Study On Structural Design And Performance Of All-dielectric Metasurface Of Fano Resonance Based On Group Theory

The all-dielectric metasurface supporting Fano resonance has become a research hotspot due to its highly identifiable asymmetric spectral features and enhancement of light and matter interaction caused by significant near-field localization.Since the geometrical symmetry breaking has become an effective means to excite Fano resonance,some novel asymmetric structures have been designed one after another.However,for the lack of universal theoretical guidance behind the design of Fano resonance metasurface,this process become very inefficient.Furthermore,most of the designed metasurfaces can only support a single functional channel,which is difficult to meet the development requirements for integration of modern optical system.More importantly,based on the current level of nanofabrication technology,it is impossible to accurately control the Quality factor of Fano resonance metasurface to reach the optimal value in the actual engineering applications.Aiming at the above problems,the group theory is introduced into the study on structural design and performance of Fano resonance metasurface.The main research contents of this work are as follows:Firstly,a geometrically-asymmetric all-dielectric metasurface with simple configuration is designed.The changes of coupling state between discrete eigenmodes supported by the structure and the radiative continuum in the free space are analyzed by employing the group theory,and the main factor contributing to such changes is discussed as well.Then,the depth regulation rules of geometrically-asymmetric parameter on resonant characteristics of different eigenmodes are studied.The numerical calculation verifies the prediction of group theory.The constructed theory can be used to guide the design of Fano resonance metasurface,which not only improves the efficiency of structural design,but also realizes the excitation of the target mode.Secondly,based on the general regulation law of asymmetric geometric parameters to different discrete eigenmodes,the properties of the selective coupling between different polarization of vertical incident wave and different discrete eigenmodes are investigated by employing the irreducible representation theory and the group theory symmetry arguments.The prediction of group theory is verified by numerical calculation,and the polarizationselective excitation of dual-band quasi-bound states in the continuum(q BICs)are realized.Then the independent control of two kinds of geometrically-asymmetric parameters over multiple quasi BICs under different polarization conditions is studied,demonstrating great potential for implementing multichannel optical devices with integrated functionality using a single metasurfaceFinally,the parameter of permittivity is proposed as a new degree of freedom to precisely regulate the formation of Fano resonance and its Q factor.The coupling state changes of different discrete eigenmodes with the change of permittivity symmetry and their polarization selective excitation characteristics are discussed using the irreducible representation theory and the group theory symmetry arguments.The numerical calculation verifies the group theory prediction,and the polarization selective excitation of multiband permittivity-asymmetry Fano resonances are realized,which not only greatly expands the degree of freedom of the design of Fano resonance metasurface,but aloso provides a feasible solution for precisely regulating Q factor in practical engineering applications.