The Coupled Mode Theory In Non-hermitian Systems

As the most effective technique to analyze the coupling between the modes,coupled mode theory(CMT)has its unique advantages including simple mathematical expression and clear physical meaning.It has been applied extensively for the analysis and design of a wide variety of optical components,which greatly accelerates the development of optical communication system.In recent years,non-Hermitian system has been the focus of research due to the existence of the exceptional point.This point is essential to many unique properties,such as coherent perfect absorber,unidirectional invisibility and simultaneous lasing and absorption etc.The optical power conservation relation breaks,in the presence of gain or loss,thus the existing CMT can't be used to describe the mode hybridization in non-Hermitian system.In this thesis,beginning with the Maxwell's equations,we strictly derive the general CMT(GCMT)that is valid in non-Hermitian system,which is the significant extension of CMT.(1)We present a method to construct CMT based on reaction conservation in physical system.The reaction defines a scalar inner-product,in which the reciprocity theorem is equivalent to self-adjointness.The reciprocity theorem demands the medium of coupled system to be reciprocal,and could be active or lossy.Under the condition of self-adjointness,we can treat the original problem a decoupled case as adjoint problem,and then to be solved independently,which significantly reduces the computation.(2)We reduce the dimension of self-adjointness defined in 3D space.Using the countering-propagating modes as mode sets in 2D space,we derive the coupled mode equation for waveguide system.(3)We introduce the time reversal operator (?) in reaction and apply it to the case where two sources sharing opposite frequency.Using the modes before and after the time reversal process as mode sets,we derive the coupled mode equation for optical cavity system.(4)We apply our GCMT to Hermitian and non-Hermitian systems by some specific examples,and obtain excellent agreement as the results with fullwave simulation.