Theory of transfer with delay for trapping of nonstationary acoustic radiation in a resonant randomly inhomogeneous medium

The propagation of a quasimonochromatic wave packet of acoustic radiation in a discrete randomly-inhomogeneous medium under the condition that the carrier frequency of the packet is close to the resonance frequency of Mie scattering by an isolated scatterer is studied. The two-frequency Bethe-Salpeter equation in the form of an exact kinetic equation that takes account of the accumulation of the acoustic energy of the radiation inside the scatterers is taken as the initial equation. This kinetic equation is simplified by using the model of resonant point scatterers, the approximation of low scatterer density, and the Fraunhofer approximation in the theory of multiple scattering of waves. This leads to a new transport equation for nonstationary radiation with three Lorentzian delay kernels. In contrast to the well-known Sobolev radiative transfer equation with one Lorentzian delay kernel, the new transfer equation takes account of the accumulation of radiation energy inside the scatterers and is consistent with the Poynting theorem for nonstationary acoustic radiation. The transfer equation obtained with three Lorentzian delay kernels is used to study the Compton-Milne effect—trapping of a pulse of acoustic radiation diffusely reflected from a semi-infinite resonant randomly-inhomogeneous medium, when the pulse can spend most of its propagation time in the medium being “trapped” inside the scatterers. This specific albedo problem for the transfer equation obtained is solved by applying a generalized nonstationary invariance principle. As a result, the function describing the scattering of a diffusely reflected pulse can be expressed in terms of a generalized nonstationary Chandrasekhar H-function, satisfying a nonlinear integral equation. Simple analytical asymptotic expressions are found for the scattering function for the leading and trailing edges of a diffusely reflected δ-pulse as functions of time, the reflection angle, the mean scattering time of the radiation, the elementary delay time, and the parameter describing the accumulation of radiation energy inside the scatterers. These asymptotic expressions demonstrate quantitatively the retardation of the growth of the leading edge and the retardation of the decay of the trailing edge of a diffusely reflected δ-pulse when the conventional radiative transfer regime goes over to a regime of radiation trapping in a resonant randomly-inhomogeneous medium. Zh. éksp. Teor. Fiz. 113, 432–444 (February 1998)     

K. Schwarzschild's problem in radiation transfer theory

We solve exactly the problem of a finite slab receiving an isotropic radiation on one side and no radiation on the other side. This problem—to be more precise the calculation of the source function within the slab—was first formulated by K. Schwarzschild in 1914. We first solve it for unspecified albedos and optical thicknesses of the atmosphere, in particular for an albedo very close to 1 and a very large optical thickness in view of some astrophysical applications. Then we focus on the conservative case (albedo=1), which is of great interest for the modeling of grey atmospheres in radiative equilibrium. Ten-figure tables of the conservative source function are given. From the analytical expression of this function, we deduce (1) a simple relation between the effective temperature of a grey atmosphere in radiative equilibrium and the temperature of the black body that irradiates it, (2) the temperature at any point of the atmosphere when it is in local thermodynamical equilibrium. This temperature distribution is the counterpart, for a finite slab, of Hopf's distribution in a half-space. Its graphical representation is given for various optical thicknesses of the atmosphere.     

A derivation of the radiation transfer theory for random media

The wave propagation in a medium with randomly varying material parameters is considered. Starting from a quite general form of the Bethe-Salpeter equation for the two-point moment of the field, a spectral balance equation is derived. In a first step, a Wigner transformation is carried out which converts the two-point moment into a function depending on position, time, wave vector and frequency. Then, for wavelengths which are long compared to the correlation length of the medium, this function is split up into a relevant part and a background. Eliminating the background leads to the usual radiation transfer theory and provides us a general and concise expression for the effective scattering in terms of the effective operators involved in the Bethe-Salpeter equation. In the case of weak heterogeneity, the result reduces to those previously obtained.     

Aerosol backscattering of intensity-modulated optical radiation

The modulation factor of intensity-modulated radiation scattered by aerosol particles is investigated. It is shown that if the optical fields scattered by individual particles interfere at the photodetector, the modulation of the received signal will be preserved. It is shown experimentally that the modulation factor of the scattered radiation decreases with increasing diameter of the receiving aperture.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 53–58, December, 1979.     

Radiative transfer theory with time delay for the effect of pulse entrapping in a resonant random medium: General transfer equation and point-like scatterer model

Abstract

A pulse propagation of a vector electromagnetic wave field in a discrete random medium under the condition of Mie resonant scattering is considered on the basis of the Bethe–Salpeter equation in the two-frequency domain in the form of an exact kinetic equation which takes into account the energy accumulation inside scatterers. The kinetic equation is simplified using the transverse field and far wave zone approximations which give a new general tensor radiative transfer equation with strong time delay by resonant scattering. This new general radiative transfer equation, being specified in terms of the low-density limit and the resonant point-like scatterer model, takes the form of a new tensor radiative transfer equation with three Lorentzian time-delay kernels by resonant scattering. In contrast to the known phenomenological scalar Sobolev equation with one Lorentzian time-delay kernel, the derived radiative transfer equation does take into account effects of (i) the radiation polarization, (ii) the energy accumulation inside scatterers, (iii) the time delay in three terms, namely in terms with the Rayleigh phase tensor, the extinction coefficient and a coefficient of the energy accumulation inside scatterers, respectively (i.e. not only in a term with the Rayleigh phase tensor). It is worth noting that the derived radiative transfer equation is coordinated with Poynting's theorem for non-stationary radiation, unlike the Sobolev equation. The derived radiative transfer equation is applied to study the Compton–Milne effect of a pulse entrapping by its diffuse reflection from the semi-infinite random medium when the pulse, while propagating in the medium, spends most of its time inside scatterers. This specific albedo problem for the derived radiative transfer equation is resolved in scalar approximation using a version of the time-dependent invariance principle. In fact, the scattering function of the diffusely reflected pulse is expressed in terms of a generalized time-dependent Chandrasekhar H-function which satisfies a governing nonlinear integral equation. Simple analytic asymptotics are obtained for the scattering function of the front and the back parts of the diffusely reflected Dirac delta function incident pulse, depending on time, the angle of reflection, the mean free time, the microscopic time delay and a parameter of the energy accumulation inside scatterers. These asymptotics show quantitatively how the rate of increase of the front part and the rate of decrease of the rear part of the diffusely reflected pulse become slower with transition from the regime of conventional radiative transfer to that of pulse entrapping in the resonant random medium.     

Nonlocal theory of stimulated Raman backscattering in a strongly magnetized plasma

A nonlocal theory of stimulated Raman backscattering (BSRS) parametric instability of a large amplitude electromagnetic (EM) mode in a strongly magnetized plasma e.g., one encountered in a plasma filled backward wave oscillator, is reported. The EM mode is unstable to parametric instability in a magnetized plasma and decays into a Trivelpiece-Gould (TG) mode and a sideband EM mode. The growth rate of instability (Γ) scales proportional to three-fourth power of plasma density. For a typical BWO the growth rate is ∼10⁸ s^-1     

Divergences in a nonsteady universe

The structure of divergences of the vacuum mean energy-momentum tensor is investigated by a simple model (a linear massive scalar field with nonconformal coupling in a spatially plane isotropic universe). The class R of physically permissible vacuums [0> is isolated; when∥0>?R the tensor contains only standard local (power-law and logarithmic) divergences; in the general case the condition that the Hamiltonian be diagonal and the “quantum equivalence principle” lead to ∥0>?R . The nongeometric structure of power-law divergences, which does not allow their elimination by renormalization of the constants in the generalized gravitational action, is established by a new regularization method (covariant smoothing of a δ-function). It is shown that all local divergences are eliminated by renormalization according to the Pauli-Villars scheme; it gives the same final results as do the adiabatic and n-wave computational procedures.     

The interference component of low-coherent radiation backscattering

An interference component of backscattering of low-coherent radiation is calculated for the first time based on the previously developed approach consisting of direct simulation of the Bethe-Salpeter equation in terms of the Monte Carlo method. It is shown that, upon an increase in the spatial coherence length, it plays the role of the characteristic scale of the backscattering instead of the transport length. The effect of localization of backscattering of an ultrashort pulse in relation to the penetration depth is revealed. Both the theory and the numerical simulation predict, in accordance with experiment, a considerable broadening of the peak of coherent backscattering with decreasing coherence length, which significantly extends the application field of the effect, especially in biomedical diagnostics.     

Coherent backscattering under conditions of pulsed radiation trapping

Coherent backscattering of pulsed radiation emitted by optically dense atomic ensembles is considered. The diagrammatic technique is used for deriving analytic expressions for correlation functions of scattered light, which make it possible to take into account all main factors affecting the dynamics of the process, including the hyperfine and Zeeman structure of the ground and first excited states of atoms, polarization of probe radiation, the actual shape and size of an atomic cloud, its spatial inhomogeneity, motion of atoms, and angular-momentum polarization of atoms. On the basis of these relations, the time dependence of the total intensity and the dependence of enhancement factor of backscattered light on the pulse duration, type of polarization of the polarization system of observation, optical thickness of the scattering medium, and the carrier frequency of the pulse are investigated. The calculations are performed for an ensemble of rubidium-85 atoms cooled in magnetooptical traps.     

On the theory of light and atomic backscattering in the Bose-Einstein condensate of a dilute gas

A semiclassical theory of light scattering from a Bose-Einstein condensate of a dilute gas is developed. It is shown that the results of theoretical calculations are in qualitative agreement with the data obtained from recent experiments on the observation of atoms scattered in the backward direction with respect to the direction of a pump laser beam. It is demonstrated that there can arise a field that propagates in the backward direction and whose intensity exceeds the intensity of conventional Rayleigh scattering.     

On the theory of transition radiation in a waveguide

The transition radiation from a particle that intersects the waveguide perpendicular to its axis is considered. The expressions are derived for the radiation fields and intensities. The example of a rectangular waveguide is used to investigate the properties of the radiation, and the conditions which determine the Vavilov-Cerenkov radiation spectrum are derived.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 15, No. 2, pp. 191–195, February, 1972.     

Effect of backscattering on the behavior of a dye ring laser

The effect of backscattering on the behavior of a dye ring laser is investigated by photoelectric counting measurements. It is found that there exist two laser regimes, a low backscattering regime in which the laser exhibits meta-bistability and random mode switching, and a high backscattering regime in which switching is suppressed. In the latter case the photon statistics are similar to those of a single-mode standing wave dye laser.     

Time-dependent radiation transfer in a semi-infinite stochastic medium with Rayleigh scattering

The time-dependent radiation transfer in a semi-infinite stochastic medium of binary Markovian mixture with Rayleigh scattering is presented. A formalism, developed to treat radiation transfer in statistical mixtures, is used to obtain the ensemble-averaged solution. The average reflectivity, radiant energy and net flux are computed for specular-reflecting boundary. For the sake of comparison, we use two different weight functions in our calculations.