Theoretical Analysis And Numerical Calculation Of Resonance Enhancement In A Multi-channel Dissipative Periodic Structure

The phenomenon of resonance enhancement means that in a resonant structure,if the frequency of the incident wave is close to the resonant frequency,the amplitude of the local field in the resonant structure will be much larger than that of the incident wave.This phenomenon has important applications in ultra-low threshold lasers,ultra-sensitive sensors and other fields.The ratio of the local field to the maximum amplitude of the incident wave in the resonant structure is defined as the resonance enhancement multiple,which is an important index to study the resonance enhancement phenomenon.The resonance enhancement factor is related to the quality factor,incident wave frequency and coefficient of the resonance mode.Bound states in the continum,ie resonant modes with an infinite quality factor,exist in dissipationless optical periodic structures.Since the resonance enhancement factor is proportional to the square root of the quality factor,the resonance enhancement factor can be of any size.In real life,any dielectric material is dissipative.At this time,the quality factor in the dissipative periodic structure contains two parts,the quality factor caused by dissipation and the quality factor caused by radiation,so the result in the non-dissipative periodic structure does not hold.At this time,it is very important to study the relationship between the resonance enhancement factor and the quality factor,the frequency and the coefficient of the incident wave in the dissipative periodic structure.In this thesis,using perturbation theory,an approximate expression for the resonance enhancement factor in dissipative periodic structures is derived.Firstly,the strict expressions of Qdis and Qrad in dissipative periodic structures are given by perturbation theory.Qdis is now related to the distribution of the resonant mode field,and its value is the ratio of the real part of the resonant frequency to twice the imaginary part of the resonant frequency related to material dissipation.While Qrad is related to the resonant mode far-field radiation,it is the ratio of the real part of the resonant frequency to twice the imaginary part of the resonant frequency related to radiation losses.In dissipative structures,there are complex continuum bound states,ie there are resonance modes with a quality factor approaching infinity due to radiation,which has similar properties to continuum bound states.Near the complex continuum bound state,Qdis is almost constant,while Qrad changes rapidly with respect to the Bloch wavenumber.Secondly,the coupling between the incident wave and the resonance mode is analyzed using the perturbation theory,and the approximate expression of the resonance enhancement factor is obtained.Our conclusions also hold for the case of multiple radiation channels.Using the approximate expression,the conditions that the incident wave needs to meet when the resonance enhancement multiple reaches the maximum value are analyzed.In the complex continuum bound state,when the incident angle of the incident wave satisfies the critical coupling condition,that is Qdis=Qrad,the resonance enhancement factor takes the maximum value.At this time,the resonance enhancement factor is proportional to(?).Finally,the above results are verified by numerical experiments,and the asymptotic relationship between the resonance enhancement multiple and the quality factor,incident wave frequency and coefficient is intuitively displayed.The work in this thesis provides a theoretical analysis method for analyzing the resonance enhancement phenomenon in dissipative optical structures and its applications.