This is a collaboration to develop a numerical model of a pulsed laser. The laser will be part of an optical radar intended for use in a collision avoidance system for an automobile. The work is supported by a contract with a commercial company. The model is needed in order to optimize the design of the laser.
The light waves are modeled as a hyperbolic system in one space dimension and time, with source terms generating photons and waves moving at the speed of light within the dielectric. Apparently, this optical pulse has not been modeled elsewhere, although the numerical model is similar to those found in chemical reaction problems.
Two models have been written, one based on Hermite collocation in space and the Petzold Dassl ODE solver in time. The second uses a second order box scheme in space with Berzin's ODE solver from NAG for the time discretization. The results from the two are currently being compared.
The plan for the future is to validate the model, compare with measurements as much as possible, and then the model will be used to design a device.