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A comparative study of the directive radiation obtained from two kinds of 2-D photonic crystal structures excited by an electric source is presented in this letter. These structures consist of a stack of periodic chains of dielectric cylinders in free space or of circular voids in dielectric media. On the basis of an in-depth description of the physical phenomena underlying the Bloch transverse-electric modal field configurations of such structures, a set of design rules to achieve highly directive leaky-wave radiation is obtained. An analysis of the two types of structures shows that it is preferable to consider holey lattices to achieve more directive radiation, obtained by the excitation of a weakly attenuated fundamental leaky mode. Indeed, radiators consisting of an integer number of periodic chains of voids drilled in a dielectric medium over a metal plate show directivity at broadside approximately 6 dB higher than in the dielectric cylinder case. This class of holey lattices can be used to design highly directive leaky-wave antennas, with significant advantages of easy manufacturing, design simplicity, and low complexity.

An efficient and rigorous approach to analyze the radiation from an electric dipole placed in 3-D woodpile electromagnetic bandgap material (EBG) structures consisting of layered periodic arrays of circular cylinders is presented. The response in the spectral domain of the woodpile EBGs excited by a dipole source is calculated using one-dimensional lattice sums, the 3-D transition matrix of a circular cylinder, and the generalized reflection and transmission matrices of the layered system. The closed-form expression of the radiated field is rigorously obtained by a finite integral of the spectral response. Comparisons with the far fields calculated using reciprocity both with the present approach and with a fully independent commercial EM software package are presented showing excellent agreement with the proposed method and demonstrating the high computational efficiency of the semianalytical formalism.

This paper presents an overview of our analytical and numerical methods to design radiative structures based on photonic crystals by means of leaky-wave theory. In particular, we present several parametric studies to justify the choice of the design parameters. Based on these studies, we show how it is possible to design highly directive devices in which the radiation can be described by a properly excited dominant leaky mode. The proposed design procedure can be easily extended to a wide class of structures, leading to the construction of sensors and antennas with high radiation efficiency and directivity.

Electromagnetic Band-Gap (EBG) media, working right above the band-gap can shape the radiation of a simple emitter embedded in their periodic structures. In this region of the dispersion diagram, degenerate lattice modes can be selectively excited with a proper positioning of the primary sources. This paper presents the design of an antenna that exploits such physical mechanism, which is potentially attractive at mm-waves since it relies on dielectric structures. An antenna fed by two sources and based on a square lattice of dielectric cylinders is presented. For the first time, the dependences of radiation properties on some geometrical parameters are investigated before moving to a final realistic design.

CA Jandieri Functional post-wall waveguides and waveguide based compact passive circuits - namely bandpass filters - that are formed by introducing additional metallic or dielectric posts inside the post-wall waveguide are analyzed. Scattering parameters (S-parameters) of the waveguide-based bandpass filters are calculated using the method of images combined with the lattice sums technique. The developed formulation is numerically very fast, hence it can be considered as one of the best-suited approaches for the analysis of multiple scattering in post-wall waveguides and for numerical structural optimization. A breeder genetic algorithm is employed as a global search heuristic in order to track down the optimal geometrical parameters for the introduced posts yielding a bandpass filter characteristic in the desired frequency bands. Comparison with other references validates the correctness and utility of our formalism. Different configurations for the specifications of post-wall waveguide-based bandpass filters are discussed.

International audience; A very efficient and accurate method is proposed to evaluate the Lattice Sums (LSs) for the analysis of leaky waves in two-dimensional (2-D) periodic waveguides. The LSs are series involving Hankel functions of arbitrary order, which are not convergent for complex wavenumbers. It is shown that by extending Ewald representations to higher-order Hankel functions, the LSs can be expressed in terms of spatial and spectral series, granting Gaussian convergence even in the case of complex and leaky waves. The method allows for the appropriate choice of the spectral determination for each space harmonic of a given LS coefficient, thus permitting one to obtain modal solutions that may correspond to physical and non-physical leaky-wave phenomena. First, the proposed LS calculation is exploited in the evaluation of the free-space one-dimensional (1-D) periodic Green's function for 2-D structures. Then, the same procedure for the LSs is implemented in a cylindrical harmonic expansion method, based on the transition-matrix and the generalized reflection-matrix approach, for the full-wave analysis of leaky modes in 2-D Electromagnetic Band-Gap waveguides formed by layered arrays of cylindrical inclusions. The presented LS formalism is numerically slim, very fast, and thus well suited for the analysis of a significant class of lossy periodic waveguides and leaky-wave antennas.

A rigorous self-contained formulation for analyzing electromagnetic scattering by a grating of plasmonic nanorods (Ag) coupled to a magneto-optical slab is presented. Bi-substituted gadolinium iron garnet is considered as the magneto-optical material. We measured the dielectric permittivity of the iron garnet and utilized the experimental data in our analyses. The method uses the Lattice Sums technique combined with the generalized reflection matrix approach. Using the method, the spectral response in reflectance as well as near-field distributions at resonance wavelengths have been numerical studied. Special attention has been paid to the coupling mechanism between the plasmonic grating and the magneto-optical slab. Physical insight is given to the strong field enhancement inside the magneto-optical material due to coupling with the plasmonic grating. Generalization of the method to the multilayered sandwiched structures, where the metal layer supporting surface plasmons is in contact with a layer possessing magnetically induced anisotropy, is straightforward. Such a combination enables one to achieve a multifold increase in sensitivity when compared with a system having just one nonmagnetic metal layer.

In this conceptual study, all-optical amplification of the light pulses in two weakly coupled nonlinear photonic crystal waveguides (PCWs) is proposed. We consider two adjacent PCWs, which consist of line defects in a 2D square lattice of periodically distributed circular rods made from dielectric material with Kerr-type nonlinearity. Dispersion diagrams of the PCW’s symmetric and antisymmetric modes are analyzed using a recently developed analytical formulation. The operating frequency is properly chosen to be located at the edge of the PCW’s dispersion diagram (i.e., adjacent to the photonic crystals low-energy band edge), where in the linear case no propagation modes are excited. However, in case of a nonlinear medium when the amplitude of the injected signal is above some threshold value, solitons are formed propagating inside the coupled nonlinear PCWs. The near field distributions of the propagating light pulse inside the coupled nonlinear PCWs and the output power of the received signal are numerically studied in a detail. A very good agreement between the analytic soliton solution based on the nonlinear Schrödinger equation and numerical result is obtained. Amplification coefficients are calculated for the various amplitudes of the input signals. The results vividly demonstrate the effectiveness of the weakly coupled nonlinear PCWs as an all-optical digital amplifier. © 2017, Electromagnetics Academy. All rights reserved.

During the last few decades, an extensive research effort has been aimed at studying and developing novel structures based on the photonic crystals composed of the multilayered arrays of periodically distributed circular rods. A photonic crystal with a complete bandgap has been used to localize electromagnetic waves to specific arrays and to guide the propagation of electromagnetic waves along certain directions at restricted frequencies. After this discovery, photonic crystals have inspired great interest because of their novel scientific and engineering applications in guiding devices for controlling the propagation of light. Various analytical and numerical methods have been developed to analyze the photonic crystal waveguides made by removing a row of either air columns or dielectric rods that result in multimode guiding [1, 2]. Recently, scientific attention has been paid to the possibility to efficiently guide electromagnetic waves along a chain formed by periodically distributed scattering elements (a simple single-layered structure) [3, 4]. A simplicity of design and fabrication could be considered as the main advantage of this structure. However, in order to validate its good guiding properties, detailed theoretical and numerical studies are needed. In this regard, we propose a Fourier series expansion method as an efficient method to study the guiding modes and leaky modes of infinite chain of periodically distributed circular rods [5]. In the proposed method a fictitious periodicity in the transverse direction (in the upper and lower regions of the guiding structure) is introduced and the original waveguide is approximated by one period of the periodic waveguide array. The electric and magnetic fields are expanded in a Fourier series and the problem is reduced to the set of linear equations for the Fourier coefficients. Based on the Fourier series expansion method we have numerically calculated the real and imaginary values of the propagation constant associated with the guiding and leaky modes, respectively. The results for the real value of the propagation constant has been compared with the results obtained based on the Lattice Sums technique and the excellent agreement has been observed between these two methods. Several numerical results have proofed the accuracy and validity of the propose formulation. Although in our studies we consider the circular rods to be the pure dielectric (without intrinsic loss), the problem can be easily generalized to study the structure composed of the periodically distributed plasmonic nanocylinders having a complex dielectric permittivity.

Interaction of light with the metallic nanostructures gives rise to various novel effects in photonics and optoelectronics [1]. Research of surface plasmons and their excitation by light is of particular interest in the studies of metamaterials, optical antennas, plasmonic sensors, and plasmonic crystals. The enhanced surface plasmon resonance in noble metallic systems at optical frequencies is expected to be a promising issue for realizing excellent scatterers and absorbers of the visible light. The surface plasmons characterize the unique response in collective motions of electrons on a metal-dielectric interface, which is allowed when the permittivity of the metal is negative for the wavelength of excitation. Recently, much attention has been paid to the light scattering from periodic nanowires coupled to a layered dielectric structure [2] for their applications to optical sensors, imaging, and integrated devices.

Light scattering by a grating made of the Ag nanocylinders onto a dielectric substrate is investigated using an accurate and rigorous formalism based on a recursive algorithm combined with the lattice sums technique. Physical insight is given to the localization of the field along the interfaces of the Ag nanocylinders, to the strong reflected field by the grating and the field enhancement at the surface of the dielectric substrate. The accuracy of the numerical analysis has been validated based on the principle of the energy conservation.

Radiation from a line source coupled to an Electromagnetic Band-Gap material is analyzed with two different methods. Using lattice sums technique combined with generalized reflection matrix method, the scattering from a crystal of infinite extension is rigorously investigated. The radiation from an electromagnetic crystal of finite extension is also solved with Cylindrical Wave Approach. The two methods show perfect agreement when the source is localized within the crystal, achieving a directive radiation. As a spacing between the two Electromagnetic Band-Gap layers is introduced, the finite structure analyzed with the Cylindrical Wave Approach shows significant edge diffraction at the boundaries. Agreement between results from the methods is recovered introducing a suitable layout of absorbers in the cavity Radiation from a line source coupled to an Electromagnetic Band-Gap material is analyzed with two different methods. Using lattice sums technique combined with generalized reflection matrix method, the scattering from a crystal of infinite extension is rigorously investigated. The radiation from an electromagnetic crystal of finite extension is also solved with Cylindrical Wave Approach. The two methods show perfect agreement when the source is localized within the crystal, achieving a directive radiation. As a spacing between the two Electromagnetic Band-Gap layers is introduced, the finite structure analyzed with the Cylindrical Wave Approach shows significant edge diffraction at the boundaries. Agreement between results from the methods is recovered introducing a suitable layout of absorbers in the cavity.

Comparison of the beam-shaping effect of a field radiated by a line source, when an ideal infinite structure constituted by two photonic crystals and an actual finite one are considered, has been carried out by means of two different methods. The lattice sums technique combined with the generalized reflection matrix method is used to rigorously investigate the radiation from the infinite photonic crystals, whereas radiation from crystals composed of a finite number of rods along the layers is analyzed using the cylindrical-wave approach. A directive radiation is observed with the line source embedded in the structure. With an increased separation distance between the crystals, a significant edge diffraction appears that provides the main radiation mechanism in the finite layout. Suitable absorbers are implemented to reduce the above-mentioned diffraction and the reflections at the boundaries, thus obtaining good agreement between radiation patterns of a localized line source coupled to finite and infinite photonic crystals, when the number of periods of the finite structure is properly chosen. Comparison of the beam-shaping effect of a field radiated by a line source, when an ideal infinite structure constituted by two photonic crystals and an actual finite one are considered, has been carried out by means of two different methods. The lattice sums technique combined with the generalized reflection matrix method is used to rigorously investigate the radiation from the infinite photonic crystals, whereas radiation from crystals composed of a finite number of rods along the layers is analyzed using the cylindrical-wave approach. A directive radiation is observed with the line source embedded in the structure. With an increased separation distance between the crystals, a significant edge diffraction appears that provides the main radiation mechanism in the finite layout. Suitable absorbers are implemented to reduce the above-mentioned diffraction and the reflections at the boundaries, thus obtaining good agreement between radiation patterns of a localized line source coupled to finite and infinite photonic crystals, when the number of periods of the finite structure is properly chosen.