k-domain method for the fast calculation of electromagnetic fields propagating in graded-index media.

A conceptually straightforward method for the fast calculation of electromagnetic fields propagating in graded-index media is presented. More specifically, in this method, we convert Maxwell's curl equations into the spatial-frequency domain to obtain an ordinary differential equation (ODE), and subsequently solve the ODE with the 4-order Runge-Kutta method. Compared to the traditional beam propagation methods, this method deals with vectorial fields accurately, without physical approximations, like the scalar field approximation or the paraxial approximation; numerically, this method takes advantage of the fast Fourier transform and the convolution theorem to achieve an efficient calculation.