Mode expansions in time domain

The paper considers some methods of modeling transient electromagnetic phenomena in regular along some dimension structures (waveguides) that are based on exploiting field decomposition into series of “modes”. In case of transverse inhomogeneous dielectric filling of the waveguide the known in frequency domain modes become dependent on frequency that makes it impossible to transfer them into the time domain as is. A time domain formulation in terms of coupled frequency independent modes is proposed and the optimal choice of the modes for expanding the fields is justified based on operator formulation.