Focussing by a random phase screen

We present experimental measurements of the statistics of intensity scintillations in light scattered by a random phase screen. The phase screen was produced in the laboratory by turbulent mixing of hot and cold air; the parameters of this screen were such that geometrical focussing effects could be studied near the screen and speckle effects were clearly visible in the far field. Results are given for the propagation of both laser light and white light through the turbulent region. We compare experimental results with the theory for a phase screen with a gaussian phase correlation function. New theoretical work which allows comparison for mean-square phase fluctuation $\text{φ}{}^2$ å 1 is also outlined.     

Generalization of a scattering theorem for plane-stratified gyrotropic media

A previously derived eigenmode scattering theorem for plane-stratified gyrotropic media established that the scattering matricesS andS′, defined, respectively, in terms of a given and a conjugate set of eigenmode amplitudes, are mutually transposed, i.e. , the theorem being valid specifically for the incoming and outgoing eigenmodes ofgyrotropic bounding media. In this paper the theorem is extended to include linearly and circularly polarized base-modes in theisotropic media which may bound the multilayered, gyrotropic structure. Transformation of the eigenmode scattering matrix leads to a generalization of the scattering theorem to include base modes which are not necessarily eigenmodes of the medium. In the important special case in which the ambient magnetic field is parallel to the plane of the stratification, the scattering matrix is shown to have a special symmetry whose form depends on the base modes chosen (eigenmodes, linear modes or circular modes).     

Eigenmode scattering relations for plane-stratified gyrotropic media

We consider the 4×4 scattering matrixS for a plane wave incident on a plane-stratified gyrotropic multilayer slab, which is assumed to have a single symmetry axis (the magnetisation vector in a ferrite sheet, or the external magnetic field direction in a plane-stratified magnetoplasma). In the given (original) problem the plane of incidence is at an azimuthal angle ϕ with respect to the magnetic meridian plane (the plane containing the normal to the stratification, and the gyrotropic symmetry axis), and there is a corresponding “conjugate” set of wave fields, in which the plane of incidence is at an azimuthal angle (π−ϕ), with a corresponding conjugate scattering matrixS′. Adjoint wave fields, obtained by reversing the magnetic symmetry vector, are used to yield the eigenmode amplitudes required in the definition of the scattering matrices. At an interface between two adjacent layers the scattering matrices are shown to be uniquely determined by the characteristic wave polarisations, and this is used to prove that the given and conjugate scattering matrices,S andS′, for the overall multilayer system are mutually transposed, i.e. .     

Propagation of a Gaussian-beam wave through a random phase screen

Tractable analytic expressions are developed for a variety of basic statistical quantities involving a Gaussian-beam wave propagating through a random medium confined to a portion of the propagation path between input and output planes, the limiting case of which defines a thin random phase screen. For a plane wave incident on a phase screen located midway between input and output planes, it is well known that the statistics in the receiver plane are in close agreement with those associated with a plane wave propagating through an extended random medium between input and output planes. For a similar comparison between a phase screen and extended turbulence in the case of a Gaussian-beam wave at the input plane, the present analysis reveals that the phase screen must be positioned between input and output planes differently from the plane-wave case, the position being dependent upon the Fresnel ratio of the Gaussian beam. The analytic results developed in this paper for the thin phase screen model are based on the Kolmogorov power-law spectrum for refractive-index fluctuations and the Rytov approximation. Extension of these results to multiple phase screens is also discussed.     

Numerical solution for an inverse scattering problem of non-periodic rough surfaces

The paper presents the first results of a numerical study of inverse diffraction devoted to non-periodic rough surfaces in optics. Two kinds of rough surfaces are considered: first gratings with a finite number of grooves, and second random rough surfaces. For shallow surfaces, adequate Fourier theories have been employed with success. On the other hand, for deeper asperities, rigorous methods are needed and generally, the reconstruction of the profile is more difficult. For both Fourier and rigorous methods, the limit of resolution is studied numerically and numerous examples of reconstruction are given.Instituto Politecnico National, Escuela Superior de Fisica y Matematicas, Mexico, D.F., Mexico     

A monostatic inverse scattering model based on polarization utilisation

The solution of the inverse problem of electromagnetic scattering by smooth, convex shaped, perfectly conducting, 3-dimensional scatterers is analysed. Certain geometrical as well as physical-optics approximations were used to incorporate the concepts of the “Minkowski problem” of differential geometry into the space-time integral solution of electromagnetic scattering to yield the formal solution for the recovery of the surface profile of the scatterer from the scattered field data. Although various efficient solutions for target identification are available, still information contained in polarization-depolarization characteristics of the scatterer is not yet exploited to its full extent. Therefore the underlying assumption in this investigation was based on the fact that the “depolarization characteristics” of the scattered field do necessarily contain information regarding the surface profile of the scatterer.     

Acceleration of femtosecond pulses to superluminal velocities by Gouy phase shift

The phase and the group velocities are calculated in a three-dimensional neighbourhood of the focus of an aberration-free lens illuminated by a spatially Gaussian beam. The Gouy phase shift caused by the diffraction results in superluminal pulse propagation on the optical axis within the Rayleigh range.     

Analytical multiple scattering extension of the mie theory

Multiple scattering of light in aerosol is described in a simple picture within the framework of the Mie theory. Our approach leads to an analytical expression of the n-fold scattered electromagnetic field and then to a generalization of the optical parameters. The multiple scattering contributions are calculated avoiding the convergency and stability problems which are often encountered in standard numerical approaches. These problems occur due to the large number of events that have to be taken into account when large optical depths and/or a low signal to noise level exists. Such conditions are frequently encountered in atmospheric measurements.     

Non-Gaussian statistical models for scattering calculations

Abstract

In calculating the properties of waves scattered by random media it is almost always assumed that variations of the media constitute a joint Gaussian process. In this paper two alternative models are investigated. It is shown that whilst some features of the statistics of the scattered waves are more sensitive to the spectrum of the fluctuations in the medium than to the basic statistical model, in general significantly different properties are predicted using the alternative models.     

Non-Gaussian statistical models for scattering calculations

In calculating the properties of waves scattered by random media it is almost always assumed that variations of the media constitute a joint Gaussian process. In this paper two alternative models are investigated. It is shown that whilst some features of the statistics of the scattered waves are more sensitive to the spectrum of the fluctuations in the medium than to the basic statistical model, in general significantly different properties are predicted using the alternative models.