Quartic Form Of The Slowly Decaying Imaginary Distance Beam Propagation Method

The governing equation of the slowly decaying imaginary distance beam propagation method (SD-IDBPM) is further modified, for calculating the eigenmodes in optical fibers and waveguides. Its convergence is analyzed in detail and compared to the earlier version of SD-ID-BPM and other methods. It is demonstrated that the method described here can converge to the same desired accuracy within fewer propagation steps than the earlier version of SD-ID-BPM and other methods. Since the governing equation of the SD-ID-BPM is a partial differential equation with higher order derivatives, it might be interesting if the discretization in the transverse x-y plane is performed by applying the numerical techniques for partial differential equations with higher order derivatives. © 2009 Optical Society of America