| Metamaterial is a new type of subwavelength composite electromagnetic material that has been widely used in the fields of optics,communication and defense due to its special ability to modulate electromagnetic waves.Metasurface(ultra-thin two-dimensional metamaterial)structures have gained great attention due to their easy processing,low loss,and high control freedom.Bound states in the continuum is first proposed in quantum systems,which have the property of ultra-high quality factor Q and are therefore widely used in sensing,nonlinear enhancement,and low-threshold lasers.However,since quantum systems are experimentally demanding and extremely expensive,the study of bound states in the continuum can be made a reality by exploiting the powerful electromagnetic modulation capability of metasurfaces.At the present stage,there are few studies on the bound states in the continuum with metallic metasurface structures,and at the same time,the theoretical analysis of the bound states in the continuum needs further improvement,so this paper investigates the physical mechanisms and phenomena of the bound states in the continuum of metasurfaces based on the coupled-mode theory.In this paper,based on the original coupled mode theory,the phase information of the metasurface structure is introduced into the coupled mode equation,which can realize the theoretical calculation for different Q cases,especially for high Q cases.In the process of solving the coupled-mode theory with the introduction of phase,the conditions for generating BIC can be obtained.Combining the conditions to design new structures for generating BIC metal metasurfaces,they make the design of BIC metasurfaces more flexible and further improve the study of the physical mechanism of BIC.The research work in this paper mainly contains the following aspects:1.The coupled mode theory and the time-domain coupled mode theory are studied in depth.Firstly,the differential expression for the coupling of double resonant oscillators is derived from the differential expression of the single resonant oscillator to time,i.e.,the transient equation,and then the transient equation is rewritten as the steady state equation,and the amplitude expression of the double resonant oscillator is obtained by solving it,and the transmission spectrum equation is also calculated.And the n resonator coupling mode equation can be obtained by generalizing the two resonators coupling equation.Secondly,the transmission spectrum formulations of coupled-mode theory and time-domain coupled-mode theory are compared,and it is demonstrated that the transmission spectrum expressions obtained from both solutions agree.2.By combining the coupled mode theory previously applied to the continuous domain bound state and introducing the phase information of the metasurface structure into it,the spectral line expressions applicable to the bound states in the continuum metasurface can be obtained.The values of physical parameters such as resonant frequency,loss,and phase of a single structure are obtained using CST simulations.By bringing them into the spectral line expressions,the transmission spectral lines of the metasurface structure can be calculated.And the calculated results of the bound states in the continuum metasurface structure almost match the CST simulation results.Finally,the coupled mode theory of this paper is compared with the previous approach,and the calculation results of this paper are better than the previous theory under different asymmetric parameters.3.The condition for the generation of bound states in the continuum is proposed and demonstrated using the examples of the cut line(CW)and symmetrically split ring(SSR)coupled,and U-ring and SSR coupled metasurfaces.The correctness of the condition is verified by combining CST simulations,theoretical calculations,electric field analysis,and experimental ways.The condition is proved that different types of coupled metasurface structures can also produce bound states in the continuum. |
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