Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: Application to photonic crystal fibers

A full-vectorial imaginary-distance beam propagation method based on a finite element scheme is newly formulated and is effectively applied to investigating the problem of leakage due to a finite number of arrays of air holes in photonic-crystal holey fibers (HFs). In order to treat arbitrarily shaped air holes and to avoid spurious solutions, a curvilinear edge/nodal hybrid element is introduced. Furthermore, in order to evaluate propagation characteristics of not only bound modes but leaky modes in HFs, an anisotropic perfectly matched layer is also employed as a boundary condition at computational window edges. It is confirmed from numerical results that the propagation loss increases rapidly with increasing wavelength, especially for HFs with one ring of smaller air holes, and that the propagation loss is drastically reduced by adding one more ring of air holes to the cladding region.