Modes of propagation of electromagnetic pulses in open dispersive slab waveguides

As a preparatory study of electromagnetic pulse propagation in open waveguides,
the modes of propagation of pulses in open slab waveguides are investigated
systematically. Core and cladding both consist of simple (linear,
homogeneous, isotropic), dispersive materials modeled by temporal convolution
with physically sound susceptibility kernels. Under these circumstances,
pulses cannot propagate along the guide unless the sum of the (first) initial
derivatives of the electric and magnetic susceptibility kernels of the medium
in the core is less than the corresponding sum for the medium in the cladding.
Only a finite number of pulse modes can be excited, and relevant temporal
Volterra integral equations of the second kind for these modes are derived.