The governing equation of the slowly decaying imaginary distance beam propagation method (SD-ID-BPM) 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
Original Manuscript: April 28, 2009
Revised Manuscript: June 18, 2009
Manuscript Accepted: June 22, 2009
Published: July 10, 2009
Hong Shu, "Quartic form of the slowly decaying imaginary distance beam propagation method," Appl. Opt. 48, 4056-4061 (2009)