50 research outputs found
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