A one-phase Stefan problem in a layer of semitransparent medium

A numerical investigation of a one-phase Stefan problem with various boundary conditions in a layer of semitransparent medium is conducted. The significant influence of the optical properties of the medium and the illuminated surface on the generation of temperature fields and radiation flow densities has been demonstrated. Superheating of the specimen near the illuminated surface at the instant of the phase transition has been recorded. The article was translated by L. Vertgeim.     

A numerical approach to Stefan problem

A one-dimensional Stefan problem for a thin plate which is heated by laser pulses is solved by approximating the enthalpy formulation of the problem byC ⁰ piecewise linear finite elements in space combined with a semi-implicit scheme in time.Dedicated to the memory of Professor Jozef Kvasnica.     

光在吸收介质中传播的折射定律

光波在均匀非吸收介质中传播时振幅不衰减,在两种非吸收介质界面处产生折射现象,由几何光学中实数形式的光折射定律定量描述.而光波在均匀吸收介质中传播时,其振幅沿传播方向衰减,且其等振幅面与等相位面会发生分离.考虑吸收对光波传播特性的影响,本文回顾了复折射率的概念和复数形式的折射定律,据此对光波由吸收介质入射到吸收介质和光波由非吸收介质入射到吸收介质的两种情况进行了讨论,阐明了复数折射定律在具体问题讨论中的必要性和便利性,同时分析了实数形式和复数形式折射定律的关系.     

A numerical solution of the Stefan problem

A two-dimensional Stefan problem is solved for a prism and a cylinder by approximating the enthalpy formulation of the problem byC ⁰ piecewise linear finite elements in space combined with a semi-implicit scheme in time. The numerical integration in space makes the scheme easy to implement.This work was partially supported by GA CR grant No. 106/93/0638.     

On photoelastic stress measurements in optically absorbing medium

The effects of optical absorption in a photoelastic medium on the formation of the fringe patterns are studied by taking into account the stress-induced anisotropy of both the refractive index and the absorption coefficient. The propagation of optical waves in a dielectric solid under the influence of stress is formulated by incorporating complex elasto-optical tensor elements in the wave equation. The expression for optical transmission from the plane polariscope configuration consisting of an absorbing photoelastic specimen is derived using the Jones calculus formalism including complex optical retardation terms. It is observed that the photoelastic fringe fields are substantially modified due to these effects which must be considered for accurate interpretation of the experimentally obtained fringes.     

ATIR proximity sensing through an absorbing medium

In this paper we describe a new simple interferometric method for measurement of the thickness of a very thin quivette filled with absorbing liquid. The method is based on the interferometric restoration and analysis of both p- and s-components of the attenuated totally internal reflected (ATIR) field. Two different liquid samples were studied experimentally. The interferometric signal obtained by measurements is compared with the theoretical prediction.     

Apparent optical properties of spherical particles in absorbing medium

An apparent absorption efficiency for spherical particles in absorbing medium is introduced to take into account the non-exponential absorption of the near-field scattered radiation in the absorbing medium. The apparent extinction, which is the summation of the apparent scattering efficiency following previous studies and the apparent absorption efficiency, is the same as the actual extinction. These apparent optical properties are suited to radiative transfer equations.     

Mechanism for optical parametric generation in an absorbing medium

A theory that makes it possible to determine the parameter regions where amplification is observed in an absorbing medium and absorption is observed in an amplifying medium is constructed. In these regions stationary generation of a pair of symmetric modes can be established in an absorbing medium. Polychromatic pumping to other modes is the energy source. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 1, 19–24 (10 January 1996)     

Modelling of radiant-conductive heat transfer in the layer of semitransparent medium in approximation of the classical solution to the single-phase Stefan problem

The single-phase Stefan problem was modelled numerically in approximation of the classical solution in application to melting of a flat semitransparent sample by radiant-conductive technique in a wide range of emissivity of the phase transition front.     

双折射吸收非线性介质薄膜中倍频的产生

从二次谐波电场满足的波动方程出发，考虑到介质对二次谐波的吸收以及把完全边界条件应用于基频波和二次谐波在介质的入射面和出射面之间的反射效应，推导出了单光轴非线性薄膜介质中的二次谐波输出功率的计算式.结果表明：当采用复折射率的概念时，可以把非线性无吸收介质的二次谐波输出功率计算式应用到非线性吸收介质二次谐波输出功率计算式中去.     

Lorenz-Mie Theory for Spheres Immersed in an absorbing host medium

Light scattering by particles is often used to determine velocities or concentrations of particles in gaseous or liquid streams. Within the Lorenz-Mie theory, light scattering is well understood both for a single compact spherical particle and a single multilayered particle in a non-absorbing surrounding medium. However, in some cases of practical importance the Lorenz-Mie theory in its present form may fail to describe the scattering because the host medium is absorbing (e.g. water droplets in oil). In this case, a new treatment of the scattering theory is required. In previous work, solutions were obtained in the far-field of the scattering sphere. In this paper, a rigorous solution is derived from the calculation of the total absorption rate of the particle in the host medium, which is valid for all distances from the surface of the encapsulated particle. It is shown that it is necessary to consider finite sizes R of the integrating sphere when dealing with absorbing host media. Cross-sections are defined which are characteristic quantities not only for the particle, depending on the size of a conceptual sphere around the scatterer and the imaginary part of the refractive index of the host medium. The results obtained are discussed for the case of non-absorbing host media and in the far-field approximation. Some numerical examples are given which are also related to experimental results.     

Diffraction longitudinal multidomain structures in a layered nonlinearly absorbing medium

A method for measuring the composed phase parameter ?=Ψ₁+Ψ₂?2Ф₁ (where Ψ₁ and Ψ₂ are the phases of the mirror reflectances and Ψ₁ is the phase of the mirror transmittance) of dielectric mirrors with small absorption coefficients is proposed. This method is based on the use of the properties of a laser with a three-mirror cavity, and the mirror under study is the internal mirror of this cavity. It is shown that the value of the parameter Ψ, differing slightly from π, can be measured, and the results of the measurement are independent of the character of saturation of the laser active medium. The phase parameter was also measured for mirrors with reflectances below 0.8 by using an external method in which the interferometer with the mirror under study was placed outside of the laser cavity. It turned out that the intracavity laser method for measuring Ψ has a number of advantages and ensures an appreciably higher accuracy in measuring the parameter ε=Ψ?π than do extracavity techniques.     

Resonance scattering of canonical elastic shells in absorbing fluid medium

Resonance scattering of elastic spherical shell and cylindrical shell while the surrounding fluid medium has absorption is studied. The normal mode solution derived using exact elastic theory and the separation of variables is still applicable. However, the scattering form function has to be modified for the absorbing medium, otherwise the unreasonable result would be obtained. The backscattering form function in the absorbing medium is redefined, and the form function of elastic spherical and cylindrical shell with vacuum or solid matter filled is calculated in various absorption conditions. The results show that the absorption of surrounding fluid leads to notable attenuation of the coincidence resonances in the mid-frequency, but it has a little influence on the low-frequency resonance scattering induced by the filler inside the shell.     

双折射吸收非线性介质薄膜中倍频的产生

从二次谐波电场满足的波动方程出发,考虑到介质对二次谐波的吸收以及把完全边界条件应用于基频波和二次谐波在介质的入射面和出射面之间的反射效应,推导出了单光轴非线性薄膜介质中的二次谐波输出功率的计算式.结果表明：当采用复折射率的概念时,可以把非线性无吸收介质的二次谐波输出功率计算式应用到非线性吸收介质二次谐波输出功率计算式中去. 关键词： 非线性 倍频 二次谐波功率     

定时间步长变坐标步长差分求解单相Stefan问题

对单相Stefan问题提出了一种定时间步长、变坐标步长的差分求解方法.在固定时间步长内,以计算得到的移动界面位置作为网格节点的坐标,前后界面位置之差为空间步长,逐步地自动形成网格的划分,计算这些节点处的温度,从而获得下一时刻的移动界面的位置.