Modeling of Microwave Waveguide System with Complex Structure in Non-Linear

Using a rigorous mathematical method, the transformation of a guided mode of a circular dielectric waveguide as a result of a stepwise change in time of the refractive index of the core has been studied. The assumption of a sharp change in the refractive index made it possible to construct an analytical solution in the form of the Laplace transform. The inverse transformation to the time domain is obtained using the residue theorem and the estimate of integrals along the cuts of the complex plane. The solutions obtained made it possible to study the transient processes and the steady-state regime, to demonstrate the possibility of a frequency shift, and also to establish the possibility of converting a guided mode into radiation modes that quickly leave the waveguide core.