Diffraction Of Plane Wave Research Articles

Singular integral equations in diffraction problem by an infinite periodic strip grating with one strip removed

The H-polarized plane wave diffraction by the infinite periodic grating with removed strip is considered. In the formulation, the current induced on each strip is divided into two currents, the current on the infinite periodic strip grating and the correction current induced by the removal of a strip. The scattered field is inducted by these currents. The problem is reduced to the dual integral equations with respect to the unknown spectral function of the correction field, and then to the singular integral equation with additional conditions. The singular integral equation of infinite periodic grating is also presented. The near and far fields scattered by the grating are analyzed.

Hybrid Ray-Mode Analysis of E-Polarized Plane Wave Diffraction by a Thick Slit

A high-frequency asymptotic method has been applied to formulate E-polarized plane wave diffraction by a thick slit. The slit structure is regarded as an open-ended parallel plane waveguide cavity, and the excitation of the waveguide modes and their reradiation are derived from a ray-mode conversion technique. Comparison with another method reveals the validity and effectiveness of our formulation.

Diffraction of electromagnetic plane wave by a slit in a homogeneous bi-isotropic medium

We investigated the diffraction of an electromagnetic plane wave by an infinite slit embedded in a homogeneous bi-isotropic medium. With the aim of deriving explicit expressions for the left- and right-handed Beltrami fields, we used the Fourier integral transform, the Wiener–Hopf technique and the steepest descent asymptotic method. The electric and magnetic fields, E and H, were determined from the Beltrami fields. Our graphical results indicate that the strength of both electric and magnetic fields reduces with the dissipation of bi-isotropic medium. While matching the diffraction pattern with the existing plane wave solution, the objective was, and is, to see how well spherical wave solution performs when it is developed for plane wave solution.

Diffraction of plane waves by a periodic array of nonlinear circular cylinders

It is well known that standing waves, as special bound states in the radiation continuum, may exist on a periodic array of dielectric cylinders at a discrete set of frequencies if the medium is linear. Recent numerical studies indicate that nonlinear standing waves could exist continuously with respect to the frequency on a periodic array of cylinders with a Kerr nonlinearity. In this paper, we study the diffraction of a normal incident plane wave by a periodic array of circular cylinders with a Kerr nonlinearity. Using a perturbation method and a highly accurate numerical method, we show that a plane incident wave may couple to a nonlinear standing wave, and in general, there are four different couplings leading to four asymmetric solutions in two pairs. The existence of these asymmetric solutions provides another example for the symmetry-breaking phenomenon. Importantly, it seems that the asymmetric solutions (thus the symmetry-breaking phenomenon) appear for incident waves of arbitrarily low intensity.

Solution of the Plane Wave Diffraction Problem by a Strip with Different Boundary Conditions on its Faces

Solution of the Plane Wave Diffraction Problem by a Strip with Different Boundary Conditions on its Faces

High-frequency plane wave diffraction by an ideal strip at oblique incidence: Parabolic equation approach

The problem of diffraction of a high-frequency plane wave by a strip with ideal boundary conditions is considered for the case of oblique incidence. The study is based on the parabolic approximation, which is used to construct an expression for the directional pattern in terms of single quadratures. A similar result is obtained using the embedding formula. It is shown that the derived expression approximates the classical Michaeli result. A proof of the optical theorem for the parabolic problem is presented.

Catastrophe optics of sharp-edge diffraction.

A classical problem of diffraction theory, namely plane wave diffraction by sharp-edge apertures, is here reformulated from the viewpoint of the fairly new subject of catastrophe optics. On using purely geometrical arguments, properly embedded into a wave optics context, uniform analytical estimates of the diffracted wavefield at points close to fold caustics are obtained, within paraxial approximation, in terms of the Airy function and its first derivative. Diffraction from parabolic apertures is proposed to test reliability and accuracy of our theoretical predictions.

Analytical investigation into the resonance frequencies of a curling probe

The term ‘active plasma resonance spectroscopy’ (APRS) denotes a class of closely related plasma diagnostic methods which utilize the natural ability of plasmas to resonate on or near the electron plasma frequency ; an electrical radio frequency signal (in the GHz range) is coupled into the plasma via an antenna or a probe, the spectral response is recorded and a mathematical model is employed to determine plasma parameters such as the plasma density and the electron temperature. The curling probe, recently invented by Liang et al (2011 Appl. Phys. Express 4 066101), is a novel realization of the APRS concept which has many practical advantages. In particular, it can be miniaturized and flatly embedded into the chamber wall, thus allowing the monitoring of plasma processes without contamination nor disturbance. Physically, the curling probe can be understood as a ‘coiled’ form of the hairpin probe (Stenzel 1976 Rev. Sci. Instrum. 47 603). Assuming that the spiralization of the probe has little electrical effect, this paper investigates the characteristcs of a ‘straightened’ curling probe by modeling it as an infinite slot-type resonator that is in direct contact with the plasma. The diffraction of an incident plane wave at the slot is calculated by solving the cold plasma model and Maxwell’s equations simultaneously. The resonance frequencies of the probe are derived and are found to be in good agreement with the numerical results of the probe inventors.

Modeling Pyramidal Absorbers Using the Fourier Modal Method and the Mode Matching Technique

The problem of plane wave diffraction from the periodic structure of an infinite PEC wall lined with pyramidal absorbers is considered. A hybrid method based on the R-matrix Fourier modal method (RFMM) and the mode matching (MM) of fields is used for the efficient and robust analysis of this class of absorbers. The hybrid method benefits from the discrete spectrum of the periodic structure in transverse directions and consequently avoids spatial discretization along the periodicity axes. This leads to considerable reduction in the number of unknown coefficients. Furthermore, the method is capable of considering dispersive and inhomogeneous materials which are frequently used in the absorber industry. Several examples are outlined, simulated, and measured to show the efficiency and accuracy of the method. The versatility and flexibility of the hybrid RFMM-MM technique makes it suitable for the optimal design of pyramidal absorbers to achieve further improvements in their performances.

Energy modeling method as applied to diffraction of stationary plane elastic waves

The energy method uses reciprocity works theorem and transformation of occurring hypersingular integrals for a system of equations consisting of singular integral equations of the first and second kind. Algorithms for the numerical solution are obtained by the method of discrete singularities. Precision of calculations is controlled due to algorithmic diversity. Application to the numerical modeling of diffraction of stationary plane waves on finite and periodic systems of different inhomogeneities is shown

Arbitrarily Oriented Perfectly Conducting Wedge Over a Dielectric Half-Space: Diffraction and Total Far Field

Complex scattering targets are often made by structures constituted by wedges and penetrable substrates which may interact at near field. In this paper, we describe a complete procedure to study this problem with possible developments in radar technologies (like GPR), antenna development, or electromagnetic compatibility (tips near substrates). The diffraction of an incident plane wave by a perfectly conducting (PEC) wedge over a dielectric half-space is studied using generalized Wiener–Hopf equations (GWHEs), and the solution is obtained using analytical and numerical–analytical approaches that reduce the Wiener-Hopf (WH) factorization to integral equations (IEs). The mathematical aspects are described in a unified and consistent theory for angular and layered region problems. The proposed procedure is valid for the general case and the paper focuses on E-polarization at normal incidence. The solutions are given in terms of geometrical/uniform theory of diffraction (GTD/UTD) diffraction coefficients and total far fields for engineering applications. This paper presents several numerical test cases that show the validity of the proposed method.

Solution of the three-dimensional problem of plane wave diffraction by a two-period plane grating

Using the discrete source method, we develop an algorithm for solving the three-dimensional problem of wave scattering by a plane grating consisting of acoustically soft or acoustically stiff bodies. An efficient algorithm is proposed for determining the periodic Green’s function of the grating. Numerical results are obtained for different geometries of the grating elements. The fulfillment of the energy conservation law is verified along with the fulfillment of the boundary condition at the surface of the central grating element.

Highly polarized emission from a GaN-based ultraviolet light-emitting diode using a Si-subwavelength grating on a SiO2 underlayer

The polarization characteristics of a 370nm GaN-based ultraviolet light-emitting diode (UV-LED) were controlled by a subwavelength grating (SWG) on a low-refractive-index SiO2 underlayer inserted between the SWG and LED surface. Highly polarized UV emission was demonstrated by utilizing the Bloch eigenmode resonance in the SWG structure for the two orthogonal polarization states. The polarization ratio of the emission reached 16:1, which is the highest reported to date for direct emission from a GaN-based UV-LED. The decrease in UV emission was also prevented by suppressing the diffracted plane wave and by increasing the amplitude of the wave incident onto the SWG structure; this increase was achieved by taking advantage of the low refractive index of SiO2.

Electromagnetic Plane Wave Diffraction by Loaded N-Slits on Thick Conducting Screen

Electromagnetic Plane Wave Diffraction by Loaded N-Slits on Thick Conducting Screen

Dynamic two-dimensional refractive index modulation for high performance acousto-optic deflector.

The performance of an acousto-optic deflector is studied for two-dimensional refractive index that varies as periodic and sinc functions in the transverse and longitudinal directions, respectively, with respect to the direction of light propagation. Phased array piezoelectric transducers can be operated at different phase shifts to produce a two-dimensionally inhomogeneous domain of phase grating in the acousto-optic media. Also this domain can be steered at different angles by selecting the phase shift appropriately. This mechanism of dynamically tilting the refractive index-modulated domain enables adjusting the incident angle of light on the phase grating plane without moving the light source. So the Bragg angle of incidence can be always achieved at any acoustic frequency, and consequently, the deflector can operate under the Bragg diffraction condition at the optimum diffraction efficiency. Analytic solutions are obtained for the Bragg diffraction of plane waves based on the second order coupled mode theory, and the diffraction efficiency is found to be unity for optimal index modulations at certain acoustic parameters.

Optimized vector sound intensity measurements with a tetrahedral arrangement of microphones in a spherical shell.

Recent times have seen the introduction of small spherical arrays whose usefulness as sound intensity probes is the focus of this paper. The presented probe consists of a spherical shell, 30 mm in diameter, housing four 14 in. microphones arranged in a regular tetrahedral configuration. Classical formulae may be used to estimate the sound intensity vector, as may methods based on spherical harmonics decomposition. Results are shown to be comparable to those obtained from classical sound intensity probes. The existence of an analytical model for a plane wave's diffraction about a sphere provides a means for adopting common optimization techniques for potentially improving the intensity vector estimate, however. This paper examines the validity of non-linear least squares optimization in conjunction with the proposed spherical sound intensity probe when placed in the following sound fields: (1) a simple plane wave; (2) a plane wave corrupted by noise; and (3) multiple incident plane waves. Under certain conditions, the probe is shown to greatly extend the operational frequency range of classical sound intensity probes. The optimization algorithm is found to lack robustness against deviations from plane wave conditions, however.

Near-wavelength diffraction gratings for surface plasmon polaritons.

In this Letter, we study numerically diffraction gratings for surface plasmon polaritons. Investigated plasmonic gratings consist of a periodic set of dielectric ridges located on the metal surface. The grating period is comparable with the wavelength of the incident wave. The simulation results obtained within the rigorous coupled-wave analysis framework have shown that the SPP diffraction on a plasmonic grating with parasitic scattering suppression is remarkably close to the diffraction of a TE-polarized plane wave on a conventional grating. A compact and efficient reflecting plasmonic grating is considered as an example. The presented results can be used for the design of high-efficiency two-dimensional optical elements for steering surface plasmon propagation.

Phase-shifted Bragg gratings for Bloch surface waves.

An analogue of phase-shifted Bragg grating (PSBG) for Bloch surface waves (BSW) propagating along the interface between a one-dimensional photonic crystal and a homogeneous medium is proposed. The studied structure consists of a set of dielectric ridges located on the photonic crystal surface, the height of which is chosen so that they encode the required distribution of the effective refractive index. Rigorous simulation results of the surface wave diffraction on the proposed structure are compared with the plane wave diffraction on a conventional phase-shifted Bragg grating. The simulation results demonstrate the possibility of using the proposed analogue of PSBG for temporal differentiation of picosecond BSW pulses. The obtained results can find application in the design of the prospective on-chip systems for all-optical analog computing.

A finite difference method for effective treatment of mild-slope wave equation subject to non-reflecting boundary conditions

A numerical model for coastal water wave motion that includes an effective method for treatment of non-reflecting boundaries is presented. The second-order one-way wave equation to approximate the non-reflecting boundary condition is found to be excellent and it ensures a very low level of reflection for waves approaching the boundary at a fairly wide range of the incidence angle. If the Newman approximation is adopted, the resulting boundary condition has a unique property to allow the free propagation of wave components along the boundary. The study is also based on a newly derived mild-slope wave equation system that can be easily made compatible to the one-way wave equation. The equation system is theoretically more accurate than the previous equations in terms of the mild-slope assumption. The finite difference method defined on a staggered grid is employed to solve the basic equations and to implement the non-reflecting boundary condition. For verification, the numerical model is then applied to three coastal water wave problems including the classical problem of plane wave diffraction by a vertical circular cylinder, the problem of combined wave diffraction and refraction over a submerged hump in the open sea, and the wave deformation around a detached breakwater. In all cases, the numerical results are demonstrated to agree very well with the relevant analytical solutions or with experimental data. It is thus concluded that the numerical model proposed in this study is effective and advantageous.

Plasmon resonances in a quartz nanofiber coated with a silver layer

A 2D problem of diffraction of the TM-polarized plane wave by a quartz nanofiber coated with a silver layer is investigated. The total scattering cross-section is numerically calculated in the range of visible light waves (400–700 nm). It is found that, at certain geometric parameters of the structure, not only dipole but also multipole plasmon resonances arise in the investigated range of wavelengths. Scattering patterns at resonance frequencies are calculated. It is demonstrated that deposition of the silver layer onto a quartz nanofiber can decrease the scattering cross section several times.