Non-hermitian Optical Systems With Robust Conservation Of Energy — Pseudo-hermitian Systems

It is generally thought that non-Hermitian systems are not energy conserved.In 1998,Bender and Bottcher found that non-Hermitian systems with PT symmetry could exhibit real spectra of eigenvalues,indicating a balance between gain and loss and that nonHermitian systems could be energy conserved.However,such a balance is not only dependent on the magnitude of gain and loss,but also easily broken due to external disturbance.In this work,a transformation-optics approach is proposed to construct a unique class of non-Hermitian systems with robustly balanced gain and loss,irrespective of the magnitude of gain/loss and the environmental disturbance.Through transformationoptics operators like space folding and stretching,gain and loss can be generated and separated in the real space.While in the virtual space,the gain and loss are still combined to each other,rendering a balance of energy that is far more robust than other nonHermitian systems.This amazing feature is verified by finite-element simulations.Our work reveals a class of non-Hermitian systems in which gain and loss are balanced robustly,thereby denoted as pseudo-Hermitian systems.The thesis is divided into five chapters and is arranged as follows:Chapter one reviews the background of this work,including metamaterials,transformation optics and non-Hermitian systems,by introducing their concepts,research significance,development and practical applications.Chapter two demonstrates the general idea for constructing pseudo-Hermitian systems proposed in this work,and the specific approaches,space folding and stretching operations in transform optics,by giving examples.In chapter three,the energy conservation properties of pseudo-Hermitian systems is verified in closed environments,with comparisons to PT-symmetric systems.It is found that in the pseudo-Hermitian systems,the increased and decreased energy are perfectly balanced,in spite of the gain and loss within it.And by constructing Hermitian systems possessing the same eigenvalues and eigenstates with the pseudo-Hermitian system,the origin of robust energy conservation of the pseudo-Hermitian systems is demonstrated more deeply.In chapter four,the energy conservation property of pseudo-Hermitian systems is verified in open environments,with comparisons to PT-symmetric systems as well.It is found that the perfect energy balance is still maintained in open environments.And the pseudo-Hermitian systems are also constructed through the space stretching operation of transform optics,which further explains the idea for constructing such systems and the robust energy balance within the systems.Chapter five presents a conclusion and an outlook of the work's possible practical applications in wireless energy transmission.