Numerical methods for calculating poles of the scattering matrix with applications in grating theory

Waveguide and resonant properties of diffractive structures are often explained through the complex poles of their scattering matrices. Numerical methods for calculating poles of the scattering matrix with applications in grating theory are discussed. A new iterative method for computing the matrix poles is proposed. The method takes account of the scattering matrix form in the pole vicinity and relies upon solving matrix equations with use of matrix decompositions. Using the same mathematical approach, we also describe a Cauchy-integral-based method that allows all the poles in a specified domain to be calculated. Calculation of the modes of a metal-dielectric diffraction grating shows that the iterative method proposed has the high rate of convergence and is numerically stable for large-dimension scattering matrices. An important advantage of the proposed method is that it usually converges to the nearest pole.Comment: 9 pages, 2 figures, 4 table

On surface plasmon polariton wavepacket dynamics in metal-dielectric heterostructures

The WKB equations for dynamics of the surface plasmon polariton (SPP) wavepacket are studied. The dispersion law for the SPP in the metal-dielectric heterostructure with varying thickness of a perforated dielectric layer is rigorously calculated and investigated using the scattering matrix method. Two channels of the SPP wavepacket optical losses related to the absorption in a metal and to the SPP leakage are analyzed. It is shown that change of the dielectric layer thickness acts on the SPP as an external force leading to evolution of its quasimomentum and to the wavepacket reversal or even to the optical Bloch oscillations (BO). Properties of these phenomena are investigated and discussed. Typical values of the BO amplitude are about tens of microns and the period is around tens or hundreds of femtoseconds.Comment: 12 pages, 5 figure