Scattering of femtosecond laser pulses on resonant transmission and
reflection gratings made of dispersive (Drude metals) and dielectric materials
is studied by a time-domain numerical algorithm for Maxwell's theory of linear
passive (dispersive and absorbing) media. The algorithm is based on the
Hamiltonian formalism in the framework of which Maxwell's equations for passive
media are shown to be equivalent to the first-order equation, ∂Ψ/∂t=HΨ, where H is a linear differential
operator (Hamiltonian) acting on a multi-dimensional vector Ψ built of the
electromagnetic inductions and auxiliary matter fields describing the medium
response. The initial value problem is then solved by means of a modified time
leapfrog method in combination with the Fourier pseudospectral method applied
on a non-uniform grid that is constructed by a change of variables and designed
to enhance the sampling efficiency near medium interfaces. The algorithm is
shown to be highly accurate at relatively low computational costs. An excellent
agreement with previous theoretical and experimental studies of the gratings is
demonstrated by numerical simulations using our algorithm. In addition, our
algorithm allows one to see real time dynamics of long leaving resonant
excitations of electromagnetic fields in the gratings in the entire frequency
range of the initial wide band wave packet as well as formation of the
reflected and transmitted wave fronts.Comment: 23 pages; 8 figures in the png forma