PROPAGATION OF ULTRA-SHORT- PULSE RADIATION IN PARTICIPATING MEDIA: A LAGUERRE-GALERKIN SOLUTION

摘要

An improved solution technique has been developed for the transient radiative transfer problem in a participating medium one boundary of which is exposed to short-pulse irradiation. In this technique, the time-dependent dimensionless radiative intensity within the one-dimensional, absorbing, non-emitting and isotropically scattering medium is expanded in a series of Laguerre polynomials with time as the argument. The moments of the radiative transfer equation, as well as of the boundary conditions, are then taken in accordance with the orthogonality property of the Laguerre polynomials, yielding a set of coupled time-independent radiative transfer problems. This set, in turn, is reduced to a set of algebraic equations utilizing the Galerkin method. The transient transmittance and reflectance are re-evaluated and compared with previously obtained ones. It has been demonstrated that this approach is not only more efficient but also yields results that agree very well with those available in the literature. It should also be noted that the method works better for small to moderate optical thicknesses where the hyperbolic approximations reported in the literature seem to fail.