Analysis of the propagation of the femtosecond laser pulse in the scattering medium

Narrow beams in scattering media: the advanced small-angle approximation

“…According to [10,27,28], we proceed in Eqs. (2) and (3) to the SAA with path length spread accounted for.…”

“…In the matrix formulation, the extension of the suggested approach to the vectorial RTE for polarized radiation is straightforward [27]. The angular distributions of the Stokes parameters and the scattering matrix of the polarized equation are expanded into a series of generalized spherical harmonics.…”

“…is straightforward [27]. In this case, the frequency spectral components of the fluxes L 1 , L 2 , and L D obey the corresponding equations [Eqs.…”

“…For a complete review of most important papers, the reader is referred to [26]. This causes a systematic error in the solution, which grows with the optical path length of the radiation, and prevents the application of the SAA solution to certain nonstationary RTE problems, where the time dispersion is the principal effect [24,27]. If the SAA solution is used in the scheme of rigorous calculation of the radiation field as the sum of the anisotropic and diffuse parts L ¼ L a þ L D [10], a large part of anisotropic radiance appears to be included in the diffuse component L D .…”

“…A stationary SAA solution for a flat unidirectional source in a flat layered medium was formulated in [28]. In [27], transient SAA solutions of the RTE have been found for femtosec ond laser pulses and their polarization states (Stokes parameters). In [10], the solution for a narrow beam in a truly threedimensional (3D) medium was formulated, and a numerical solution for a PD source in a two-dimensional scattering medium [29] is presented.…”