Exceptional Points of Degeneracy induced in Uniform and Periodic Coupled Systems

Abstract

Exceptional points of degeneracy (EPDs) are points in parameters space of a waveguide system where two or more eigenmode coalesce into a single degenerate eigenmode. EPDs are obtained in electromagnetic structures through proper engineering to one or more system parameters such as dielectric constant, structural dimensions, coupling coefficients, etc. At EPD, the matrix describing the evolution of the system (i.e. the system matrix in uniform waveguides or the transmission matrix in periodic waveguides) is defective which means it is either similar to a Jordan matrix or to a matrix containing a Jordan block. Such condition is achieved either through the involvement of gain and loss in parity-time (PT-) symmetric structures, or via periodicity in the system, for example. Moreover, uniform coupled waveguide can exhibit EPDs in their dispersion diagram by properly coupling evanescent modes to propagating modes, without the need to resort to loss and/or gain.