Modes of propagation of electromagnetic pulses in open dispersive circular waveguides

Modes of propagation of electromagnetic pulses in open circular 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. A theory of functions of integral operators is developed in order to
obtain the results.