GPU-based solution of nonlinear Maxwell’s equations for inhomogeneous dispersive media

Abstract : A new approach is developed for fast solution of complex dynamic problems in nonlinear optics. The model is based on the nonlinear Maxwell’s equations coupled with time-dependent electron density equation. The system of nonlinear equations is solved by an iterative fixed-point procedure [Ref 1]. The proposed method is shown to stay stable even for complex nonlinear media and strong fields leading to such effects as non-linearphotoionization including both multi-photon effect and tunneling described by Keldysh theory [Ref 2] . Special attention is paid to the possibility of embedding different sub-micrometric inhomogeneities with transient optical properties in the main matrix materials such as transparent dielectrics. GPU technique is implemented by using an an efficient algorithm enabling solution of a massively three-dimensional problems within reasonable time. The proposed procedure can be used for a wide range of applications. In particular, the method is advantageous in the case of ultra-fast laser material processing, for modeling ultra-short laser-nanoparticle interaction, and to study the periodic nanostructure formation in dielectric materials by femtosecond laser irradiation