Research On The Physical Mechanism And Algorithm Of Bound States In The Continuum In Optical Systems

Traditionally,resonant states in an open system are always coupled to the free space and thus radiate energy outward.However,bound states in the continuum(BICs)go beyond this conventional understanding and are a special class of resonant states:although they have the same momentum and energy as the propagating modes in free space,but are not coupled to them and thus have infinite lifetimes.As early as 1929,von Neumann and Wigner proposed this concept in the quantum system,but their model requires precise inverse design of the potential function and has not yet been implemented experimentally.In 1975,Friedrich and Wintgen proposed a method to realize BIC using the interference of multiple resonant modes,and then it was found that BIC is a wave phenomenon widely existing in classical wave systems,such as photonic,acoustic and plasmonic system.According to the formation mechanism,all BICs discovered up to now can be classified into four types: symmetry-protected BIC,accidental BIC,Friedrich-Wintgen BIC,and Fabry-Pérot BIC.In recent years,with the rapid development of micro-nano fabrication technology,micro-nano photonic structures are able to modulate the motion of photons at sub-wavelength scales,and have become an ideal platform for experimental observation and practical application of BICs.Meanwhile,BICs are widely applied in lasers,sensors and nonlinear optics because of their ultra-high quality factor and strong local-field enhancement.With the intensive study of BIC in optical systems,many new physics have been discovered,such as topological polarization singularities and multipole singularities.However,the search of BICs mainly relies on numerical simulation software,and there is no efficient algorithm for BICs so far.Moreover,in previous studies,BIC is generally restricted to a single radiation channel,while BIC in the high-frequency region with multiple radiation channels is rarely studied,which limit the applications of BIC.In addition,it is also worthwhile to explore whether the BIC in photonic structures has a universal physical mechanism.In this paper,we develop an efficient BIC solver based on the proposed mechanism: total internal reflection of Bloch waves.This solver is also applicable to high-frequency regions with multiple radiation channels,and the novel topological properties of multi-channel BICs are revealed.Further,we discover that all the BICs in photonic-crystal slab are Friedrich-Wintgen BICs,and a global phase diagram of BIC is proposed accordingly to study the evolution in momentum space.The specific contents of the article are as follows:Firstly,the physical mechanism of "total internal reflection of Bloch waves" is elaborated from the perspective of diffraction,of which the key point is that the incidence has additional degrees of freedom with respect to the transmission,and the generalized Fresnel equations applicable to Bloch waves are derived.Based on the equations,we can directly obtain the total internal reflection of Bloch waves at the interface of photonic crystal.The formation of BICs requires a total internal reflection condition at both interfaces between the slab and free space.We also obtain the analytical formula of total internal reflection of Bloch waves under the weak contrast limit,and thus obtain the limit behavior of BIC.Secondly,a BIC solver with low computational complexity and fast convergence speed is developed based on the mechanism of "total internal reflection of Bloch waves",which can search for BICs in a large parameter space of phtonic-crystal slab.This solver can also work efficiently at high frequencies beyond the diffraction limit where multiple radiation channels exist.Two examples of multi-channel BICs are shown,and their topological nature in momentum space is also revealed: they originate from the accidental coincidence of integer topological charges in different radiation channels in momentum space.These integer topological charges can split into two half-integer charges without breaking the spatial symmetry of the structure.Finally,based on the idea of Friedrich and Wintgen,we find that the BICs in photonic-crystal slab all come from the coupling of two modes: the accidental BICs come from the coupling of the guided resonance and the Fabry-Pérot modes,the symmetry-protected BICs from the coupling between two degenerate guided resonance modes,and the original Friedrich-Wintgen BIC from the coupling of two different guided resonance modes.Therefore,all BICs in photonic-crystal slabs can be regarded as Friedrich-Wintgen BICs.Based on these three different Friedrich-Wintgen origins,we can draw a global phase diagram of BICs to investigate their evolution.When a phase transition occurs,BICs can merge,emerge or disappear in momentum space.During these evolution,the Fabry-Pérot modes in a single slab play a significant role.We further carry out experiments to observe the critical points of the phase transitions,including the merging process of BICs at off-(38)point.The proposed mechanism of total reflection of Bloch waves provides an intuitive physical picture of the BIC in photonic-crystal slabs,and the developed BIC solver provides an efficient method to explore the BIC.The Friedrich-Wintgen origin of the BIC and the global phase diagram further enrich the picture of the BIC and provide new schemes in the experiment designs and applications.