A fast and accurate numerical tool to model the modal properties of photonic-bandgap fibers

We describe a finite-difference numerical method that allows us to simulate the modes of air-core photonic-bandgap fibers (PBF) of any geometry in minutes on a standard PC. The modes' effective indices and fields are found by solving a vectorial transverse magnetic-field equation in a matrix form, which can be done quickly because this matrix is sparse and because we reduce its bandwidth by rearranging its elements. The Stanford Photonic-Bandgap Fiber code, which is based on this method, takes about 4 minutes to model 20 modes of a typical PBF on a PC. Other advantages include easy coding, faithful modeling of the abrupt discontinuities in the index profile, high accuracy, and applicability to waveguides of arbitrarily complex profile.