Study of bifurcation processes in a multimode waveguide with statistical irregularities

We consider the theoretical principles of the original investigation of irregular optical waveguides in the form of a dynamic dissipative system. The scattering of guided modes in an irregular optical waveguide is considered as a process of gradual transition of a dynamic dissipative system from an 'ordered' state into 'chaos.' The growth of scattering losses in an irregular optical waveguide is represented as an increase in chaos in the system under analysis. The phase retardation factor of a multimode waveguide is used as a control parameter of the process. The use of the methods of catastrophe theory can explain the behaviour of the dissipative system under study in the process of changing the control parameter. It is found that an increase in chaos in the system (an increase in losses due to scattering in an irregular waveguide under excitation of modes of increasingly higher order) can be explained by a sequence of direct bifurcations, i.e., the existence of stable cycles in the system. As a result, the irregular optical waveguide can be regarded as a system in which the energy of a regular process (the process of propagation of a guided mode) passes into the energy of a 'disordered' process, i.e., the energy of radiation modes.