Discontinuity between dielectric and plasmonic waveguides

A finite-element approach based on Blocked Schur algorithm is introduced to accurately analyze structures with very large longitudinal discontinuities. Although a number of Padé approximations has been conventionally used to calculate the square root of the characteristic matrix appearing at the discontinuity section with desired damping of evanescent modes, Padé approximations fail with such challenging structures like in couplers between dielectric and plasmonic waveguides and lead to a serious stability problem. Alternatively, we suggest calculating the exact solution of square root operators by the very fast Blocked Schur algorithm. The suggested approach overcomes the stability and accuracy problems of the conventional rational approximations of square root operators thanks to a physically treatment of evanescent and surface waves.