Multimodal Transfer Matrix Method Applied to 3-D Periodic Structures

In this work, we discuss the application of the multimodal transfer matrix method (MMTMM) to compute the dispersion diagram of 3-D periodic structures. The problem of finding the complex wavenumber (both the phase and/or attenuation constants) of the different modes is posed as a standard linear eigenvalue problem in terms of the transfer matrix of the unit cell. The numerical drawbacks associated with the search of complex solutions in the complex plane are then avoided, thus making the MMTMM a useful tool to analyze and design periodic structures.