Calculation of field evolution in dielectric waveguide by progressive and oscillatory approaches

Two ways for calculation of an initial value problem in a dielectric waveguide is presented. Each way describes one of two complementary approaches: progressive or Brillouin waves approach and oscillatory or eigenfrequency approach. Evolution of a transient electromagnetic field in the waveguide after instant change of its permittivity is considered and calculated. The results show pure coincidence of two ways of calculation but the Brillouin approach is more intuitive and visual and makes less demands to computation resources.