Shendeleva Margarita L
Photonic Processes Department, Institute of Physics, 46 Prospect Nauki, Kiev 03028, Ukraine.
J Opt Soc Am A Opt Image Sci Vis. 2010 Jul 1;27(7):1521-8. doi: 10.1364/JOSAA.27.001521.
The photon migration in two semi-infinite highly scattering media with different refractive indices is studied in the diffusion approximation for two sets of boundary conditions at the interface. In commonly used boundary conditions, the ratio of the intensity (fluence rate) to the squared refractive index is assumed continuous across an interface and the normal component of flux is required to be continuous. However, a more rigorous approach shows that the boundary condition for the intensity may be different. As was shown by Aronson [J. Opt. Soc. Am. A12, 2532 (1995)], the ratio of the intensity to the squared refractive index undergoes a jump across an interface that is proportional to the diffuse flux. A diffusion model with an instantaneous point source that can be solved analytically for both sets of boundary conditions is considered. The analytical solutions are derived and compared with the results of Monte Carlo simulations that take into account the reflections and refractions at the interface according to Fresnel's formulas. It is shown that the analytical solutions with the Aronson boundary condition for intensity match the Monte Carlo results better than the solutions with a continuous ratio of the intensity to the squared refractive index.
在扩散近似下，针对界面处的两组边界条件，研究了光子在两种具有不同折射率的半无限高散射介质中的迁移情况。在常用的边界条件中，强度（通量率）与折射率平方的比值被假定在界面处连续，且通量的法向分量需保持连续。然而，一种更为严格的方法表明，强度的边界条件可能有所不同。正如阿隆森[《美国光学学会志A》12, 2532 (1995)]所指出的，强度与折射率平方的比值在界面处会发生跃变，该跃变与漫射通量成正比。考虑了一个具有瞬时点源的扩散模型，该模型对于两组边界条件均可解析求解。推导了解析解，并与根据菲涅耳公式考虑界面处反射和折射的蒙特卡罗模拟结果进行了比较。结果表明，采用阿隆森强度边界条件的解析解比强度与折射率平方比值连续的解与蒙特卡罗结果的匹配度更高。
