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This paper presents an analytical and numerical investigation of the radiation features of an interesting class of electromagnetic bandgap (EBG) structures excited by an electric line source. The radiation from two-dimensional (2-D) lattices made with lossless dielectric cylinders, typically optimized by using the Bloch analysis of the corresponding 2-D photonic crystals, are originally investigated in terms of leaky waves. A thorough modal analysis of open waveguides, composed by a finite number of periodic chains of circular dielectric rods, is presented that shows a multiplicity of bound and leaky modes. Two radiation windows are identified and the relevant directive features are described in terms of properly excited dominant leaky modes. The possible excitation of higher order leaky modes and guided modes has been carefully considered, by also capturing the relevant residue contributions in a nonspectral representation of the excited fields. The final results on radiated fields by realistic truncated structures, obtained by ad-hoc software as well as full-wave EM simulators, are in excellent agreement with those predicted by the proposed leaky-wave approach.

A full-wave numerical approach for the analysis of bounded and leaky modes in periodic chain composed of both lossless and lossy 2-D cylindrical inclusions is proposed. An effective method based on the lattice sums technique is adapted to the analysis of modes with complex propagation wavenumbers, thus allowing for the appropriate choice of the spectral determination for each spatial harmonic. Periodic chains of both dielectric and silver nanocylinders are studied and the relevant modal phase and attenuation constants are rigorously calculated in all the different propagation regimes, including bound and radiative regions as well as plasmonic behaviors.

The thickness-dependent multimodal nature of three-dimensional (3D) coupled photonic crystal waveguides is investigated with the aim of realizing a medium for controlled optical gap soliton formation in the slow light regime. In the linear case, spectral properties of the modes (dispersion diagrams), location of the gap regions versus the thickness of the 3D photonic crystal, and the near-field distributions at frequencies in the slow light region are analyzed using a full-wave electromagnetic solver. In the nonlinear regime (Kerr-type nonlinearity), we infer an existence of crystal-thickness-dependent temporal solitons with stable pulse envelope and use the solitonic pulses for driving quantum transitions in localized quantum systems within the photonic crystal waveguide. The results may be useful for applications in optical communications, multiplexing systems, nonlinear physics, and ultrafast spectroscopy.

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.

We study the dispersion and scattering properties of electromagnetic modes coupled to a helically ordered spin lattice hosted by a dielectric oxide with a ferroelectric polarization driven by vector spin chirality. Quasianalytical approaches and full-fledged numerics evidence the formation of a chiral magnonic photonic band gap and the presence of gate-voltage dependent circular dichroism in the scattering of electromagnetic waves from the lattice. Gating couples to the emergent ferroelectric polarization and hence, to the underlying vector-spin chirality. The theory relies on solving simultaneously Maxwell's equations coupled to the driven localized spins taking into account their spatial topology and spatial anisotropic interactions. The developed approach is applicable to various settings involving noncollinear spins and multiferroic systems with potential applications in noncollinear magnetophotonics.

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.

Purpose The purpose of this paper is to develop a rigorous self-contained formulation for analyzing electromagnetic scattering by grating of plasmonic nanorods. The authors investigate this structure from the viewpoint of the practical application as a refractive index plasmonic sensor. The presented rigorous formulation is accompanied with a neat implementation providing a high computation efficiency and could be considered as an important tool for designing and optimizing compact sensors. Design/methodology/approach Scattering of an incident plane wave by grating made of a periodic arrangement of metal-coated dielectric nanocylinders on a dielectric slab is rigorously investigated using the recursive algorithm combined with the lattice sums technique. As a dielectric slab, the authors consider glass material, which is widely used in experiments, whereas silver (Ag) is used as a low loss metal suitable to excite plasmon resonances. The main advantage of the developed self-contained formulation is that first the authors extract the reflection and transmission matrices of a single planar array from a separate analysis of the grating and the slab and then obtain the scattering characteristics of the whole structure by using a recursive formula. The method is computationally fast. Findings Dependence of the surface plasmon resonance wavelength on the refractive index of the surrounding medium is carefully investigated. The resonance peaks are red-shifted with respect to an increasing refractive index of surrounding medium showing an almost linear behavior. Near field distributions are analyzed at the resonance wavelengths of the spectral responses. Special attention is paid to the formation of the dual-absorption bands because of the excitation of the localized surface plasmons. The authors give physical insight to the coupling between grating and the glass slab. The authors found that a strong enhancement of the field inside the slab occurs when the scattered wave of the grating is phase-matched to the guided modes supported by the slab. Originality/value In the authors’ formulation, they do not use any approximation and it is rigorous and accurate. The authors use their original method. The method is based on the lattice sums technique and uses the recursive algorithm to calculate the generalized reflection and transmission characteristics by grating. Such fast and accurate method is an effective tool apt for designing and optimizing tailored sensors, for e.g. advanced biomedical applications.

Functional post-wall waveguides that are formed by periodically distributed dielectric posts are numerically analyzed. In this preliminary study, the propagation constant and attenuation constant of the dielectric post-wall waveguide is rigorously calculated using our originally developed numerical method. The developed formulation is accurate and numerically very fast. Structural parameters of the dielectric post-wall waveguide are properly chosen in order to achieve the confinement of the field in the guiding region as strong as possible even in case of one-layered dielectric structure. The final goal of our investigations is to realize the functional dielectric post-wall waveguide-based filters, which are expected to have a practical application in THz region, where the metallic (PEC) rods are losing their properties.

A full-wave theoretical formalism for the propagation of temporal solitons in 2D Photonic Crystal (PhC) waveguides based on a multi-harmonic treatment (full-wave modal analysis) of the nonlinear setup is presented.

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.

Propagation of the temporal soliton in Kerr-type photonic crystal waveguide is investigated theoretically and numerically. An expression describing the evolution of the envelope of the soliton based on the full-wave modal analysis, taking into account all space-harmonics, is rigorously obtained. The nonlinear coefficient is derived, for the first time, based on a modification of the refractive indices for each space-harmonic due to the Kerr-type nonlinearity. For illustrating the general formulation and results, we performed extensive computational electromagnetics simulations for the propagation of gap solitons in an experimentally feasible photonic crystal waveguides, endorsing the correctness and usefulness of the proposed formalism.

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.

The realization of all-optical AND logic gates for pulsed signal operation based on the photonic bandgap transmission phenomenon is proposed. We are using realistic planar air-hole type coupled photonic crystal waveguides (C-PCWs) with Kerr-type nonlinear background medium. The novelty of our analysis is that the proposed AND logic gate operates with the temporal solitons, which maintain a stable envelope propagating in the nonlinear C-PCWs, enabling true ultrafast full-optical digital signal processing in the time-domain. The bandgap transmission takes place when the operating frequency is chosen at the very edge of the dispersion curve of one of the supermodes in the C-PCWs. In this regard, our original fast and accurate method is used to efficiently calculate the supermodes of the C-PCW system. The underlying semi-analytical full-wave modal analysis is based on the evaluation of the lattice sums for complex wavenumbers using the transition-matrix method in combination with the generalized reflection-matrix approach. As a proof of concept successful pulse operation of the all-optical AND logic gate is demonstrated in the framework of extensive full-wave finite-difference time-domain electromagnetics analysis.

In this manuscript we propose an easily scalable true all-optical AND logic gate for pulsed signal operation based on band-gap transmission within nonlinear realistic air-hole type coupled photonic crystal waveguides (C-PCW). We call it "true" all-optical AND logic gate, because all AND gate topologies operate with temporal solitons that maintain a stable pulse envelope during the optical signal processing along the different C-PCW modules yielding ultrafast full-optical digital signal processing. We directly use the registered (output) signal pulse as new input signal between multiple concatenated nonlinear C-PCW modules (i.e. AND gates) to setup a multiple-input true all-optical AND logic gate. Extensive full-wave computational electromagnetic analysis proves the correctness of our theoretical studies and the proposed operation principle of the multiple-input AND logic gate is vividly demonstrated for realistic C-PCWs. CA Jandieri

Scattering of light by metal-coated dielectric nanocylinders periodically distributed along a cylindrical surface is investigated both theoretically and numerically. The structure is under the authors' interest because of its practical application in design and fabrication of plasmonic devices such as plasmonic ring resonators, Plasmonic Crystals and THz waveguides. The method is based on the T-matrix approach and the field expansion into the cylindrical Floquet modes. The method is rigorous, straightforward and can be easily applied to various cylindrical configurations with different types and locations of the excitation sources. Scattering cross section and absorption cross section of three and four silver (Ag) coated-dielectric nanocylinders periodically situated along a cylindrical surface are studied. Near field distributions are investigated at particular wavelengths corresponding to the resonance wavelengths in the spectral responses. Special attention is paid to the unique and interesting phenomena characterizing the cylindrical structure composed of the metal-coated nanocylinders such as: a ) localization of the field at the outer and inner interfaces of the metal-coated nanocylinders; b) excitement of the field in the gap region between the nanocylinders through the coupled plasmon resonance and c) strong confinement of the field inside the cylindrical structure. Detailed investigations have shown that unique phenomena characterizing the cylindrical configurations of the nanocylinders can be realized using a relatively simple structure composed of three nanocylinders and there is no need to further increase a number of the scatterers (nanocylinders).

Functional post-wall waveguide (PWW) based passive circuits are formed by introducing specific arrangements of additional posts into the PWW structure. Each arrangement represents a circuit element and consists of a circular array of cylindrical posts periodically distributed on the circumference of the corresponding ring. The circular arrays (i.e. the circuit elements) provide enough degrees of freedom to tailor the spectral response in the framework of an ultra-compact planar filter topology. The PWW circuit is analyzed using image theory in combination with the lattice sums technique yielding a highly-efficient semi-analytical computational scheme that is perfectly suitable for the numerical structural optimization of mm-wave band-pass filters. Along an exemplary study we demonstrate the feasibility of steep skirt selectivity within a device footprint of around 0.75A2.

International audience; Full-wave numerical approach for the analysis of leaky modes in periodic and bandgap structures composed of two-dimensional cylindrical inclusions has been proposed. A self-contained formulation is developed that uses a fast and accurate calculation of the lattice sums, which allows us for an appropriate choice of the spectral determination for each spatial harmonic. We analyze numerically a periodic chain composed of dielectric rods. Phase and attenuation constants are calculated and compared with those obtained by Fourier series expansion method with perfectly matched layers. A very good agreement is observed in a wide frequency range, while the computation time of the proposed approach is much faster.

Modal analysis of infinite periodic chain composed of a square scatterer within the unit cell has been analyzed using the Fourier series expansion method combined with PML. Phase constant and attenuation constant associated with the guiding and leaky modes, respectively have been efficiently calculated.

Full-wave numerical approaches for the analysis of leaky modes propagating in Electromagnetic-Bandgap (EBG) waveguides composed by multilayered arrays of two-dimensional (2D) cylindrical inclusions have been proposed. A first method based on the lattice sums technique for periodic structures with inclusions of circular section has been suitably adapted to the analysis of modes with complex propagation wavenumbers. The self-contained formulation uses a fast and accurate calculation of the lattice sums, which allows for an appropriate choice of the spectral determination for each spatial harmonic. A further full-wave modal method based on the Fourier Series Expansion in conjunction with perfectly matched layers (PMLs) has been developed, which can take into account cylindrical inclusions with arbitrary geometry of the transverse section. Real and imaginary parts of the propagation wavenumber are calculated with the two proposed approaches for a typical EBG waveguide and a very good agreement is observed in a wide frequency range.

International audience; The efficient calculation of the Lattice Sums (LSs) for evaluating the free-space periodic Green's function (PGF) of an infinite phased array of line sources is addressed here and is extended for the first time to leaky waves. The method is based on the Graf's addition theorem for the 0-th order Hankel function that leads to an expansion in terms of Bessel functions of the relevant PGF. The coefficients of the expansion, called LSs, are slowly convergent series involving higher-order Hankel functions. Their efficient computation is performed by resorting to an extension of the standard Ewald method, in terms of spectral and spatial series having Gaussian convergence even in the case of complex waves and improper harmonics. The adopted approach allows for the analysis of a wide class of periodic waveguides supporting leaky modes, and it is particularly suitable for the treatment of infinite array of dielectric fibers and rods.

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.

We introduce a weakly coupled photonic crystal waveguide as a promising and realistic model for all-optical amplification. A symmetric pillar type coupled photonic crystal waveguide consisting of dielectric rods periodically distributed in a free space is proposed as all-optical amplifier. Using, the unique features of the photonic crystals to control and guide the light, we have properly chosen the frequency at which only one mode (odd mode) becomes the propagating mode in the coupled photonic crystal waveguide, whereas another mode (even mode) is completely reflected from the guiding structure. Under this condition, the all-optical amplification is fully realized. The amplification coefficient for the continuous signal and the Gaussian pulse is calculated.

A semi-analytical approach for a periodic planar array formed by a finite number of circular cylinders is presented using a model of layered cylindrical arrays. The method consists in extracting the reflection and transmission matrices of a cylindrically periodic array of circular cylinders and then obtaining the characteristics of layered structures by using a recursive formula.

A semi-analytical approach for analyzing the electromagnetic radiation of a line source in cylindrical electromagnetic bandgap (EBG) structure is presented. The cylindrical structure is composed of circular rods periodically distributed along concentrically layered circular rings. The method uses the T-matrix of a circular rod in isolation, the reflection and transmission matrices of a cylindrical array expressed in terms of the cylindrical waves as the basis, and the generalized reflection and transmission matrices for a layered cylindrical structure. Using the proposed method, the radiated field from a line source placed inside a three-layered cylindrical EBG structure with defects is investigated. The defects are created by removing the particular circular rods from each circular ring. The structure is prominent from the viewpoint of flexible design of the directive antennas. Numerical examples demonstrate that the cylindrical EBG structures are very effective at forming and controlling the directed beam in the radiated fields.

The mutual correlation function of the phase ∞uctuations of scattered ordinary and extraordinary waves by the magnetized plasma slab with electron density ∞uctuations and the variance of the Faraday angle is calculated by the perturbation method. Analytical expression of broadening of the spatial spectrum of scattered radiation is obtained for arbitrary ∞uctuation spectrum. Numerical calculations are carried out for the anisotropic Gaussian ∞uctuation spectrum at difierent anisotropy factor and the angle of inclination of prolate irregularities with respect to the external magnetic fleld. Isolines of the normalized root mean square deviation of the Faraday angle nonlinearly depends on the angle of inclination of prolate irregularities and increases in proportion to the anisotropy factor; two receiving antennas are located in orthogonal planes. It is shown that the broadening of the spatial spectrum of scattered electromagnetic waves

Scattering of the electromagnetic waves by a randomly inhomogeneous electrically gyrotropic slab are studied using the perturbation method. Second order statistical moments of the ordinary and extraordinary waves scattered by the magnetized plasma slab are obtained using the boundary conditions for an arbitrary correlation function of electron density fluctuations. Normalized correlation functions at quasi-longitudinal propagation along the external magnetic field are calculated for the carrier frequency 0.1 MHz and 40 MHz. Isolines of the normalized variance of Faraday angle are constructed for the anisotropic Gaussian correlation function at various anisotropy factors of irregularities. Obtained results are in a good agreement with the experimental data.

A method for reducing ground clutter contribution from ground penetrating radar (GPR) data is proposed for discrimination of landmines located in shallow depth. The algorithm of this method is based on the Matching Pursuit (MP) that is a technique for non-orthogonal signal decomposition using dictionary of functions. As the dictionary of function, a wave-based dictionary constructed by taking account of scattering mechanisms of electromagnetic (EM) wave by rough surfaces is employed. Through numerical simulations, performance of ground clutter reduction is evaluated. The results show that the proposed method has good performance and is effective for GPR data preprocessing for discrimination of shallowly buried landmines.

A rigorous semi-analytical approach for the scalar field in a microstructured optical fiber, which is formed of layered cylindrical arrays of circular rods symmetrically distributed on each concentric cylindrical layer, is presented. The method uses the T-matrix of a circular rod in isolation and the generalized reflection and transmission matrices of cylindrical arrays. Numerical examples of the mode index for three-layered hexagonal structure of circular air holes are demonstrated and compared with those obtained by a variational method.

Directivity of radiation from a localized source coupled to electromagnetic crystals is investigated theoretically using a two-dimensional model. The closed form expression for the far field of radiation is derived and used to examine two primary factors governing the directivity. It is shown that the directivity is uniquely characterized by the transmission windows of the electromagnetic crystals in the frequency and angular spectral domains and the Fabry-Perot resonance condition for the radiated field in the space surrounding the source.

Features of spatial power spectrum (SPS) of scattered radiation in a randomly inhomogeneous medium with strongly prolated anisotropic inhomogeneities of dielectric permittivity are investigated. In single scattering approximation, it has been shown that a pronounced gap along a direction of prolate inhomogeneities appears in SPS. Features of SPS of multiple scattered waves at oblique illumination of a boundary of randomly-inhomogeneous medium with prolate irregularities have been analytically studied using smooth perturbation method taking into account diffraction effects. Numerical calculations have shown that with an increase of a distance passing by 192 Gavrilenko et al. the wave in random media, SPS has a double-peaked shape and a gap substantially increases. Its maximum is slightly changed and the width is broadening. The results have been obtained analytically for the first time and could find extensive practical application in optics and be useful in development of principles of remote sensing of random media.

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.

A novel formulation of radiation from a localized line source placed in two-dimensional photonic crystals consisting of layered periodic arrays of parallel circular cylinders is presented. The method employs the spectral domain approach. The spectral response of the photonic crystals to the line source excitation is calculated using the lattice sums, the T-matrix of a circular cylinder, and the generalized reflection and transmission matrices of the layered system. The far-zone radiated field is obtained using the conventional asymptotic method to the spectral response. The radiation patterns of the localized line source sandwiched by two photonic crystals are numerically studied.

All-optical amplification of the light pulse in a weakly coupled nonlinear photonic crystal waveguides (PCWs) is proposed. We consider pillar-type PCWs, which consist of the periodically distributed circular rods made from a Kerr-type dielectric material. The operating frequency is properly chosen to be located at the edge of the dispersion diagram of the modes. In case of nonlinear medium when the amplitude of the injected signal is above some threshold value, solitons are formed and they are propagating inside the coupled nonlinear PCWs. Near field distributions of the light pulse and the output powers of the registered signals are studied in a detail. A good agreement between the numerical and theoretical studies is observed.

Electromagnetic scattering from two-dimensional photonic crystals with two-dimensionally periodic defects is analyzed using a model of multilayered periodic arrays of parallel circular cylinders. The reflectance of the photonic crystals of finite thickness, which are free-standing or embedded in a dielectric slab, is obtained in terms of the lattice-sums, the T-matrix of a circular cylinder, and the generalized reflection matrix for a layered system. Numerical examples demonstrate that the refection and transmission bands of the crystals are reformed by introducing the periodic defects and their band natures are very sensitive to the polarization of excitation and the relative position of the defect element within a unit cell.