Non Hermitian Effective Medium Theory Of Photonic Crystals

By designing accidental degeneracy in two-dimensional photonic crystals,monopole and dipole resonances induce the dispersion behavior of Dirac like cones.Previous work has proved that the double zero effective medium theory can perfectly explain this phenomenon.Later,it was found that the Dirac like cone dispersion in the Hermitian system becomes the rings of exceptional points dispersion in the nonHermitian system with a certain gain or loss.However,there is no specific effective medium theory to explain this phenomenon.The traditional coupled mode theory cannot explain the dispersion of large k-value nondegenerate case.Based on this,we propose an effective medium theory for non-Hermitian photonic crystal system,that is,when the normalized frequency is close to zero,the real part and imaginary part of the effective permittivity and effective permeability function are linearly dependent on the real part and imaginary part of the frequency respectively,which can perfectly predict the dispersion of small K value and large K value and the additional longitudinal mode flat band near the EP point.We have proved the validity of the non-Hermitian effective medium theory of this kind of photonic crystal through various methods.At the same time,through this set of effective medium theory,we have revealed that there are two other strange dispersion relations in the non-Hermitian photonic crystal,including the Dirac like cone in the complex space and the band gap in the real part of the frequency and the degenerate point in the imaginary part of the frequency,even zero index materials can be designed.We describe a new picture of effective medium theory and propose a series of new concepts,such as Dirac like cone in complex frequency space of non-Hermitian system.The full text is divided into five chaptersIn the first chapter,the background of this work,such as photonic crystals,metamaterials,non-Hermitian systems,is introduced,and their concepts,development,related work and functions are sorted out;The second chapter introduces the effective medium theory,including the effective medium theory of the eigenmode,the effective medium theory of the double zero medium,the longitudinal mode analysis of the photonic crystal,the effective medium theory of the limit of the long wavelength of the photonic crystal and the effective medium theory of the anisotropy.In the third chapter,the theory of non-Hermitian effective medium in photonic crystal system is proposed.It consists of four groups of linear effective parameters,and the dispersion equation is used to reconstruct the dispersion of EP ring.It not only explains the appearance of EP ring,but also deduces the position of EP point.At the end of this chapter,we use two methods to verify the validity of the effective medium theory.In Chapter 4,the inference of non-Hermitian effective medium is explained.Different dispersion relations can be obtained by changing the intercept of linear equation.We explain these dispersion relations in detail.In addition,we can use the non-Hermitian effective medium theory to design the zero refractive index materials.The fifth chapter is the summary and prospect.We summarize the problems of this paper and summarize the vision of this paper.