Three-dimensional vector radiative transfer in a semi-infinite, Rayleigh scattering medium exposed to spatially varying polarized radiation: generalized reflection matrix

Three-dimensional vector radiative transfer in a semi-infinite medium exposed to spatially varying, polarized radiation is studied. The problem is to determine the generalized reflection matrix for a multiple scattering medium characterized by a 4×4 scattering matrix. A double integral transform is used to convert the three-dimensional vector radiative transfer equation to a one-dimensional form, and a modified Ambarzumian's method is then applied to derive a nonlinear integral equation for the generalized reflection matrix. The spatially varying backscattered radiation for an arbitrarily polarized incident beam can be found from the generalized reflection matrix. For Rayleigh scattering and normal incidence and emergence, the generalized reflection matrix is shown to have five non-zero elements. Benchmark results for these five elements are presented and compared to asymptotic results. When the incident radiation is polarized, the vector approach used in this study correctly predicts three-dimensional behavior, while the scalar approach does not. When the incident radiation is unpolarized, both the vector and scalar approaches predict a two-dimensional distribution of the intensity, but the error in the scalar prediction can be as high as 20%.     

Emergent intensity from a plane-parallel medium exposed to a Gaussian laser beam: A comparison of Rayleigh and isotropic scattering

The focus of this two-dimensional study is the radially varying intensity emergent from a plane-parallel scattering medium exposed to a collimated, Gaussian laser beam directed perpendicular to the upper surface. The method of analysis is the integral transform technique. Specifically, this work uses the generalized reflection and transmission functions from a previous study to construct the emergent intensity with the use of an inverse Hankel transform. Radially varying backscattered and transmitted intensities are calculated for media with isotropic and Rayleigh scattering phase functions and optical thicknesses that range from 0.125 to 8.0. The behavior of the emergent radiation inside and outside the beam is investigated for both narrow and wide beams. A new integration method is implemented to compute the emergent intensity at the beam center. The emergent intensity at the beam center is used to quantify when a one-dimensional model may be used. As expected, for small optical thicknesses and near the beam the phase function has significant influence, while far from the beam multiple scattering reduces the influence of the Rayleigh phase function. Results from this study will be useful in understanding and interpreting more complicated situations, such as those that include polarization.     

Three-dimensional radiative transfer in an anisotropically scattering, plane-parallel medium: generalized reflection and transmission functions

The problem of spatially varying, collimated radiation incident on an anisotropically scattering, plane-parallel medium is considered. A very general phase function is allowed. An integral transform is used to reduce the three-dimensional radiative transport equation to a one-dimensional form, and a modified Ambarzumian's method is applied to derive nonlinear integral and integro-differential equations for the generalized reflection and transmission functions. The integration is over the polar and azimuthal angles—this formulation is referred to as the double-integral formulation. The integral equations are used to illustrate symmetry relationships and to obtain single- and double-scattering approximations. The generalized reflection and transmission functions are important in the construction of the solutions to many multidimensional problems. Coupled integral equations for the interior and emergent intensities are developed and, for the case of two identical homogeneous layers, used to formulate a doubling procedure. Results for an isotropic and Rayleigh scattering medium are presented to illustrate the computational characteristics of the formulation.     

Oscillator strengths of optical transitions of a cylindrical shell: Crossed static electric and magnetic fields

The single-electron eigenstates of a cylindrical shell are determined as functions of the applied crossed electric and magnetic fields in the effective-mass approximation. The system considered consists of donor charges taken to be uniformly distributed within an inner core of infinitely long length. The core is concentrically enveloped by a semiconducting material of finite thickness; which is essentially the host material. This configuration of the donor charges sets up a spatially varying electric field nonetheless with only the radial component. In addition, a uniform magnetic field is applied parallel to the axis of symmetry of the inner core. As is well known, the axial applied magnetic field lifts the double degeneracies of the electron’s subbands characterized by the same azimuthal quantum numbers which differ only in sign. The main effect of increasing the external electric field is to elevate the various energy subbands, more or less to the same extent, to higher values. Further, evaluations of the oscillator strengths of optical transitions of the cylindrical shell are carried out within the dipole approximation. The radiation field is taken to be that of circularly polarized light incident along the axis of the core. The oscillator strengths of optical transitions are found to increase with an increase of the applied magnetic field, particularly in the regime of small magnetic fields. In contrast, the oscillator strengths of these optical interactions become suppressed as the donor charge density is increased.     

Efficient extracavity generation of radially and azimuthally polarized beams

We demonstrate an efficient transformation of a linearly polarized Gaussian beam to a radially or an azimuthally polarized doughnut (0,1)* Laguerre-Gaussian beam of high purity. We use a spatially variable retardation plate, composed of eight sectors of a lambda/2 retardation plate, to transform a linear polarization distribution to radial/azimuthal distribution. We transformed an Nd:YAG Gaussian beam with M(2)=1.3 to a radially and azimuthally polarized (0,1)* Laguerre-Gaussian beams with M(2)=2.5 and degree of radial/azimuthal polarization of 96-98%.     

Three-dimensional radiative transfer in an anisotropically scattering, semi-infinite medium: generalized reflection function

Three-dimensional radiative transfer in an anisotropic scattering medium exposed to spatially varying, collimated radiation is studied. The generalized reflection function for a semi-infinite medium with a very general scattering phase function is the focus of this investigation. An integral transform is used to reduce the three-dimensional transport equation to a one-dimensional form, and a modified Ambarzumian's method is applied to formulate a nonlinear integral equation for the generalized reflection function. The integration is over both the polar and azimuthal angles; hence, the integral equation is said to be in the double-integral form. The double-integral, reflection function formulation can handle a variety of anisotropic phase functions and does not require an expansion of the phase function in a Legendre polynomial series. Complicated kernel transformations of previous single-integral studies are eliminated. Single and double scattering approximations are developed. Numerical results are presented for a Rayleigh phase function to illustrate the computational characteristics of the method and are compared to results obtained with the single-integral method. Agreement between the two approaches is excellent; however, as the transform variable increases beyond five the number of quadrature points required for the double-integral method to produce accurate solutions significantly increases. A new interpolation scheme produces accurate results when the transform variable is large.     

Three-dimensional radiative transfer in an isotropically scattering, semi-infinite medium: generalized reflection function

The focus of this study is the generalized reflection function of multidimensional radiative transfer. The physical situation considered is spatially varying, collimated radiation incident on the upper boundary of an isotropically scattering, semi-infinite medium. An integral transform is used to reduce the three-dimensional transport equation to a one-dimensional form, and a modified Ambarzumian's method is applied to formulate a nonlinear integral equation for the generalized reflection function. The resulting equation is said to be in double-integral form because the integration is over both angular variables. Computational issues associated with this generalized reflection function formulation are investigated. The source function and reflection function formulations are compared, and the relative merits of the two approaches are discussed.     

激光辐照猫眼光学镜头时的反射特性机理研究

运用矩阵光学理论以及将硬边光阑窗口函数展开为有限个复高斯函数之和的方法, 对激光束辐照猫眼光学镜头时产生的猫眼效应机理进行了理论推导. 通过数值计算对猫眼效应的反射规律进行了分析, 并利用532nm激光辐照一个变焦范围为12—72mm的光学镜头进行了猫眼效应的实验验证, 从而得出了猫眼效应反射光特性与入射激光参数以及猫眼光学镜头的口径、焦距、离焦量等基本参数之间的关系. 研究表明, 猫眼效应反射光特性与猫眼光学镜头参数和入射激光参数密切相关, 且当猫眼光学镜头位于近场和远场的情况有很大不同. 根据入射光束 关键词： 猫眼光学镜头 猫眼效应 高斯光束 反射特性     

Simple parametric representations of the polarization optical properties of birefringent biological tissues in reflection polarization spectroscopy

The use of polarization reflection spectroscopy for investigating complex scattering media, including orientationally ordered optically anisotropic elements, requires a special choice of output parameters (represented by spectra) that characterize polarized light scattering by objects under study because the standard characteristics, such as the Mueller matrices, depend on the azimuthal orientation of the medium. We propose compact and convenient sets of experimentally determined output parameters that involve separate detection of co- and cross-polarized components of light scattered by a sample irradiated by a normally incident linearly polarized beam and include characteristics invariant with respect to the azimuthal rotation of the sample.     

A high-efficient method for generating radially and azimuthally polarized Bessel beams using biaxial crystals

As was shown previously, in propagation of a circularly polarized Bessel light beam along the optical axes of a biaxial crystal, there takes place the conversion of the order of Bessel function. In this paper, a new result is presented which is obtained by varying the polarization state of an input beam. Namely, a linearly polarized beam can be transformed into a beam with the radial or azimuthal polarization state. At that the order-transformation also occurs. The switching between radial and azimuthal polarization states of the output beam is performed by the proper switching between two orthogonal linear polarization states of the input beam. The efficiency of polarization conversion is high and can be practically full at an appropriate choice of the cone angle of the input beam or crystal length.     

Quasi-stationary stage of a nonequilibrium optical discharge in the field of a Bessel wave beam

The self-consistent stationary distributions of the field and plasma produced by Bessel wave beams in a gas with the ionization and Kerr nonlinearities are studied analytically. Using a stationary model based on the condition of a constant field amplitude in the ionized region, the structures are considered to be formed by Bessel beams of two types: with an azimuthal electric field equal to zero at the symmetry axis and a quasitrans-verse field having a maximum at the axis. A specific feature of the plasma channel formed in the first case is the presence of a nonionized region in its central part (tubular discharge), whose radius is independent of the incident power. In the second case, the channel is continuous. The relation is found between the incident radiation power and the external radius of the discharge. It is shown that the Kerr nonlinearity, which is especially important at small divergence angles of the beam, enhances the maximum plasma density and reduces the discharge radius. The parameters of plasma structures produced upon focusing a Gaussian beam by a conical lens are estimated using the model proposed.     

Material processing with pulsed radially and azimuthally polarized laser radiation

We report on the generation of radially and azimuthally polarized Q-switched laser radiation and its application in material processing. The power levels were sufficiently high to study micro-hole drilling in different metals. Depending on the optical properties of the metal, either radial or azimuthal polarization shows the best efficiency and the effect is attributed to waveguiding. For steel, a comparison to linearly or circularly polarized laser radiation indicates that the doughnut-shaped beam with azimuthal polarization is the most energy-efficient in producing holes of the same diameter and depth. PACS 79.20.Ds; 29.27.Hj; 81.05.Bx     

Formation of elliptically polarized ring-shaped electric field structures on the self-focusing of light in an isotropic medium featuring a spatially disperse nonlinearity

The possibility is demonstrated that the self-focusing of an elliptically polarized beam in a medium featuring a spatially disperse cubic nonlinearity can give rise to several radially symmetric ring-shaped regions of the same sense of rotation (right or left) of the electric-field vector in the cross-section of the beam. The formation dynamics and propagation features of such electric field structures are studied for various parameters of the incident radiation and nonlinear medium.     

High-efficiency frequency-modulation non-redundant scanning of a light beam in a half space

It is shown that a large fraction of the energy of the impinging light beam on a parallel plate grating can be injected into only one transmitted order, which is not the zeroth transmitted order, when the incident angle of the beam and the refractive indices of the lossless dielectric bounding media satisfy the condition of total reflection. This signififies that non-redundant scanning of the radiation transmitted through the grafting can be obtained by varying the frequency of the incident radiation with little of the incident energy being scattered into the reflected orders.     

Diffraction of X-ray spatially inhomogeneous beam in a crystal with cubic nonlinearity

Diffraction of a spatially inhomogeneous X-ray wave was theoretically studied in a crystal with cubic nonlinear response to the strength of an external electric field. Using numerical calculations in case of two-beam diffraction of a narrow incident beam, the intensity distributions on the output surface of the crystal was investigated depending on the thickness and intensity of the incident beam. The results of numerical calculations of integral (spatial) coefficients of transmission and reflection are given as functions of incident wave intensity for fixed thickness of the crystal.     

Nonlinear reflection of a femtosecond spectral supercontinuum

The spatio-temporal spectrum of optical radiation reflected from a nonlinear dielectric medium with nonresonant dispersion is obtained as a function of the parameters of the spatio-temporal spectrum of a paraxial light beam incident on the boundary of the medium at small angles. Nonlinear reflection of various types of femtosecond spectral supercontinua from the interface between air and fused silica is simulated. It is shown that the time duration and the transverse dimensions of a beam of multiple-frequency radiation generated during the reflection of a superposition of high-intensity fields of two few-cycle pulses with different central wavelengths may be smaller than those of incident ultrashort pulses.     

Multichannel high extinction ratio polarized beam splitters based on metasurfaces

Separating lights into different paths according to the polarization states while keeping their respective path's polarizations with high purification is keen for polarization multiplex in optical communications. Metallic nanowire gratings with multi-slits in a period are proposed to achieve polarized beam splitters(PBSs) in reflection and diffraction. The setting of multi-slits largely reduces the reflection of photons with a transverse magnetific field via the plasmonic waveguiding effect, which leads to highly polarized output lights with extinction ratio larger than 20 dB in each channel. The proposed reflection/diffraction PBSs enrich the approaches to control the polarization states with the advantages of wide incident angles and flexible beam splitting angles.     

Vectorial laws of refraction and reflection using the cross product and dot product

We demonstrate that published vectorial laws of reflection and refraction of light based solely on the cross product do not, in general, uniquely determine the direction of the reflected and refracted waves without additional information. This is because the cross product does not have a unique inverse operation, which is explained in this Letter in linear algebra terms. However, a vector is in fact uniquely determined if both the cross product (vector product) and dot product (scalar product) with a known vector are specified, which can be written as a single equation with a left-invertible matrix. It is thus possible to amend the vectorial laws of reflection and refraction to incorporate both the cross and dot products for a complete specification with unique solution. This enables highly efficient, unambiguous computation of reflected and refracted wave vectors from the incident wave and surface normal.     

Approximate solution for describing polarization characteristics of radiation in a Rayleigh scattering medium

An approximate analytical solution for the 4 × 4 Green’s matrix of the problem of polarized radiation transfer in a plane-parallel layer of an absorptive Rayleigh scattering medium is proposed. It permits one to perform fast estimates of angular distributions of the Stokes parameters that are created by an incident beam with an arbitrary polarization state at different levels in a layer when the layer thickness, absorption magnitude, and albedo of the underlying surface are varied. The developed solution is compared with data obtained by the numerical doubling method. The value of the scattering coefficient for a circularly polarized radiation is shown to be somewhat smaller than that for linearly polarized radiation.     

慢波介质自由电子激光器

本文采用一维流体模型导出了慢波介质自由电子激光器的线性色散方程,建立了电子和波相互作用的同向回旋同步机理和反向回旋同步机理.