. The analysis is not restricted to scattering from a medium in thermal equilibrium and applies in both off-resonance and near-resonance regions of the medium.

It was recently shown that, when light is scattered from a random medium whose response function (e.g., the dielectric susceptibility) has appropriate correlation properties, the spectrum of the scattered light may be frequency shifted with respect to the spectrum of the incident light.1,2 In general the relative frequency shifts produced by this mechanism will be different for different spectral lines. We show that under certain circumstances the relative shifts generated by scattering from appropriately correlated space-time fluctuations may become frequency independent and may be arbitrarily large. This scattering mechanism then imitates the Doppler effect, even though the source, the scattering medium, and the observer are at relative rest with respect to each other.