Photon diffusion in a homogeneous medium bounded externally or internally by an infinitely long circular cylindrical applicator. VI. Time-domain analysis.

Abstract

Part VI analytically examines time-domain (TD) photon diffusion in a homogeneous medium enclosed by a "concave" circular cylindrical applicator or enclosing a "convex" circular cylindrical applicator, both geometries being infinite in the longitudinal dimension. The aim is to assess characteristics of TD photon diffusion, in response to a spatially and temporally impulsive source, versus the line-of-sight source-detector distance along the azimuthal or longitudinal direction on the concave or convex medium-applicator interface. By comparing to their counterparts evaluated along a straight line on a semi-infinite medium-applicator interface versus the same source-detector distance, the following patterns are indicated: (1)the peak photon fluence rate is always reached sooner in concave and later in convex geometry; (2)the peak photon fluence rate decreases slower along the azimuthal and faster along the longitudinal direction on the concave interface, and conversely on the convex interface; (3)the total photon fluence decreases slower along the azimuthal and faster along the longitudinal direction on the concave interface, and conversely on the convex interface; (4)the ratio between the peak photon fluence rate and the total fluence is always greater in concave geometry and smaller in convex geometry. The total fluence is equivalent to the steady-state photon fluence analyzed in Part I [J. Opt. Soc. Am. A27, 648 (2010)10.1364/JOSAA.27.000648JOAOD61084-7529]. The patterns of peak fluence rate, time to reaching peak fluence rate, and the ratio of these two, correspond to those of AC amplitude, phase, and modulation depth of frequency-domain results demonstrated in Part IV [J. Opt. Soc. Am. A29, 1445 (2012)10.1364/JOSAA.29.001445JOAOD61084-7529].