Modelling nonlinear and dispersive propagation problems by using the TLM method

The transmission-line modelling (TLM) method is extended to the analysis of dispersive and nonlinear propagation problems, significantly increasing the range of application of the method. Dispersion and nonlinearities are incorporated into the TLM scheme by loading with appropriate stubs. The modelling of nonlinear effects is illustrated by the incorporation of a nonlinear capacitor model, using the nonlinear discrete transform method, into the TLM method. Correct operation and energy conservation of the nonlinear discrete-transform method is discussed. The method is applied to the analysis of soliton propagation on a lumped component transmission line, and also to the self-focusing of femtosecond pulses in a Kerr medium. A dispersive stub, designed to model electromagnetic waves propagating in a plasma, is introduced which may be used to load one, two and three-dimensional TLM field nodes