Simulation of beam propagation with time-dependent nonlinear processes in optical limiting applications

A scheme based on the Cranck–Nicholson model has been realized in Matlab code and used to simulate the intensity propagation of various temporal pulse shapes through optically nonlinear materials. The differential equations associated with three- and five-level systems were solved numerically in each point over the active time–space grid. Instantaneous two-photon absorption and dynamic multilevel systems, one at the time, or in combination, can be used to model material responses. A typical Rayleigh length was 0.5 mm and a pulse length up to a few nanometers for sample lengths of typically 2 mm.