Modal methods for 3D modelling of advanced photonic structures

In this contribution we present the basics of four frequency-domain modal methods for numerical modelling of advanced photonic and plasmonic structures that have been independently developed at three collaborating institutions within a joint project. The rigorous coupled-wave analysis (RCWA) method originally built up for modelling periodic 1D and crossed diffraction grating structures was developed and adapted also for modelling 3D photonic waveguiding structures. A very similar but independently developed bi-directional mode expansion propagation method (BEP) based on Fourier series has been extended for modelling 3D structures, too. Implementation of adaptive spatial resolution technique helps reduce the number of expansion terms and thus dramatically increase the numerical efficiency of the methods. Another two variants of the BEP approach differ in the way how the eigenmodes of the structures are searched for; they exploit the finite-difference and the finite-element methods, respectively. Results of modelling of two simple structures (effective indices of guided modes in a SOI photonic wire and reflections from a gap in the waveguide) are mutually compared and other results of modelling of some other promising photonic and plasmonic nanostructures as subwavelength grating waveguides and hybrid dielectric-plasmonic gap waveguides are finally presented, too.