Research On The Mechanism And Application Of Fano Resonance Based On Degeneracy Modes

High Q-factor Fano resonances are very popular for various applications,such as high-sensitive biosensing,lasing and switching.Fano resonances with an unusual asymmetric lineshape arisen from the interference of a dark mode and a bright mode,have attracted tremendous attentions in numerous physical fields,such as metamaterials,electromagnetics,optics,and plasmonics for achieving high Q-factor.The inevitable losses in metals distracted the interests from plasmonic to Mie resonances in dielectric nanoparticles.Recently,the study of Fano resonance and bound states in the continuum(BIC)generated by Mie scattering mode has attracted a lot of attention in photonics for the exponential growth of Q-factor,which in turn reaches infinity.However,the scattering wave is difficult to be guided,and the extremely high dielectric constant requirements(?_r>60)greatly reduce the application of ordinary dielectric materials in this field.The photonic crystal(PhC)resonator has the advantages of high Q value and low mode volume because the PhC bandap has excellent localization characteristics.Through combining photonic bandgap(PBG)with Fano resonance,more excellent characteristics of Fano resonance and wave localization can be obtained.In the classical Fano resonance structures based on photonic crystals,waveguide-cavity coupling or cavity-cavity coupling is used for the coupling of bright mode and dark mode,which results in Fano resonance.Such structures have large volume and the Fano resonance line is not easy to control.The Fano resonances with Q value up to 10⁸ in simulation and 80000 in experiment were also obtained by using the double-layer photonic crystal slab,which,to the best knowledge of the author,is the highest value of experimental Q in the Fano resonance based on PhCs.Nonetheless,such a flat plate structure is not easy to integrate,and the Fano resonance line is still not easy to control.In this paper,it is proposed to realize Fano resonance by using the degenerate modes in a single PhC cavity,which is small in size and thus overcomes the problem of not easy to integrate;in addition,by introducing the asymmetric structure,it overcomes the problem of not easy to control the Fano resonance.In this paper,the finite-element method and plane-wave expansion method are used to study the structure proposed;the research content of this paper mainly includes the following:(1)A cavity with circular dielectric defect is constructed in the PhC.The relationship between the dispersion curves and the geometric dimension of the dielectric defect column is studied.It is found that with the increase of the geometric parameter of the defect column,the dispersion curves move toward the lower frequency region and several dispersion curves intersect,which means mode degeneracy.At the degenerate points of modes,by adjusting the number of layers of the background columns,Fano resonance is obtained in the transmission spectrum.The transmission spectra of elliptic-shape and cross-shape dielectric column defect cavities are also studied.In these cavity structures with azimuthally asymmetric dielectric column defects,the Fano line shape can be tuned or controlled by changing the geometric dimension.(2)Based on the Fano resonances in a single cavity with rectangular defect cylinder,the mode field characteristics of various dispersion curves are studied,and the mode degeneracy points are classified as two types according to the different directions of the average power-flow density after mode degeneracy.The characteristics of Fano resonances of two different types of degenerate points are analyzed from the perspectives of transmittance and Q value.It is found that the second type can obtain super-high Q value Fano resonances;the Q value increases with the number of background column layers,and under the condition of high transmittance,it can be over 10¹⁰.At the same time,the mechanism of super-high Q value Fano resonances produced by degeneracy modes is explained from the perspective of average power-flow density.(3)Direct-coupling(series coupling)and side-coupling(parallel coupling)structures of planar PhC cavity and PhC waveguide are proposed with rectangular dielectric column defect.And the evolution of the properties,such as asymmentric factor q,quality factor Q value and so on,of the two structures are studied.The results show great potential value in application of silicon-based integrated optical devices,and it provides a foundation for using waveguide to guide the Fano modes in optical integrated circuits.(4)Based on the azimuthal asymmetry of elliptic-shape,cross-shape,and rectangular-shape defect columns,the properties for the same type of Fano modes in these cavity structures for sensor applications are studied.Also,the sensor properties for Fano modes in the cavity with a hollow rectangular defect column are studied.This lays a foundation for the sensor application of the single cavity Fano resonance.The major innovative points of this thesis are as follows:(1)For the first time,Fano resonance is obtained by using the degenerate modes of band intersection in a single PhC cavity in the forbidden band,which greatly reduces the size and volume.Mie scattering is combined with photonic crystal band gap to enhance the coupling between degenerate modes.(2)Based on the average energy flow density(S_av),the physical mechanism of realizing high Q value is disclosed.Through the analysis of S_av,it is found that in the x-axis direction(the direction of incident light),there is only the y-axis component.However,the increase of the number of layers of the background medium column in the y-axis direction enhances the Bragg reflection in this direction,resulting in the exponential growth of the Q value of Fano resonance,and the Q value can reach more than 10¹⁰.(3)By changing the angular asymmetry of the filling column in the cavity to change the dispersion characteristics of the cavity,the separation of the two degenerate modes is realized,so that the Fano resonance can be completely tuned or controlled,and the defect that the degenerate modes in the classical circular-defect PhC cavity cannot be separated into two modes is overcome.