Light Scattering And Transport In Complex Nanophotonic Structures

The phenomenon of light scattering and transport in nanostructures is widespread in the field of science and engineering,and people have been very interested in it for a long time.This field is not only closely related to many disciplines,such as cosmology,meteorology,oceanography,optical communication,etc.,but also constantly emerging new insights and important applications,such as optical tweezers,optical capture,anisotropic or bianisotropic waveguide,etc.In the analysis of light scattering,multipole theory is an important tool used to describe the electromagnetic field distribution.Previous studies have only focused on radiation intensity,polarization and parity symmetry in the direction of strong radiation.However,the topological properties in the directions of dark radiation are ignored.It is rather puzzling,because the study of topological theory is in full swing today.The appearance of the topological properties in the basic tools will inevitably bring a wide range of novel phenomena in theory and application,such as the topological invariance in scattering,the microscopic mechanism of BIC,and the splitting of BIC to circularly polarized light.In addition,in the two-mode coupling model,we found that the redistribution of the far-field radiation pattern will cause dramatic changes of Q-factor,which allows people to rediscover the macro concept of Q factor from the microscopic perspective of radiation distribution in the far field.In the analysis of optical transport,the classical coupled-mode theory cannot handle the waveguide problem composed of more general bianisotropic materials,therefore we complete the neglected conditions of completeness and orthogonality,and propose a generalized coupled-mode theory to solve this problem.The main content of the paper includes the following points:First,in the two-mode coupling model,it is discovered that the multipolar conversions from lower to higher orders in the far field of the supermode cause the dramatic enhancement of Q-factor,revealing the subtle relation between the redistribution of the far field and the Qfactors enhancement.By introducing the generalized Kerker effects,two features of high-Q and unidirectional radiation is realized in the sub wavelength supermode.Second,the topological properties of the multipole are discussed,and the Poincare singularities(intensity singularities)and the Hopf singularities(polarization singularities)in the far field on the momentum sphere are discovered.These singularities correspond to topological indices of integers and half integers.The intrinsic topological nature of the multipole is exactly the microscopic mechanism of BIC formation and the essential reason for the phenomenon of BIC splitting into circularly polarized light.We also propose the global Mie scattering theory,and give the topological invariant in electromagnetic scattering,that is,the topological index of the singular point of the far field of any scatterer is a constant 2.This is the perfect application of the Poincare-Hopf theorem in electromagnetic scattering theory.Third,we found that even for achiral materials,the asymmetrical geometric appearance or external illumination can cause scattering activities.We give a unified framework to estimate whether the system has scattering activities only through the analysis of parity symmetry and reciprocity.Finally,we propose a generalized coupled mode theory to deal with waveguide problems involving gain/loss,anisotropy and bianisotropy.In this theory,the waveguide problem is re-expressed as a generalized eigenvalue problem.By introducing the adjoint generalized eigenvalue problem,the orthogonality and completeness of the mode set are guaranteed,and the same-? argument and pairing-? argument provide the symmetry of the dual mode set.In conclusion,we present novel research and development for basic theoretical tools in the field of light scattering and transport,providing a richer physical view and deeper insights for novel phenomena.