Modeling the tight focusing of beams in absorbing media with Monte Carlo simulations.

A severe drawback to the scalar Monte Carlo (MC) method is the difficulty of introducing diffraction when simulating light propagation. This hinders, for instance, the accurate modeling of beams focused through microscope objectives, where the diffraction patterns in the focal plane are of great importance in various applications. Here, we propose to overcome this issue by means of a direct extinction method. In the MC simulations, the photon paths' initial positions are sampled from probability distributions which are calculated with a modified angular spectrum of the plane waves technique. We restricted our study to the two-dimensional case, and investigated the feasibility of our approach for absorbing yet nonscattering materials. We simulated the focusing of collimated beams with uniform profiles through microscope objectives. Our results were compared with those yielded by independent simulations using the finite-difference time-domain method. Very good agreement was achieved between the results of both methods, not only for the power distributions around the focal region including diffraction patterns, but also for the distribution of the energy flow (Poynting vector).