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The term photonic crystals appears because of the analogy between electron waves in crystals and the light waves in artificial periodic dielectric structures. During the recent years the investigation of one-, two-and three-dimensional periodic structures has attracted a widespread attention of the world optics community because of great potentiality of such structures in advanced applied optical fields. The interest in periodic structures has been stimulated by the fast development of semiconductor technology that now allows the fabrication of artificial structures, whose period is comparable with the wavelength of light in the visible and infrared ranges.

http://ieeexplore.ieee.org/iel5/6354/16969/00781867.pdf

Photonic crystals

Metamaterials are typically engineered by arranging a set of small scatterers or apertures in a regular array throughout a region of space, thus obtaining some desirable bulk electromagnetic behavior. The desired property is often one that is not normally found naturally (negative refractive index, near-zero index, etc.). Over the past ten years, metamaterials have moved from being simply a theoretical concept to a field with developed and marketed applications. Three-dimensional metamaterials can be extended by arranging electrically small scatterers or holes into a two-dimensional pattern at a surface or interface. This surface version of a metamaterial has been given the name metasurface (the term metafilm has also been employed for certain structures). For many applications, metasurfaces can be used in place of metamaterials. Metasurfaces have the advantage of taking up less physical space than do full three-dimensional metamaterial structures; consequently, metasurfaces offer the possibility of less-lossy structures. In this overview paper, we discuss the theoretical basis by which metasurfaces should be characterized, and discuss their various applications. We will see how metasurfaces are distinguished from conventional frequency-selective surfaces. Metasurfaces have a wide range of potential applications in electromagnetics (ranging from low microwave to optical frequencies), including: (1) controllable “smart” surfaces, (2) miniaturized cavity resonators, (3) novel wave-guiding structures, (4) angular-independent surfaces, (5) absorbers, (6) biomedical devices, (7) terahertz switches, and (8) fluid-tunable frequency-agile materials, to name only a few. In this review, we will see that the development in recent years of such materials and/or surfaces is bringing us closer to realizing the exciting speculations made over one hundred years ago by the work of Lamb, Schuster, and Pocklington, and later by Mandel'shtam and Veselago.

An Overview of the Theory and Applications of Metasurfaces: The Two-Dimensional Equivalents of Metamaterials

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Methods Of Modern Mathematical Physics

The recent reformulation of the coupled-wave method by Lalanne and Morris [ J. Opt. Soc. Am. A13, 779 ( 1996)] and by Granet and Guizal [ J. Opt. Soc. Am. A13, 1019 ( 1996)], which dramatically improves the convergence of the method for metallic gratings in TM polarization, is given a firm mathematical foundation in this paper. The new formulation converges faster because it uniformly satisfies the boundary conditions in the grating region, whereas the old formulations do so only nonuniformly. Mathematical theorems that govern the factorization of the Fourier coefficients of products of functions having jump discontinuities are given. The results of this paper are applicable to any numerical work that requires the Fourier analysis of products of discontinuous periodic functions.

https://mcgrating.com/references/ref11.pdf

Use of Fourier series in the analysis of discontinuous periodic structures

Simple analytical formulas are introduced for the grid impedance of electrically dense arrays of square patches and for the surface impedance of high-impedance surfaces based on the dense arrays of metal strips or square patches over ground planes. Emphasis is on the oblique-incidence excitation. The approach is based on the known analytical models for strip grids combined with the approximate Babinet principle for planar grids located at a dielectric interface. Analytical expressions for the surface impedance and reflection coefficient resulting from our analysis are thoroughly verified by full-wave simulations and compared with available data in open literature for particular cases. The results can be used in the design of various antennas and microwave or millimeter wave devices which use artificial impedance surfaces and artificial magnetic conductors (reflect-array antennas, tunable phase shifters, etc.), as well as for the derivation of accurate higher-order impedance boundary conditions for artificial (high-) impedance surfaces. As an example, the propagation properties of surface waves along the high-impedance surfaces are studied.

Simple and Accurate Analytical Model of Planar Grids and High-Impedance Surfaces Comprising Metal Strips or Patches

A new implementation of the coupled-wave method for TM polarization is proposed. We use a second-order differential operator established by Neviere together with a scattering-matrix approach. Thus we obtain for metallic gratings a convergence rate as quick as that in TE polarization.

Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization

The coordinate-transformation-based differential method of Chandezon et al. [J. Opt. (Paris) 11, 235 (1980); J. Opt. Soc. Am. 72, 839 (1982)] (the C method) is one of the simplest and most versatile methods for modeling surface-relief gratings. However, to date it has been used by only a small number of people, probably because, traditionally, elementary tensor theory is used to formulate the method. We reformulate the C method without using any knowledge of tensor, thus, we hope, making the C method more accessible to optical engineers.

Rigorous and efficient grating-analysis method made easy for optical engineers

The lamellar grating problem is reformulated through the concept of adaptive spatial resolution. We introduce a new coordinate system such that spatial resolution is increased around the discontinuities of the permittivity function. We derive a new eigenproblem that we solve by using Fourier expansions for both the field and the coefficients of Maxwell’s equations. We provide numerical evidence that highly improved convergence rates can be obtained.

Reformulation of the lamellar grating problem through the concept of adaptive spatial resolution

Recently a new structure showing a super-enhanced transmission [Optics Commun. 209, 17–22 (2002); Phys. Rev. B, 67, 155314, (2003)] has been proposed. The origin of this phenomenon was not clearly explained. In this paper, by using a numerical Order-N FDTD spectral method, we study the eigenmodes, the band structure and the dispersion curves of a photonic 2-D crystal made with coaxial circular cavities and made from a real metal. We show that the super-enhanced transmission of the finite structure is due to a cavity resonance of a single guided mode. An extensive characterization of this mode is presented, in terms of the spatial mode structure and effective index dispersion curve.

/pdf/origin-of-the-super-enhanced-light-transmission-through-a-2-130zwjtznw.pdf

Gérard Granet

Papers

Simple and Accurate Analytical Model of Planar Grids and High-Impedance Surfaces Comprising Metal Strips or Patches

Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization

Rigorous and efficient grating-analysis method made easy for optical engineers

Reformulation of the lamellar grating problem through the concept of adaptive spatial resolution

Origin of the super-enhanced light transmission through a 2-D metallic annular aperture array: a study of photonic bands