A K-Domain Method for Fast Propagation of Electromagnetic Field through Graded-lndex Media

摘要

In this work we offer a k-domain-based method for the fast calculation of fields propagating through graded-index (GRIN) media. It is potentially fast because of two reasons: (1) in the k-domain, Maxwells equations for GRIN media become ordinary differential equations, so that we can take advantage of Runge-Kutta-type mathematical approaches to reduce the numerical effort; (2) taking advantage of fast Fourier transform algorithms to convert the convolution-type calculation (O(N2)) into a multiplication (O(N)). Several advantages arise when comparing this work with the famous split-step method: there is no paraxial approximation and the GRIN dependence along the main propagating direction can be accurately modeled.