Runge-Kutta Beam Propagation Method (RK-BPM) for GRIN Medium

The RK-BPM solver works in the spatial domain (x domain), in a pointwise manner. Mathematically, it solves, simultaneously,

• one ordinary differential equation (ODE) for the light path, and
• another ODE for the field polarization vector.

The solution of the ODEs is based on the standard Runge-Kutta (RK) forth-order method. In comparison to the ray tracing for GRIN medium – that solves the light path – we extend it to embrace the field quantities i.e. the complex amplitude and polarization.