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  1. Free, publicly-accessible full text available September 30, 2024
  2. Free, publicly-accessible full text available August 31, 2024
  3. Abstract This work presents a rigorous theory for topological photonic materials in one dimension. The main focus is on the existence of interface modes that are induced by topological properties of the bulk structure. For a general 1D photonic structure with time-reversal symmetry, we investigate the existence of an interface mode that is induced by a Dirac point upon perturbation. Specifically, we establish conditions on the perturbation which guarantee the opening of a band gap around the Dirac point and the existence of an interface mode. For a periodic photonic structure with both time-reversal and inversion symmetry, the Zak phase is quantized, taking only two values 0 , π . We show that the Zak phase is determined by the parity (even or odd) of the Bloch modes at the band edges. For a photonic structure consisting of two semi-infinite systems on the two sides of an interface with distinct topological indices, we show the existence of an interface mode inside the common gap. The stability of the mode under perturbations is also investigated. Finally, we study resonances for finite topological structures. Our results are based on the transfer matrix method and the oscillation theory for Sturm–Liouville operators. The methods and results can be extended to general topological Sturm–Liouville systems in one dimension. 
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    Free, publicly-accessible full text available December 8, 2023
  4. We investigate the Fano resonance in grating structures using coupled resonators. The grating consists of a perfectly conducting slab with periodically arranged subwavelength slit holes, where inside each period, a pair of slits sit very close to each other. The slit holes act as resonators and are strongly coupled. It is shown rigorously that there exist two groups of resonances corresponding to poles of the scattering problem. One sequence of resonances has imaginary part in the order of ε , where ε is the size of the slit aperture, while the other sequence has imaginary part in the order of ε 2 . When coupled with the incident wave at resonant frequencies, the narrow-band resonant scattering induced by the latter will interfere with the broader background resonant radiation induced by the former. The interference of these two resonances generates the Fano-type transmission anomaly, which persists in the whole radiation continuum of the grating structure as long as the slit aperture size is small compared to the incident wavelength. 
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