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ABSTRACT
Transient radiative transfer (TRT) in a two-dimensional scattering medium with graded refractive index distribution subjected to a collimated short-pulse irradiation is solved by a modified Monte Carlo (MMC) method coupled with the time shift and superposition (TSS) principle. The boundaries are considered as Fresnel surfaces, the refractive index at the boundary mismatches with that of the surroundings, making the reflectivity at the boundary change with the incident directions. The incident pulse consists of two parts when it hits the boundary: bundles directly reflected by the outside boundary and bundles refracted into the medium. The accuracy of the present algorithm is confirmed first. Numerical results show that by using the TSS principle, the computational efficiency is greatly improved. Afterward, the TRT in the media with different graded refractive index distributions is investigated. The time-resolved reflectance and transmittance at different locations are given. Several trends on the time-resolved signals are observed and analyzed.
Nomenclature
| a | = | anisotropic factor |
| c0 | = | light speed in vacuum, ms−1 |
| H(t) | = | Heaviside step function |
| I | = | radiation intensity, Wm−2 sr−1 |
| L | = | medium thickness in direction z, m |
| Nx | = | number of sub-layers in the x direction |
| Ny | = | number of sub-layers in the y direction |
| m0 | = | discrete time steps of the incident pulse |
| N | = | total number of simulated bundles |
| n | = | refractive index |
| r | = | radial coordinate |
| r0 | = | radius of incident laser beam, mm |
| ri | = | radius of the detector, mm |
| tp | = | incident pulse width, s |
| = | dimensionless incident pulse width, | |
| t* | = | dimensionless time, t* = βc0t |
| Φ | = | scattering phase function |
| μ | = | direction cosine |
| β | = | extinction coefficient, m−1 |
| ω | = | scattering albedo |
Nomenclature
| a | = | anisotropic factor |
| c0 | = | light speed in vacuum, ms−1 |
| H(t) | = | Heaviside step function |
| I | = | radiation intensity, Wm−2 sr−1 |
| L | = | medium thickness in direction z, m |
| Nx | = | number of sub-layers in the x direction |
| Ny | = | number of sub-layers in the y direction |
| m0 | = | discrete time steps of the incident pulse |
| N | = | total number of simulated bundles |
| n | = | refractive index |
| r | = | radial coordinate |
| r0 | = | radius of incident laser beam, mm |
| ri | = | radius of the detector, mm |
| tp | = | incident pulse width, s |
| = | dimensionless incident pulse width, | |
| t* | = | dimensionless time, t* = βc0t |
| Φ | = | scattering phase function |
| μ | = | direction cosine |
| β | = | extinction coefficient, m−1 |
| ω | = | scattering albedo |