• Real transmission and reflection zeros of periodic structures with a bound state in the continuum

    分类: 光学 >> 量子光学 提交时间: 2023-02-21

    摘要: For lossless periodic structures with a proper symmetry, the transmission and reflection spectra often have peaks and dips that are truly $100\%$ and $0\%$, respectively. The full peaks and zero dips typically appear near resonant frequencies, and they are robust with respect to structural perturbations that preserve the required symmetry. However, current theories on the existence of full peaks and zero dips are incomplete and difficult to use. For periodic structures with a bound state in the continuum (BIC), we present a new theory on the existence of real transmission and reflection zeros that correspond to the zero dips in the transmission and reflection spectra. Our theory is relatively simple, complete, and easy to use. Numerical examples are presented to validate the new theory.

  • Complex modes in optical fibers and silicon waveguides

    分类: 光学 >> 量子光学 提交时间: 2023-02-19

    摘要: At a fixed frequency, a general wave field in an open optical waveguide is a sum of finite number of guided modes and an integral of radiation modes. Most studies on open lossless dielectric waveguides are concerned with regular guided modes which are confined around the waveguide core, have a real propagation constant, and propagate along the waveguide axis without attenuation. However, there may be guided modes with a complex propagation constant even though the waveguide consists of lossless isotropic dielectric materials, and they are the so-called complex modes. The complex modes are proper modes confined around the waveguide core, and are different from the leaky modes which have divergent wave fields in the transverse plane. For waveguides with discontinuities and defects, the complex modes can be excited and must be included in eigenmode expansions. However, existing studies on complex modes in open lossless dielectric waveguides are very limited. In this Letter, we consider circular fibers and silicon waveguides, study the formation mechanism of complex modes, and calculate the dispersion relations for several complex modes in each waveguide. For circular fibers, we also determine the minimum refractive-index ratio for the existence of complex modes. Our study fills a gap in optical waveguide theory and provides a basis for realizing potential applications of complex modes.

  • Parametric dependence of bound states in the continuum in periodic structures: vectorial cases

    分类: 光学 >> 量子光学 提交时间: 2023-02-19

    摘要: A periodic structure sandwiched between two homogeneous media can support bound states in the continuum (BICs) that are valuable for many applications. It is known that generic BICs in periodic structures with an up-down mirror symmetry and an in-plane inversion symmetry are robust with respect to structural perturbations that preserve these two symmetries. For two-dimensional (2D) structures with one periodic direction and the up-down mirror symmetry (without the in-plane inversion symmetry), it was recently established that some scalar BICs can be found by tuning a single structural parameter. In this paper, we analyze vectorial BICs in such 2D structures, and show that a typical vectorial BIC with nonzero wavenumbers in both the invariant and the periodic directions can only be found by tuning two structural parameters. Using an all-order perturbation method, we prove that such a vectorial BIC exists as a curve in the 3D space of three generic parameters. Our theory is validated by numerical examples involving periodic arrays of dielectric cylinders. The numerical results also illustrate the conservation of topological charge when structural parameters are varied, if both BICs and circularly polarized states (CPSs) are included. Our study reveals a fundamental property of BICs in periodic structure and provides a systematically approach for finding BICs in structures with less symmetry.

  • Frequency perturbation theory of bound states in the continuum in a periodic waveguide

    分类: 光学 >> 量子光学 提交时间: 2023-02-19

    摘要: In a lossless periodic structure, a bound state in the continuum (BIC) is characterized by a real frequency and a real Bloch wavevector for which there exist waves propagating to or from infinity in the surrounding media. For applications, it is important to analyze the high-$Q$ resonances that either exist naturally for wavevectors near that of the BIC or appear when the structure is perturbed. Existing theories provide quantitative results for the complex frequency (and the $Q$-factor) of resonant modes that appear/exist due to structural perturbations or wavevector variations. When a periodic structure is regarded as a periodic waveguide, eigenmodes are often analyzed for a given real frequency. In this paper, we consider periodic waveguides with a BIC, and study the eigenmodes for given real frequencies near the frequency of the BIC. It turns out that such eigenmodes near the BIC always have a complex Bloch wavenumber, but they may or may not be leaky modes that radiate out power laterally to infinity. These eigenmodes can also be complex modes that decay exponentially in the lateral direction. Our study is relevant for applications of BICs in optical waveguides, and it is also helpful for analyzing photonic devices operating near the frequency of a BIC.

  • Computing diffraction anomalies as nonlinear eigenvalue problems

    分类: 光学 >> 量子光学 提交时间: 2023-02-19

    摘要: When a plane electromagnetic wave impinges upon a diffraction grating or other periodic structures, reflected and transmitted waves propagate away from the structure in different radiation channels. A diffraction anomaly occurs when the outgoing waves in one or more radiation channels vanish. Zero reflection, zero transmission and perfect absorption are important examples of diffraction anomalies, and they are useful for manipulating electromagnetic waves and light. Since diffraction anomalies appear only at specific frequencies and/or wavevectors, and may require the tuning of structural or material parameters, they are relatively difficult to find by standard numerical methods. Iterative methods may be used, but good initial guesses are required. To determine all diffraction anomalies in a given frequency interval, it is necessary to repeatedly solve the diffraction problem for many frequencies. In this paper, an efficient numerical method is developed for computing diffraction anomalies. The method relies on nonlinear eigenvalue formulations for scattering anomalies and solves the nonlinear eigenvalue problems by a contour-integral method. Numerical examples involving periodic arrays of cylinders are presented to illustrate the new method.

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