Direct computation of higher-order propagation modes using the imaginary-distance beam propagation method

In this paper we present an extension to the standard method of eigenmode-e xtraction using the imaginary-distance beam propagation method. We show tha t it is possible to directly extract higher-order propagation modes of arbi trary shaped waveguide structures by propagating the field along the imagin ary axis when the parameters are chosen in an appropriate manner. This meth od requires an assumption of the propagation constant of the eigenmode. In many cases this value can be determined using fast approximate techniques l ike the effective index method. Additionally, the approximate mode shape ma y be introduced as a starting condition and can further accelerate the extr action of the eigenmode. The overall number of propagation steps needed to extract multiple eigenmodes is then significantly smaller than in the case when extracting the modes sequentially with the former method.