Analytical Perspective of Interfering Resonances in High-Index-Contrast Periodic Photonic Structures

We investigate the extraordinary behavior of periodic photonic structures within radiation continuum from the perspective of interfering resonance. The coupled-channel equations of both TE-like and TM-like polarizations are reformulated into the similar forms of the quantum-defect theory that describes the interference of resonances belonging to different Coulombic quantum channels. The concepts of closed-channel, open-channel, coupling potential, and eigenvalues are well interpreted. Some iteration techniques, i.e., field-iteration and k-iteration, are proposed to obtain self-consistent solution of the coupled-channel equations. The iterations are important to guarantee quantitative accuracy for high-index-contrast structure, in which the strength of wave interactions is significantly enhanced compared with its low-index-contrast counterpart. The semianalytical results of resonance wavelength, transmissivity/reflectivity spectrum, and band structure agree well with the rigorous coupled-wave analysis (RCWA) and finite-difference time-domain (FDTD) simulation, confirming the accuracy of the iterations. The interfering resonance provides a clear and consistent picture to understand the periodic photonic structure within radiation continuum, and also reveals the intrinsic similarities between the photonic and quantum systems.