Pulse Laser Radiation Transfer: Monte Carlo Simulation and Comparison with Experiment

A three-dimensional Monte Carlo simulation of transient radiative transfer is performed for short pulse laser transport in scattering and absorbing medium. Experimental results of a 60 ps pulse laser transmission in scattering medium are presented and compared with simulation. Good agreement between the Monte Carlo simulation and experimental measurement is found. The refractive index of the scattering particles is found to influence strongly the prediction of transmitted pulse shape. Scaled isotropic scattering modeling is shown to be not sufficient in transient radiative transfer. INTRODUCTION The study of pulsed laser radiation transfer in strongly scattering medium has received increasing attention during the past few years, partly as a result of its wide applications to medical diagnosis and thermal therapy [1,2], remote sensing [3], and laser material processing of microstructures [1,4]. With the laser pulse width in the picosecond to femtosecond range, the time-dependence of radiative transport must be incorporated and transient radiation transfer formulated for such kinds of systems is salient. The propagation of light in optically dense random media is characterized by multiple scattering, so that the diffusion approximation was often used to describe the transient radiation transport [5]. However, recent studies have demonstrated that the diffusion approximation fails to fully describe the backscattering light, because such light is compromised of a significant contribution of multiply scattered modes whose path lengths are comparable to the transport mean free path [6]. It also failed to describe transmitted light in some other experimental studies [7]. Very few studies have addressed transient radiative transfer by considering the fully transient radiative transfer equation. Kumar and Mitra [8] and Kumar et al. [9] are among the first to consider the entire transient radiative equation by using a variety of models for short-pulse applications. Previously, transient radiative transfer equation with a source of constant strength at the boundaries using Laplace transform and adding-doubling methods had been solved by Rackmil and Buckius [10]. Recently, Mitra et al. [11] solved wave-like transient radiative transfer equation using the P1 approximation for a boundary-driven two-dimensional problem. Guo and Kumar [12] evaluated the scaled isotropic scattering results with the anisotropic scattering in transient radiative transfer. Tan and Hsu [13] developed integral equation formulation for transient radiative transfer. Monte Carlo (MC) methods have been used extensively in steady-state simulations of radiative heat transfer [14]. Many researchers have also used the MC method to address transient laser-tissue interactions [15, 16]. However, an instantaneous, isotropic and point source was generally used to simulate the incident laser beam, and the system was generally restricted in one-dimensional slab. Recently, Guo et al. [17] studied the characteristics of multi-dimensional transient radiative transfer using the MC method. They found that the MC method is very suitable for the study of pulse laser radiation transport in highly scattering medium because of its feasibility in handling the realistic physical conditions and the relatively inexpensive computation cost since only the incident laser photons are to be traced, even though the MC method is subject to statistical errors. In the present study, a Monte Carlo approach is developed to simulate transient radiative transport of short pulse laser incident upon three-dimensional highly scattering media. The realistic physical models, such as the temporal and spatial Gaussian distributions of the laser beam, the Fresnel reflection at the media/air boundaries, the position and angle of the detector, and the anisotropic scattering of the media, are incorporated. The sensitivity and accuracy of the MC method are examined. The MC method is used to simulate a 60 ps laser pulse transport through a block containing scattering silica micro-spheres. The predicted temporal transmittance is compared with the experimental measurement. The influence of the refractive index of the scattering particles is discussed. MONTE CARLO MODEL The pulse laser source is normally incident upon the participating medium from the origin of the Cartesian coordinates. The incident laser intensity is axisymmetric and has temporal and spatial Gaussian profiles expressed by         − ×                 − × − = = 2 2 2 0 exp 2 2 ln 4 exp ) , 0 , , ( ν r t t I t z y x I p c (1) where the pulse width, tp, is full width at half maximum (FWHM), , and is the spatial variance of the Gaussian incident beam. In the present study, the input pulse is simulated at the time range t ⊆ [0, 4t 2 2 2 y x r + = 2 / 2 ν p] for Gaussian temporal profile. The anisotropic scattering phase function is specified by the Henyey-Greenstein form as follows: