Monte Carlo simulation of photon migration path in turbid media

A new method of Monte Carlo simulation is developed to simulate the photon migration path in a scattering medium after an ultrashort-pulse laser beam comes into the medium.The most probable trajectory of photons at an instant can be obtained with this method.How the photon migration paths are affected by the optical parameters of the scattering medium is analyzed.It is also concluded that the absorption coefficient has no effect on the most probable trajectory of photons.     

Transient radiative transfer in participating media with pulse-laser irradiation—an approximate Galerkin solution

An assessment is made of the Galerkin technique as an effective method of solution for transient radiative transfer problems in participating media. A one-dimensional absorbing and isotropically scattering plane-parallel gray medium irradiated with a short-pulse laser on one of its boundaries is considered for the application of the method. The medium is non-emitting and the boundaries are non-reflecting and non-refracting. In the integral formulation of the problem for the source function, the time-wise variation of the radiation intensity at any point and in any direction in the medium is assumed to be the same as the time-wise variation of the average intensity at the same point as an approximation for the application of the method. The transient transmittance and reflectance of the medium are evaluated for various values of the optical thickness, scattering albedo and pulse duration. The results are in agreement with those available in the literature. It is demonstrated that the method is relatively simple to implement and yields accurate results.     

Canonical Quantization of Electromagnetic Field in the Presence of Nonlinear Anisotropic Magnetodielectric Medium with Spatial-Temporal Dispersion

Modeling a nonlinear anisotropic magnetodielectric medium with spatial-temporal dispersion by two continuum collections of three dimensional harmonic oscillators, a fully canonical quantization of the electromagnetic field is demonstrated in the presence of such a medium. Some coupling tensors of various ranks are introduced that couple the magnetodielectric medium with the electromagnetic field. The polarization and magnetization fields of the medium are defined in terms of the coupling tensors and the oscillators modeling the medium. The electric and magnetic susceptibility tensors of the medium are obtained in terms of the coupling tensors. It is shown that the electric field satisfy an integral equation in frequency domain. The integral equation is solved by an iteration method and the electric field is found up to an arbitrary accuracy.     

The Iterative-DRESOR method to solve radiative transfer in a plane-parallel, anisotropic scattering medium with specular-diffuse boundaries

Using the intensity with high directional resolution obtained by the Basic-DRESOR method as an initial guess, which is substituted into the integrated radiative transfer equation (IRTE), an iterative algorithm is proposed, called the Iterative-DRESOR method. This method can reduce the error levels of the intensity from several percent using the Basic-DRESOR method to a level of less than 1.0×10⁻⁶ with acceptable computation costs. The method is also validated against the exact heat flux in literature in some cases. It further clarifies some uncertain results for the reflectance in a pure, linearly anisotropic scattering medium with specular-diffuse boundaries. The directional distributions of intensity are obviously influenced by the reflecting modes of the boundary, especially in the zone near the boundary. The reflecting mode of an emitting boundary has little effect on the transmittance or reflectance. The reflecting mode of a non-emitting boundary also has little effect on the transmittance, but it obviously influences the reflectance. The difference between the reflectance for specular and diffuse boundaries increases at first, and then decreases, as the optical thickness of the medium increases. The difference will decrease as the scattering albedo of the medium increases, and it is negligible when the medium is pure scattering. The effect of the scattering phase function of the medium on the difference can also not be ignored. The Iterative-DRESOR method is expected to strengthen the capability of the Monte Carlo method to produce accurate results and to validate the results of other methods to solve RTE.     

Mode theory of plane Fabry-Pérot resonator with inhomogeneous active medium

A new method of the eigenvalue problem solution for a resonator with inhomogeneous active medium is given. The approach is based on Maxwell's wave equation and impedance boundary conditions of resonance-type at open resonator ends. A resonator equipped with mirrors in the form of infinite long strips is studied as an example. A rigorous solutions for the cases of stepped and bounded parabolic active medium profiles are obtained. Transcendental eigenvalue equations are investigated, distributions of field amplitude of active resonator modes are found. Asymptotic behavior of rigorous solutions is investigated. A multilayer approximation method is proposed for the eigenvalue problem solution for a resonator with an arbitrary gradient profile of active medium. The testing of this method was carried out with the rigorous solutions for the bounded parabolic profile.     

The evolution of polarization in an inhomogeneous birefringert,optically active medium

This note presents a method giving the change of polarization of an e.m. wave propagating in an inhomogeneous medium which is birefringent and optically active. The method has proved useful in a problem where the medium is a plasma with a magnetic field: it can be applied to other cases of interest, e.g. liquid crystals, as is here briefly discussed.     

Transient coupled heat transfer in a rectangular medium with black surfaces

The main objective of this paper is to extend to two-dimensional (2-D) medium the ray tracing-node analyzing method, which has already been successfully used to solve one-dimensional (1-D) problem of coupled heat transfer in a semitransparent medium. For simplicity, an infinitely long rectangular semitransparent medium with four black opaque surfaces is chosen as our studying object. A control volume method in the implicit scheme is adopted for discretizing the partial transient energy equation. In combination with spectral band model, the radiative heat source term is calculated using the radiative transfer coefficients (RTCs), which are deduced by the ray tracing method. The Partankar's linearization method is used to linearize the radiative source term and the opaque boundary condition, and the linearized equations are solved by the ADI method. Effects of absorption coefficient, refractive index and conductivity on transient cooling process in the 2-D gray rectangular medium are investigated under the condition that the radiation and convection processes cool one side of the rectangular medium while heat the remaining three sides.     

A finite difference method for a coupled model of wave propagation in poroelastic materials

A computational method for time-domain multi-physics simulation of wave propagation in a poroelastic medium is presented. The medium is composed of an elastic matrix saturated with a Newtonian fluid, and the method operates on a digital representation of the medium where a distinct material phase and properties are specified at each volume cell. The dynamic response to an acoustic excitation is modeled mathematically with a coupled system of equations: elastic wave equation in the solid matrix and linearized Navier-Stokes equation in the fluid. Implementation of the solution is simplified by introducing a common numerical form for both solid and fluid cells and using a rotated-staggered-grid which allows stable solutions without explicitly handling the fluid-solid boundary conditions. A stability analysis is presented which can be used to select gridding and time step size as a function of material properties. The numerical results are shown to agree with the analytical solution for an idealized porous medium of periodically alternating solid and fluid layers.     

Imaging through an inhomogeneous layer with an acoustic antenna array

A method is proposed for obtaining images through a layer of an inhomogeneous medium by using an antenna array scanning in angle or space. The method is based on the wave front inversion, which allows one to form an undisturbed sound field on the object of location in an inhomogeneous medium. This property makes it possible to suppress the effect of the thin inhomogeneous layer on the signals observed at the array output. The technique consists in a mutual processing of two received signals, one of which is obtained by locating the objects through the inhomogeneous medium and the other is obtained by locating the same objects, in the same medium, by the front-inverted wave. The mutual processing procedure consists in using the first received signal to form a filter for the second signal. The method is tested by a numerical simulation.     

The DRESOR method for radiative heat transfer in a one-dimensional medium with variable refractive index

This paper extends the DRESOR (Distribution of Ratios of Energy Scattered by the medium Or Reflected by the boundary surface) method to radiative transfer in a variable refractive index medium. In this method, the intensity is obtained from the source term along the curved integration paths determined only by the variable refractive index, and the DRESOR values are calculated by the Monte Carlo method in which the propagation of the energy bundles are affected by Snell's law. With given temperatures on the black boundaries of a one-dimensional medium, the temperature distribution inside the medium with a variable scattering property is calculated under the condition of radiative equilibrium. It is shown that the DRESOR method has a good accuracy in the cases studied. For an isotropic-scattering medium with the same optical thickness, the scattering albedo has no effect on the temperature distribution, which can be obtained from the general equations and can be seen as an extension of what exists for a constant refractive index; however, the different refractive index causes obvious changes in the temperatures inside the medium. The effect of anisotropic scattering on the temperature distribution cannot be ignored, although it is still weaker than the effect caused by variation in the refractive index.     

Refractive index sensitivity characteristic of long-period grating in holey fiber with dual-channel measuring method

Dual-channel measuring method based on long-period grating in holey fiber (LPHFG) is proposed, in which cladding mode interacts with medium filled in air holes and surrounding LPHFG simultaneously. Mode coupling properties and resonance spectral response of LPHFG are numerically investigated with respect to refractive index sensitivity characteristic to the variation of medium with dual-channel measuring method. It is proved that dual-channel measuring method can enhance the index sensitivity characteristic, which can be further improved by elaborately choosing appropriate cladding mode. Dual-channel measuring method provides an excellent alternative to the index-based sensors and detectors. Cladding mode in holey fiber with special radius is very sensitive to the variation of wavelength and medium, and it can turn into high-order or low-order cladding mode. The characteristics of cladding mode to wavelength and medium could be used to optimize the index-based sensor, and it also can be used in mode conversion.     

Excitation of Raman optical processes in an ultradispersed medium by radiation from a pulsed-periodic laser

A new method of taking Raman and two-photon-excited luminescence spectra in an ultradispersed medium is proposed. In this method, optical fibers serve to introduce an exciting radiation into and extract the secondary radiation from an ultradispersed medium placed in a cavity-type metallic cell. The spectra are initiated with a pulsed-periodic light source (copper vapor laser) and are recorded using a gating system. The contrast of the secondary radiation spectra is high with respect to the exciting radiation, allowing for molecular analysis of ultradispersed media by means of a single small-size monochromator.     

Method for eliminating the influence of the antenna — studied medium interface on accuracy in contact radiometric measurements of the medium temperature

We present the results of development of a method for eliminating the influence of an a priori unknown coefficient of reflection from the antenna — studied medium interface on accuracy of radiometric measurements of the medium temperature with the antenna contacting the medium. The method is based on modulation of receiver input noise and permits continuous automatic measurement of the reflection coefficient using the designed circuitry and algorithms for operating the radiometer and processing its output signal. Equations proving the efficiency of this method are obtained. The radiometer block diagram that realizes the proposed method is developed and a device for medical use is manufactured on its basis. Technical performance of the radiometer is given and test results of its measurement accuracy are presented.     

A Monte Carlo approach for the calculation of polarized light: application to an incident narrow beam

Monte Carlo approaches to compute multiple scattering of polarized light are examined. A Backward Monte Carlo (BMC) method is developed to solve the Stokes vector of the multiple scattered light for an inhomogeneous scattering medium with boundaries. A generalized form of the BMC method in vector notation is proposed. This method can determine the scattered light with sufficient accuracy in both intensity and polarization compared to the same calculation using the doubling-adding method for a plane parallel medium.For application to a narrow incident beam and an inhomogeneous medium, a modified BMC method is developed, borrowing a concept from the Forward Monte Carlo (FMC) method for the first scattering events. Furthermore, a modification of the total scattering matrix, i.e., the combination of the derived scattering matrix with its time inverse, is discussed. This BMC method can be used successfully for model calculations of lidar and other laser measurements of polarized light.     

Anderson localization and propagation of electromagnetic waves through disordered media

We have used the dynamic method to calculate the frequency dependence of the localization length in a disordered medium, using the amplitude change and the redshift of the spectral density of the propagating incident pulse. The frequency dependence of the localization length in an effectively one-dimensional disordered medium is computed in terms of the strength of the disorder. The results obtained with the dynamic method are confirmed by computing the same results using the transfer-matrix method.     

Analysis of oscillatory processes in lasers using the method of generalized eigenfunctions

The method of generalized eigenfunctions, which is used in the theory of diffraction, is applied to analyze stationary and narrow-band nonstationary processes in lasers. Using this method, one can avoid difficulties associated with integration of the eigenfunctions of an emitting system over the continuous spectrum, difficulties typical of the conventional frequency method. The method employs expansion in modes that are orthogonal inside the lasing medium. The problem of exponential growth of modes at infinity is eliminated. In addition, the field distribution inside the lasing medium is better described using the generalized eigenfunctions in a number of important cases.     

Propagation of ultrasonic waves in porous ceramics

Theoretical problems concerning the propagation of ultrasonic waves in a porous medium are outlined. The propagation velocity of longitudinal ultrasonic waves in an elastic medium with spherical gaseous inclusions is considered in detail. The calculation method adopted consists of determining equivalent elasticity moduli of the porous medium. The calculation of these moduli is based on the work of H. Mackenzie on media containing spherical gaseous inclusions of various diameters. The theoretical results obtained for the propagation velocity of ultrasonic waves, are compared with those measured on electrical porcelain, the latter constituting a model of a porous medium. Also a method allowing for the effect of composition of the porcelain mass to be taken into account, is described. The results of measurements of the propagation velocity of a longitudinal wave are found to be in good agreement with theoretical data. This conformity allows for non-destructive tests of products containing spherical gaseous inclusions.     

On the solution of a vectorial radiative transfer equation in an arbitrary three-dimensional turbid medium with anisotropic scattering

The authors developed a numerical method of the boundary-value problem solution in the vectorial radiative transfer theory applicable to the turbid media with an arbitrary three-dimensional geometry. The method is based on the solution representation as the sum of an anisotropic part that contains all the singularities of the exact solution and a smooth regular part. The regular part of the solution could be found numerically by the finite element method that enables to extend the approach to the arbitrary medium geometry. The anisotropic part of the solution is determined analytically by the special form of the small-angle approximation. The method development is performed by the examples of the boundary-value problems for the plane unidirectional and point isotropic sources in a turbid medium slab.     

Detection and Location of a Target in Layered Media without Prior Knowledge of Medium Parameters

Without prior knowledge of medium parameters, a method is proposed to detect and locate a target in layered media. Experiments were carried out for liquid/liquid and solid/liquid layered media, and the location of a target in them was obtained using three methods combined, i.e., the least-square method, the method of finding minimum dispersal degree of target distribution, and the snapshot time reversal and reverse time migration mixed method. The medium parameters, i.e., the acoustic velocities of upper and lower media as well as the thickness of the upper medium, were inversed simultaneously. The results show that the position of target is consistent with its actual position. Thus, the detection and location of a target in layered media are achieved without prior knowledge of medium parameters, and it overcomes the difficulty that the common time reversal method only detects the target, but cannot locate it.     

Motion of a group of microparticles in a viscoelastic medium under the action of acoustic radiation force

We theoretically and experimentally substantiate the method of detecting microcalcifications in mammary gland tissue. Calcium salts accumulate in soft tissues, primarily forming clusters of individual microparticles. We study the motion of solid microparticles distributed in a viscoelastic medium. Displacement of particles is caused by the radiation force occurring as a consequence of energy scattering and absorption of an ultrasound beam focused in the particle region. The radiation force acts over the course of 200 μs, after which the medium with distributed particles relaxes to the initial state. Motion of the medium is tracked by the cross-correlation method with short probing pulses following at a frequency of 5 kHz. The presence of solid microparticles leads to a change in the character of motion of the medium after pulsed ultrasound action. The amplitude and duration of displacements increases in comparison to the homogeneous medium, and the motion character itself becomes significantly complicated.