Diffuse reflection of light from a dense random medium using fibres dipped into the medium

Diffuse reflection of a narrow collimated light beam from a slab of a dense random medium is considered theoretically and experimentally for the case of the source and the detector fibres dipped into the random medium, as is the case for an endoscopic catheter. By use of the diffusion approximation, a simple and physically clear analytical expression is derived for the distribution of the diffuse reflectance of the light beam along the surface of the random medium slab. We include the effects of reflections from the top and bottom surfaces of the slab. The analytical expression derived predicts that, in the case of small absorption, the relative reflectance is a universal function defined by the geometrical parameters and is independent of specific properties of the random medium. The theoretical prediction is found to show good agreement with the results of measurements.     

Radiative transport in a planar medium exposed to azimuthally unsymmetric incident radiation

An analytical solution is developed for the radiation field engendered by illuminating an absorbing/anisotropically scattering planar medium with an azimuthally unsymmetric incident flux. The boundaries of the medium are allowed to possess both specular and diffuse reflection characteristics. The problem is mathematically reduced to solving a system of azimuthally independent equations which may be analyzed by many existing techniques. A solution scheme is formulated in terms of singular eigenfunctions and solved using a modified F_N method. Computations are performed for the azimuthally symmetric case of irradiation by parallel rays at oblique incidence. Several different phase functions are considered and results are presented for the discrete eigenvalues, the heat flux distributions within the medium, the reflectance and transmittance of the slab and the angular distribution of the intensities at the boundaries.     

Ponderomotive action of light in the problem of multiple scattering of light in a randomly inhomogeneous medium

The time correlation function of light reflected diffusely from a semi-infinite randomly inhomogeneous medium is calculated with allowance for the acceleration of the scatterers in the field of the laser beam incident on the medium. An analytical expression is found for the characteristic coherence time due to the ponderomotive action of light. It is shown that even with laser radiation power densities of the order of 1–10 W laser-acceleration effects substantially alter the character of the time autocorrelation function of the scattered light and must be taken into account in theoretical calculations. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 9, 611–615 (10 May 1998)     

On an integral equation arising in the transport of radiation through a slab involving internal reflection

In an earlier contribution to this journal [M.M.R. Williams, Eur. Phys. J. B 47, 291 (2005)], we derived an integral equation for the transmission of radiation through a slab of finite thickness which incorporated internal reflection at the surfaces. Here we generalise the problem to the case when there is a source on each face and the reflection coefficients are different at each face. We also discuss numerical and analytic solutions of the equation discussed in [M.M.R. Williams, Eur. Phys. J. B 47, 291 (2005)] when the reflection is governed by the Fresnel conditions. We obtain numerical and graphical results for the reflection and transmission coefficients, the scalar intensity and current and the emergent angular distributions at each face. The incident source is either a mono-directional beam or a smoothly varying distribution which goes from isotropic to a normal beam. Of particular interest is the philosophy of the numerical solution and whether a direct numerical approach is more effective than one involving a more elegant analytical solution using replication and the Hilbert problem. We also develop the solution of this problem using diffusion theory and compare the results with the exact transport solution. An erratum to this article is available at .     

FDTD analysis on the effect of plasma parameters on the reflection coefficient of the electromagnetic wave

In this paper, the dielectric constant of dispersive medium is written as rational polynomial function, and the relationship between D and E is derived in time-domain. It is named shift operator FDTD (SO-FDTD) method. Compared to the analytical solution, the high accuracy and efficiency of this method is verified by calculating the reflection coefficient of the electromagnetic wave through a cold plasma slab. The effect on reflection coefficient is calculated by using the SO-FDTD method. The result shows that some factors effect on reflection coefficient. They are as follows: plasma thickness, electron density, electron distribution and incident frequency. And on most conditions, parabola distribution helps reduce reflection coefficient more effectively than homogeneous distribution.     

Amplification by reflection from an active medium

The reflectance R of an active (inverted) medium is theoretically shown to be equal to the inverse of the Fresnel reflectance of an absorbing medium when the imaginary parts of the dielectric permeabilities of the active and the absorbing medium differ only in sign. The reflected wave is always amplified (R > 1). The phase shifts upon reflection at the active and the absorbing medium are equal. These results for monochromatic light presuppose a sufficient thickness of the active medium.     

On the refractive index for a nonmagnetic two-component medium: Resolution of a controversy

The refractive index of a dielectric medium comprising both passive and inverted components in its permittivity was determined using two methods: (i) in the time-domain, a finite-difference algorithm to compute the frequency-domain reflectance from reflection data for a pulsed plane wave that is normally incident on a dielectric half-space and (ii) in the frequency-domain, the deflection of an obliquely incident Gaussian beam on transmission through a dielectric slab. The dielectric medium was found to be an active medium with a negative real part for its refractive index. Thereby, a recent controversy in the scientific literature was resolved.     

Plane waves in a layered weakly dissipative randomly inhomogeneous medium

Abstract

In the framework of the embedding method the authors consider the stationary and non-stationary problem of a plane-wave incident on a randomly inhomogeneous medium. For the stationary problem there are three regions of sufficiently different behaviour of the wavefield intensity moments inside a weakly dissipative medium. For the non-stationary problem they succeeded in calculating the average intensity at t→+∞ by means of analytical prolongation of the stationary problem solution with respect to the absorption parameter. The time asymptotic of the averaged intensity on the boundary slab is also obtained for a finite-thickness slab.     

A simple model for diffuse reflection

Diffuse reflection from a matte nonabsorbing inhomogeneous medium such as white paint or paper can be described by a simple model in which light rays enter the volume of medium and then undergo a random walk until they reemerge from the surface. Lambert's law of diffuse reflection is an immediate consequence of the random walk. Another consequence of the volume interaction is that the light emerges from a different point than where it enters. This spreading of the light was measured for BaSO₄ white reflectance paint and for several kinds of paper. The random walk model implies a diffusion equation which makes predictions that are in reasonable agreement with the experiments. The spreading is proportional to an interaction length which, in this model, represents the range of distances that light rays penetrate before beginning their random walk.     

Determination of the final equilibrium radius and the increase in the emittance of a nonequilibrium relativistic electron beam during transport along an external magnetic field in a gas-plasma scattering medium

An equation describing the evolution of the transverse energy of a segment of a paraxial axisymmetric relativistic electron beam (REB) propagating in a gas-plasma scattering medium along an external magnetic field is used to find the equation relating the final equilibrium radius of the beam to its initial nonequilibrium value. An analytical expression for the increase in the mean-square emittance of an REB during transport up to achievement of the equilibrium state is found for the case considered. The dependence of the final equilibrium radius and the corresponding increase in the mean-square emittance on the density of the scattering medium and the induction of the external magnetic field is investigated. Pis’ma Zh. Tekh. Fiz. 67, 108–111 (July 1997)     

Reflection and transmission of strongly focused vector beams at a dielectric interface

The reflection and transmission of tightly focused azimuthally and linearly polarized electromagnetic wave beams with subwavelength spot size at a dielectric interface are investigated. A substantial increase of the reflectance of a light beam that is normally incident from a higher-index medium to a lower-index medium and a decrease of the reflectance of a beam that is incident from a lower-index medium to a higher-index dielectric medium in comparison with the Fresnel reflectance are predicted.     

Total internal reflection in gain medium slab

The problem of light propagation through a slab of gain medium is studied in terms of the transfer matrix pole distribution. Identifying the lasing by the existence of the poles in the upper half-space of the complex frequencies, we demonstrate that under the condition of total internal reflection lasing may be observed at a finite thickness of the slab; further increase in the thickness results in the quenching of lasing. However, in the latter case the amplification of reflected wave is possible.     

Propagation of Gaussian beams through parabolic index optical waveguides with random dielectric constant gradient

Abstract

The propagation of gaussian beams through parabolic index optical waveguides having random irregularities in the dielectric constant gradient has been studied. For fundamental mode propagation, the perturbation approach has been employed and an analytic expression for the loss of power from the fundamental mode has been obtained. For an incident gaussian beam with arbitrary width, geometrical optics approximation has been used and an exact analytical expression for the average value of the beamwidth has been derived for a particular random process, namely, the dichotomic Markov process. The fluctuations in the beamwidth have also been calculated.     

Diffuse waves in a random medium layer with rough boundaries

Abstract

The problem of scattering from a random medium layer with rough boundaries is formulated as an integral equation in which the random fluctuations are represented as a zero-mean random operator. The analysis for the diffuse fields is based on the ladder-approximated Bethe–Salpeter equation. An integral equation for the diffuse intensities thus derived displays the various multiple-scattering processes involved in our problem. Transport equations are also derived and several special cases are considered to illustrate the characteristics of the results and to compare them with those in the literature.     

Random lasing in porous scattering medium

The spectrum behavior evolution and the threshold of random lasing depending on the way of photon walk randomization in an active random medium were investigated. The following three ways of photon walk randomization were implemented: multiple light scattering by corundum and silica particles embedded into a solid polymer solution of dye (astrafloxin), multiple light reflection at sub-millimeter extensive air pores (mean diameter 200 μm) produced in the medium, and the combined action of both these effects. The most effective lasing is observed in the case of an active medium with air pores and scattering particles in the interpore space. Such a combined porous scattering medium acts as a network of dielectric waveguides transmitting effectively the random light. This spatial structure of the random active medium significantly increases the photon path in the medium, thereby promoting photon multiplication due to stimulated emission. In this combined medium the random lasing reveals the narrowest spectrum, the lowest threshold, and the highest density of spectral energy in the spectrum maximum.     

On the acoustic wave attenuation in a turbulent medium

Abstract

The equation for the mean acoustic field has been obtained for a random turbulent medium using the Green function approach. The correlation function was described by the Karman distribution with the index n=2 approximately?11/6. Applying Bourret's approximation, the exact expression for the mass operator has been calculated analytically. The frequency dependence of the scattering coefficient of the mean field has been derived. Conditions of Cherenkov radiation are discussed.     

Strong scattering of radio waves by a two-layered medium with a rough boundary

Radiowave scattering by a two-layered medium with a rough boundary is studied in the Kirchhoff approximation. We consider the case of oblique incidence of waves and mean square heights of the upper boundary roughnesses, which are nonsmall compared with the wavelength λ. An analytical expression and the conditions under which P₁ turns out to be large are derived for the term P₁ of the two-frequency correlation function P = (E_m(w₁)E_n(w₂)), which is proportional to the first degree of the coefficient of reflection from the lower boundary. Such effect is shown to emerge only for the resonant frequency relation. In particular, the following resonant relationship is written for the mirror reflection direction: w_2,1(√ε-sin²θ/cosθ-1), where θ is the incidence angle and ε is the layer permittivity. Research Institute of Physics, Rostov-on-Don, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 6, pp. 733–743, June, 1997.     

Positive and Negative Lateral Shifts from an Anisotropic Metamaterial Slab Backed by a Metal

The lateral shift of a light beam at the surface of an anisotropic metamaterial (AMM) slab backed by a metal is investigated. Analytical expressions of the lateral shifts are derived using the stationary-phase method, in the case that total reflection does and does not occur at the first interface. The sign of the lateral shift in two situations is discussed, and the necessary conditions for the lateral shift to be positive or negative are given. It is shown that the thickness and physical parameters of the AMM slab and the incident angle of the light beam strongly affect the properties of the lateral shift. Numerical results validate these conclusions. The lossy effect of the metamaterial on the lateral shift is also investigated.     

Albedo and gain threshold of a diffusive Raman random laser

The diffuse reflectance (albedo) and transmittance of a Raman random gain medium are derived from a diffusion equation with power dependent gain. The results show good agreement with the experimental data for barium nitrate powder. Both the Raman albedo A_R and Raman transmittance T_R diverge at a critical gain γ_c, interpreted as the threshold for diffusive Raman laser generation. The parametric dependence of the albedo and threshold gain on the scattering characteristics of the random medium is analysed and the feedback effect of Fresnel reflection at the gain boundaries evaluated. The addition of external mirrors, particularly at the pumped surface, significantly reduces the generation threshold.     

Joint moments of the wave beam amplitude and inverse power in an absorbing random medium with lens properties

Abstract

This paper presents a derivation of a system of closed equations for joint moments of the amplitude and inverse power of a wave beam propagating in a regularly inhomogeneous dissipative random medium. The radiation transfer in the medium is characterized by non-conservation of the total radiation energy flux and by the existence of power fluctuations. The statistics of the wave beam power fluctuations have been studied. Information on the power statistical characteristics is applied to close the system of equations for joint moments. For task parameters which are not very strict (an effective radius of the wave beam should be considerably less than the outer scale of the turbulence) a system of independent equations for arbitrary joint moments has been obtained. The equations for the first two lower joint moments of the beam intensity and inverse power have been solved analytically. With the solutions obtained the effective wave beam parameters were calculated, i.e. the beam mean displacement, effective broadening and tremble variance (the beam wandering variance) for the propagation of radiation in the refractive channel of an absorbing turbulent medium. Radically new characteristics of the behaviour of the effective parameters in random absorbing and transparent media have been revealed.