Nanooptics and photonics

Exact solution for wave equation in a
layered system
Los V.F.
 Institute of Magnetism of the NAS and Min. Edu. Sci of Ukraine. Vernadsky Blvd. 36-b, Kyiv-03142, Ukraine. 
E-mail: victorflos43@gmail.com

     Exact space-time propagator for the wave (second-order in
time) equation in a layered system, made up of a layer sandwiched
between two other different semi-infinite layers, is obtained by
means of the multiple scattering theory (MST) approach. The MST
approach is made possible due to obtained effective potentials
localized at interfaces and responsible for reflection from and
propagation through them. 
     The obtained space-time propagator
exactly solves the considered wave equation for any initial value and
allows for following in time the processes of reflection and
transmission. 
     The solution for an initial Gaussian wave packet is
obtained, analyzed, numerically visualized and discussed for the case
of the perpendicular-to-interfaces incoming wave. In particular, the
contribution of the backward-moving components of the wave packet
is revealed.