Leaky-mode photonic lattices exhibit intricate resonance effects originating in quasi-guided lateral Bloch modes. Key spectral properties are associated with phase-matched modes at the second (leaky) stop band. One band edge mode suffers radiation loss generating leaky-mode resonance whereas the other band edge mode becomes a bound state in the continuum (BIC). Here, we present analytical and numerical results on the formation and properties of the leaky stop band. We show that the frequency of the leaky-mode resonance band edge, and correspondingly the BIC edge, is determined by superposition of Bragg processes chiefly generated by the first two Fourier harmonics of the spatial modulation. We derive conditions for the band closure and band flip wherein the leaky edge and the bound-state edge transit across the band gap. Our work elucidates fundamental aspects of periodic photonic films and has high relevance to the burgeoning field of metamaterials.Metamaterials constitute a new class of photonic platforms wherein principal performance metrics are controlled by the properties of a collection of subwavelength particles. Periodic and aperiodic metasurfaces and metagratings can be fashioned to provide complex functionality in extremely compact format even as single-layer films. Lossless dielectric media are particularly promising for highefficiency applications [1]. Thus, there is great interest in exploring metamaterials as building blocks for high-performance photonic devices including metalenses [2], perfect reflectors [3], and metaholograms [4]. Advances in theoretical modeling, numerical design methods, fabrication, and physical and spectral characterization are discussed in numerous recent review articles [5][6][7][8].Periodic subwavelength metastructures, including one-dimensional (1D) and two-dimensional (2D) metagratings in photonic-crystal slab geometry, are governed by principles that depend strongly on the scale of the operational wavelength  relative to the period . In the deep subwavelength regime Λ λ,  classic effective-medium theory [9] becomes accurate and the material is effectively homogenized enabling facile phase control, anti-reflection properties, and polarization manipulation. In the subwavelength resonance regime with the period moderately smaller than the wavelength Λ λ,  effective medium theory fails on account of coupling of incident light to lateral leaky resonant modes. Such devices exhibit guided-mode resonance (GMR) effects caused by lateral Bloch modes in both 1D and 2D periodic lattices [10]. The resonance regime enables a great variety of novel device concepts including efficient wide-band reflectors, narrow bandpass filters, and polarizers [11].In this paper, we address fundamental properties of the photonic band structure of resonant leakymode metamaterials. The band structure admits a leaky edge and a non-leaky edge for each supported resonant Bloch mode if the lattice is symmetric. The non-leaky edge is associated with a bound state in the continuum (BIC), or embedded eig...

We show that line defects can give rise to the bending and splitting of self-collimated beams in two-dimensional photonic crystals from the equifrequency contour calculations and the finite-difference time-domain simulations. The power ratio between two split self-collimated beams can be controlled systematically by varying the radii of rods or holes in the line defect. We also show that the bending and controllable splitting of self-collimated beams can be useful in steering the flow of light in photonic crystal integrated light circuits.

We propose a method to design antireflection structures to minimize the reflection of light beams at the interfaces between a two-dimensional photonic crystal and a homogeneous dielectric. The design parameters of the optimal structure to give zero reflection can be obtained from the one-dimensional antireflection coating theory and the finite-difference time-domain simulations. We examine the performance of a Mach-Zehnder interferometer utilizing the self-collimated beams in two-dimensional photonic crystals with and without the optimal antireflection structure introduced. It is shown that the optimal antireflection structure significantly improves the performance of the device.

When two nonorthogonal resonances are coupled to the same radiation channel, avoided crossing arises and a bound state in the continuum (BIC) appears with appropriate conditions in parametric space. This paper presents numerical and analytical results on the properties of avoided crossing and BIC due to the coupled guided-mode resonances in one-dimensional (1D) leaky-mode photonic lattices with slab geometry. In symmetric photonic lattices with up-down mirror symmetry, Friedrich–Wintgen BICs with infinite lifetime are accompanied by avoided crossings due to the coupling between two guided modes with the same transverse parity. In asymmetric photonic lattices with broken up-down mirror symmetry, quasi-BICs with finite lifetime appear with avoided crossings because radiating waves from different modes cannot be completely eliminated. We also show that unidirectional-BICs are accompanied by avoided crossings due to guided-mode resonances with different transverse parities in asymmetric photonic lattices. The Q factor of a unidirectional-BIC is finite, but its radiation power in the upward or downward direction is significantly smaller than that in the opposite direction. Our results may be helpful in engineering BICs and avoided crossings in diverse photonic systems that support leaky modes.

A two-dimensional photonic crystal asymmetric Mach-Zehnder filter (AMZF) based on the self-collimation effect is studied by numerical simulations and experimental measurements in microwave region. A self-collimated beam is effectively controlled by employing line-defect beam splitters and mirrors. The measured transmission spectra at the two output ports of the AMZF sinusoidally oscillate with the phase difference of pi in the self-collimation frequency range. Position of the transmission peaks and dips can be controlled by varying the size of the defect rod of perfect mirrors, and therefore this AMZF can be used as a tunable power filter.

We experimentally confirm that the antireflection structures effectively minimize unnecessary reflections of self-collimated microwave beams at the interfaces of a two-dimensional photonic crystal, which is composed of cylindrical alumina rods. Optimized design parameters for the antireflection structures are obtained from the one-dimensional antireflection coating theory and the finite-difference time-domain simulations. Measured transmittance through the photonic crystal samples with and without the antireflection structures agree well with the simulation results. The measured results show that the photonic crystal with an antireflection structure yields about 90% transmission of incident power on the average in the frequency range of 12.0 to 13.0 GHz.

We demonstrate that surface waves in structured perfect electric conductor surfaces can be self-collimated using the finite-difference time-domain method. The self-collimation frequency is obtained from the equi-frequency contours of a perfect electric conductor patterned with an array of square holes. The field patterns of the self-collimated surface wave, obtained using the periodic boundary conditions, show that the surface waves propagate with almost no spreading. We also show that self-collimation phenomena can be observed for the hybrid surface plasmon waves in structured metal surfaces using the finite-difference time-domain method with the Drude model. It is shown that for a structured silver surface the self-collimation can be achieved at the frequencies in the infrared region.

We present a high-efficiency antireflection structure for both TE and TM polarizations in two-dimensional self-collimating square lattice photonic crystal consisting of air holes in silicon. The design parameters of the optimal antireflection structure can be obtained by using the concept of Fresnel coefficients and the finite-difference time-domain simulations. The photonic crystal operating in almost identical self-collimation frequencies for two polarizations exhibits a large reflection coefficient for TE and a very small one for TM polarization. In this case, the antireflection structure for TE can also improve the transmission for TM polarization. To confirm a highly efficient antireflection structure designed, we investigate the transmission data of three finite photonic crystal samples consisting of 36, 38 and 40 unit cells for the cases without and with the antireflection structures through finite-difference time-domain simulations.