Showing papers on "Physical optics published in 2011"

The Dicke model in quantum optics: Dicke model revisited

Abstract: A short review of recent developments of the Dicke model in quantum optics is presented. The focus is on the model in a cavity at zero temperature and in the rotating wave approximation. Topics discussed include spectroscopic structures, the giant quantum oscillator, entanglement and phase transitions.

Polarization sensitive elements fabricated by femtosecond laser nanostructuring of glass [Invited]

Abstract: We review recent progress in application of femtosecond laser nanostructuring of fused silica. The tight control of nanostructures’ properties through writing parameters is demonstrated implementing elements with unique optical properties, which can be widely used in material processing, microscopy, optical trapping and manipulation.

Classical and quantum properties of cylindrically polarized states of light

Abstract: We investigate theoretical properties of beams of light with non-uniform polarization patterns. Specifically, we determine all possible configurations of cylindrically polarized modes (CPMs) of the electromagnetic field, calculate their total angular momentum and highlight the subtleties of their structure. Furthermore, a hybrid spatio-polarization description for such modes is introduced and developed. In particular, two independent Poincare spheres have been introduced to represent simultaneously the polarization and spatial degree of freedom of CPMs. Possible mode-to-mode transformations accomplishable with the help of Bconventional polarization and spatial phase retarders are shown within this representation. Moreover, the importance of these CPMs in the quantum optics domain due to their classical features is highlighted.

Scattering and absorption of light by ice particles: Solution by a new physical-geometric optics hybrid method

Abstract: A new physical-geometric optics hybrid (PGOH) method is developed to compute the scattering and absorption properties of ice particles. This method is suitable for studying the optical properties of ice particles with arbitrary orientations, complex refractive indices (i.e., particles with significant absorption), and size parameters (proportional to the ratio of particle size to incident wavelength) larger than ∼20, and includes consideration of the edge effects necessary for accurate determination of the extinction and absorption efficiencies. Light beams with polygon-shaped cross sections propagate within a particle and are traced by using a beam-splitting technique. The electric field associated with a beam is calculated using a beam-tracing process in which the amplitude and phase variations over the wavefront of the localized wave associated with the beam are considered analytically. The geometric-optics near field for each ray is obtained, and the single-scattering properties of particles are calculated from electromagnetic integral equations. The present method does not assume additional physical simplifications and approximations, except for geometric optics principles, and may be regarded as a “benchmark” within the framework of the geometric optics approach. The computational time is on the order of seconds for a single-orientation simulation and is essentially independent of the size parameter. The single-scattering properties of oriented hexagonal ice particles (ice plates and hexagons) are presented. The numerical results are compared with those computed from the discrete-dipole-approximation (DDA) method.

Exploiting the time-reversal operator for adaptive optics, selective focusing, and scattering pattern analysis

Abstract: We report on the experimental measurement of the backscattering matrix of a weakly scattering medium in optics, composed of a few dispersed gold nanobeads. The decomposition of the time-reversal operator is applied to this matrix and we demonstrate selective and efficient focusing on individual scatterers, even through an aberrating layer. Moreover, we show that this approach provides the decomposition of the scattering pattern of a single nanoparticle. These results open important perspectives for optical imaging, characterization, and selective excitation of nanoparticles.

Three-dimensional polarization ray-tracing calculus I: definition and diattenuation

Abstract: A three-by-three polarization ray-tracing matrix method for polarization ray tracing in optical systems is presented for calculating the polarization transformations associated with ray paths through optical systems. The method is a three-dimensional generalization of the Jones calculus. Reflection and refraction algorithms are provided. Diattenuation of the optical system is calculated via singular value decomposition. Two numerical examples, a three fold-mirror system and a hollow corner cube, demonstrate the method.

Point spread function and two-point resolution in Fresnel incoherent correlation holography.

Abstract: Fresnel Incoherent Correlation Holography (FINCH) allows digital reconstruction of incoherently illuminated objects from intensity records acquired by a Spatial Light Modulator (SLM) The article presents wave optics model of FINCH, which allows analytical calculation of the Point Spread Function (PSF) for both the optical and digital part of imaging and takes into account Gaussian aperture for a spatial bounding of light waves The 3D PSF is used to determine diffraction limits of the lateral and longitudinal size of a point image created in the FINCH set-up Lateral and longitudinal resolution is investigated both theoretically and experimentally using quantitative measures introduced for two-point imaging Dependence of the resolving power on the system parameters is studied and optimal geometry of the set-up is designed with regard to the best lateral and longitudinal resolution Theoretical results are confirmed by experiments in which the light emitting diode (LED) is used as a spatially incoherent source to create object holograms using the SLM

Ray optical light trapping in silicon microwires: exceeding the 2n(2) intensity limit.

Abstract: We develop a ray optics model of a silicon wire array geometry in an attempt to understand the very strong absorption previously observed experimentally in these arrays. Our model successfully reproduces the n2 ergodic limit for wire arrays in free space. Applying this model to a wire array on a Lambertian back reflector, we find an asymptotic increase in light trapping for low filling fractions. In this case, the Lambertian back reflector is acting as a wide acceptance angle concentrator, allowing the array to exceed the ergodic limit in the ray optics regime. While this leads to increased power per volume of silicon, it gives reduced power per unit area of wire array, owing to reduced silicon volume at low filling fractions. Upon comparison with silicon microwire experimental data, our ray optics model gives reasonable agreement with large wire arrays (4 μm radius), but poor agreement with small wire arrays (1 μm radius). This suggests that the very strong absorption observed in small wire arrays, which is not observed in large wire arrays, may be significantly due to wave optical effects.

A Uniform Asymptotic Solution for the Diffraction by a Right-Angled Dielectric Wedge

Abstract: We propose a uniform asymptotic solution for the field diffracted by a lossless right-angled dielectric wedge illuminated by a plane wave at normal incidence. The diffraction problem is solved by splitting the observation domain in the inner region of the wedge and the surrounding free-space. The scattered electric field in each region is assumed to be originated by a set of equivalent electric and magnetic surface currents involved in the well-known radiation integral. Such currents are localized on the interior and exterior faces of the wedge, and expressed in terms of the corresponding geometrical optics field. Useful analytical manipulations and asymptotic evaluations of the resulting integrals allow one to obtain the diffraction coefficients in terms of the Fresnel's reflection and transmission coefficients of the structure and the transition function of the uniform geometrical theory of diffraction. The related diffracted field compensates the discontinuities of the geometrical optics field and gives total field levels in good agreement with finite difference time domain results.

Reduced-Size Double-Shell Lens Antenna With Flat-Top Radiation Pattern for Indoor Communications at Millimeter Waves

Abstract: We investigate the capabilities of reduced-size integrated lens antennas to produce flat-top radiation patterns for broadband wireless communication systems at millimeter waves. The main challenge consists in controlling accurately the lens radiation performance over a broad frequency band while reducing its size; this constitutes a difficult task since producing highly shaped beams usually leads to oversized lens antennas. The design procedure is based on the geometrical optics/physical optics method (GO/PO), and the antenna characteristics are confirmed by full-wave simulations since the antenna size is only a few wavelengths. Our numerical results demonstrate that one anti-reflection coating is necessary even if the lens is made in a low-permittivity material (Rexolite). The resulting double-shell dielectric lens antenna has been fabricated and measured. The experimental results are in very good agreement with the simulations, and the radiation characteristics are stable over a 14% relative bandwidth, which is enough for broadband communications at millimeter waves.

Three-dimensional polarization ray-tracing calculus II: retardance

Abstract: The concept of retardance is critically analyzed for ray paths through optical systems described by a three-by-three polarization ray-tracing matrix. Algorithms are presented to separate the effects of retardance from geometric transformations. The geometric transformation described by a “parallel transport matrix” characterizes nonpolarizing propagation through an optical system, and also provides a proper relationship between sets of local coordinates along the ray path. The proper retardance is calculated by removing this geometric transformation from the three-by-three polarization ray-tracing matrix. Two rays with different ray paths through an optical system can have the same polarization ray-tracing matrix but different retardances. The retardance and diattenuation of an aluminum-coated three fold-mirror system are analyzed as an example.

Determination of Reflected and Transmitted Fields by Geometrical Optics

Abstract: By an extension of ordinary geometrical optics (or acoustics) the intensity of the reflected and transmitted fields due to a point source in the presence of an arbitrary interface between two media is found. Particular consequences of the solution are the general lens and mirror law and the equations for the caustic surfaces.

PO/Mec-Based Scattering Model for Complex Objects on a Sea Surface

Abstract: In this contribution a model based on asymptotic methods is proposed to compute the scattered fleld from complex objects on a sea surface. The scattering model combines the geometrical optics, the physical optics and the method of equivalent currents. It includes the shadowing efiects and multiple-bounce up to order 3. This model is used, in the following, for Radar Cross Section (RCS) estimation and to generate Synthetic Aperture Radar (SAR) raw data for imaging applications. The theoretical aspects are reviewed in this paper and the proposed model is detailed. Numerical results are provided to validate the approach through the computation of RCS for canonical objects and complex scenes. Both the bistatic and the monostatic conflgurations are studied in this work. Finally some flrst results dealing with SAR imaging of objects on a sea surface are provided. These images are constructed from the simulated raw data thanks to a chirp scaling-based algorithm.

Electromagnetic Wave Scattering from a Wedge with Perfectly Reflecting Boundaries: Analysis of Asymptotic Techniques

Abstract: High-frequency asymptotic (HFA) techniques are reviewed through a classical, canonical problem: electromagnetic wave scattering from a wedge-shaped object with perfectly electrically conducting (PEC) boundaries. The Physical Optics (PO) and Physical Theory of Diffraction (PTD) approaches are compared against the exact solution through many scenarios and illustrations.

Physical foundations of quantum electronics

Abstract: Introduction Stimulated Quantum Transitions Density Matrix, Populations and Relaxation Susceptibility of the Matter Non-Stationary Optics Nonlinear Optics Statistical Optics.

Analyzing optics test data on rectangular apertures using 2-D Chebyshev polynomials

Abstract: We use the two-dimensional Chebyshev polynomials as the basis for decomposition of test data over rectangular apertures, particularly for anamorphic optics. This includes simple optics such as cylindrical lenses and mirrors as well as complex optics, such as aspheric cylindrical optics. The new basis set is strictly orthogonal over rectangles of arbitrary aspect ratio and they correspond well with the aberrations of systems containing such type of optics. An example is given that applies the new basis set to study the surface figure error of a cylindrical Schmidt corrector plate. It is not only an excellent fitting basis but also can be used to flag misalignment errors that are critical to fabrication.

Optics for Engineers

Abstract: Introduction Why Optics? History Optical Engineering Electromagnetics Background Wavelength, Frequency, Power, and Photons Energy Levels and Transitions Macroscopic Effects Basic Concepts of Imaging Overview of the Book Problems Basic Geometric Optics Snell's Law Imaging with a Single Interface Reflection Refraction Simple Lens Prisms Reflective Systems Problems Matrix Optics Matrix Optics Concepts Interpreting the Results The Thick Lens Again Examples Problems Stops, Pupils, and Windows Aperture Stop Field Stop Image-Space Example Locating and Identifying Pupils and Windows Examples Problems Aberrations Exact Ray Tracing Ellipsoidal Mirror Seidel Aberrations and OPL Spherical Aberration for a Thin Lens Chromatic Aberration Design Issues Lens Design Problems Polarized Light Fundamentals of Polarized Light Behavior of Polarizing Devices Interaction with Materials Fresnel Reflection and Transmission Physics of Polarizing Devices Jones Vectors and Matrices Partial Polarization Problems Interference Mach-Zehnder Interferometer Doppler Laser Radar Resolving Ambiguities Michelson Interferometer Fabry-Perot Interferometer Beamsplitter Thin Films Problems Diffraction Physics of Diffraction Fresnel-Kirchhoff Integral Paraxial Approximation Fraunhofer Diffraction Equations Some Useful Fraunhofer Patterns Resolution of an Imaging System Diffraction Grating Fresnel Diffraction Problems Gaussian Beams Equations for Gaussian Beams Gaussian Beam Propagation Six Questions Gaussian Beam Propagation Collins Chart Stable Laser Cavity Design Hermite-Gaussian Modes Problems Coherence Definitions Discrete Frequencies Temporal Coherence Spatial Coherence Controlling Coherence Summary Problems Fourier Optics Coherent Imaging Incoherent Imaging Systems Characterizing an Optical System Problems Radiometry and Photometry Basic Radiometry Spectral Radiometry Photometry and Colorimetry Instrumentation Blackbody Radiation Problems Optical Detection Photons Photon Statistics Detector Noise Photon Detectors Thermal Detectors Array Detectors Nonlinear Optics Wave Equations Phase Matching Nonlinear Processes Appendix A Notation and Drawings for Geometric Optics Appendix B Solid Angle Appendix C Matrix Mathematics Appendix D Light Propagation in Biological Tissue Appendix E Useful Matrices Appendix F Numerical Constants and Conversion Factors Appendix G Solutions to Chapter Problems References Index

A MATLAB-Based Virtual Tool for the Electromagnetic Wave Scattering from a Perfectly Reflecting Wedge

Abstract: A MATLAB-based virtual diffraction tool, using analytical exact as well as well-known high-frequency asymptotic (HFA) techniques, is introduced. Electromagnetic wave scattering from a wedge-shaped object with perfect electrical conductor (PEC) boundaries, under both line-source and plane-wave illuminations, can be automatically analyzed. Effects of various parameters on the reflection, refraction, and diffraction can be investigated. Comparisons among Geometrical Optics (GO), Uniform Theory of Diffraction (UTD), Physical Optics (PO), Physical Theory of Diffraction (PTD), and Parabolic Equation (PE) models are possible through many scenarios and illustrations.

Uniform Ray Description for the PO Scattering by Vertices in Curved Surface With Curvilinear Edges and Relatively General Boundary Conditions

Abstract: A new high-frequency analysis is presented for the scattering by vertices in a curved surface with curvilinear edges and relatively general boundary conditions, under the physical optics (PO) approximation. Both, impenetrable (e.g., impedance surface, coated conductor) as well as transparent thin sheet materials (e.g., thin dielectric, or frequency selective surface) are treated, via their Fresnel reflection and transmission coefficients. The PO scattered field is cast in a uniform theory of diffraction (UTD) ray format and comprises geometrical optics, edge and vertex diffracted rays. The contribution of this paper is twofold. First, we derive PO-based edge and vertex diffraction coefficients for sufficiently thin but relatively arbitrary materials, while in the literature most of the results (especially for vertex diffraction) are valid only for perfectly conducting objects. Second, the shadow boundary transitional behavior of edge and vertex diffracted fields is rigorously derived for the curved geometry case, as a function of various geometrical parameters such as the local radii of curvature of the surface, of its edges and of the incident ray wavefront. For edge diffracted rays, such a transitional behavior is found to be the same as that obtained heuristically in the original UTD. For vertex diffracted rays, the PO-based transitional behavior is a novel result providing offers clues to generalize a recent UTD solution for a planar vertex to treat the present curved vertex problem. Some numerical examples highlight the accuracy and the effectiveness of the proposed ray description.

Analysis and Modeling of Near-Ground Wave Propagation in the Presence of Building Walls

Abstract: An efficient semi-analytic model for near-ground wave propagation in indoor scenarios is presented. For transceivers deployed in indoor environments on or near the ground, since RF wave propagation is dominated by Norton surface waves, these higher order waves and their interactions with building walls and other indoor obstacles have to be captured for accurate field calculations. Existing ray tracing routines which are commonly used for indoor field prediction, are inadequate for evaluating signal coverage of transceiver nodes very close to the ground (less than a wavelength above ground) since such routines neglect higher order surface waves. In addition, geometrical optics alone is inadequate to treat finite-size and possible irregular-shaped obstacles at low radio frequencies (VHF and lower UHF). Our approach for calculation of near-ground wave propagation and scattering is based on a hybrid physical optics and asymptotic expansion of dyadic Green's function for a half-space dielectric medium. Equivalence principle in conjunction with physical optics approximation is utilized to handle scattered field from building walls which are the dominant scatterers in indoor settings. Simulation results for various indoor propagation scenarios based on the new approach is validated by using both measurement results and full-wave numerical solvers.

Airy pulsed beams.

Abstract: The Airy beam (AiB) has attracted a lot of attention recently because of its intriguing features; the most distinctive ones are the propagation along curved trajectories in free space and the weak diffraction. We have previously shown that the AiB is, in fact, a caustic of the rays that radiate from the tail of the Airy function aperture distribution. Here we derive a class of ultra wideband Airy pulsed beams (AiPBs), which are the extension of the AiB into the time domain. We introduce a frequency scaling of the initial aperture field that renders the ray skeleton of the field, including the caustic, frequency independent, thus ensuring that all the frequency components propagate along the same curved trajectory and that the AiPB does not disperse. The resulting AiPB preserves the intriguing features of the time-harmonic AiB discussed above. An exact closed-form solution for the AiPB is derived using the spectral theory of transients. We also derive wavefront approximations for the field in the time window around the pulse arrival, which are valid uniformly in the vicinity of the caustic. These approximations are based on the so-called uniform geometrical optics, which is extended here to the time domain.

Plane-wave diffraction by an obtuse-angled dielectric wedge.

Abstract: Uniform high-frequency solutions in closed form are derived for the diffraction of a plane wave normally impacting on a penetrable wedge having an obtuse apex angle and arbitrary dielectric permittivity. The approach used here takes advantage of a physical optics approximation for the electric and magnetic equivalent surface currents in the scattering integrals related to the inner region of the wedge and the surrounding space. Numerical tests and comparisons with finite-difference time-domain results demonstrate the accuracy and effectiveness of the proposed solutions.

Lagrangian-Hamiltonian formulation of paraxial optics and applications: Study of gauge symmetries and the optical spin Hall effect

Abstract: In the context of the paraxial regime, usually valid for optical frequencies and also in the microwave spectrum of guided waves, the propagation of electromagnetic fields can be analyzed through a paraxial wave equation, which is analogous to the nonrelativistic Schroedinger equation of quantum mechanics but replacing time t with spatial coordinate z. Considering that, here it is shown that for lossless media in optical frequencies it is possible to construct a Lagrangian operator with an one-to-one correspondence with nonrelativistic quantum mechanics, which allows someone to use the same mathematical methods and techniques for solving problems. To demonstrate that, we explore a few applications in optics with increasing levels of complexity. In the spirit of a Hamiltonian formulation, the ray-tracing trajectories of geometric optics in paraxial regime are obtained in a clear manner. Following that, the gauge symmetries of the optical-field Lagrangian density is discussed in a detailed way, leading to the general form of the interaction Hamiltonian. Through the use of perturbation theory, we discuss a classical analog for a quantum not gate, making use of mode coupling in an isotropic chiral medium. At last, we explore the optical spin Hall effect and its possible applications using an effectivemore » geometric optics equation derived from an interaction Hamiltonian for the optical fields. We also predict within the framework of paraxial optics a spin Hall effect of light induced by gravitational fields.« less

Reconstructing Distortions on Reflector Antennas With the Iterative-Field-Matrix Method Using Near-Field Observation Data

Abstract: This work extends the mathematical formulation of the iterative-field-matrix method for observed data from the near-field region of a Perfect Electric Conductor. The method is used as a diagnosis tool for reflector antennas, to determine the positions and extent of distortions from their idealized shapes. The new formulation is tested on a reflector antenna with several significant bumps, and excellent results are achieved. This work also presents an example where the Method of Moments is used to generate the synthetic data and the inversion is performed using Physical Optics. Such a configuration ensures that the forward model is unbiased with respect to the inversion model, demonstrating that the new formulation is also robust for these realistic scenarios.

Adaptive Aperture Partition in Shooting and Bouncing Ray Method

Abstract: The shooting and bouncing ray (SBR) method may give rise to a divergence problem when ray tubes intersect discontinuous parts of the target, such as the boundary, and this affects the accuracy to some extent. This paper proposes an adaptive aperture partition algorithm to solve this problem. The proposed algorithm adaptively splits the virtual aperture into continuous irregular beams instead of discrete uniform ray tubes according to the geometry of the target during the recursive beam tracing. These beams form a beam tree, the level of which represents the number of reflections. Geometric optics is applied to the representative propagation path of each leaf beam to obtain the exit field, and then physical optics is used to evaluate each leaf beam's scattered field. The proposed algorithm could generate the convergent solution of the SBR method when the ray-tube size tends toward infinitesimal. Additionally, this paper describes the beam-triangle intersection in detail and utilizes the kd-tree to accelerate the beam-target intersection. Numerical experiments demonstrate that adaptive aperture partition can greatly improve the accuracy of the SBR method, and the computational efficiency can be also significantly enhanced in several applications, such as the RCS prediction in the THz band.

Diffraction and external reflection by dielectric faceted particles

Abstract: The scattering of light by dielectric particles much larger than the wavelength of incident light is attributed to diffraction, external reflection and outgoing refracted waves. This paper focuses on diffraction and external reflection by faceted particles, which can be calculated semi-analytically based on physical optics. Three approximate methods; the surface-integral method (SIM), the volume-integral method (VIM), and the diffraction plus reflection pattern from ray optics (DPR) are compared. Four elements of the amplitude scattering matrix in the SIM and the VIM are presented in an explicit form. Of interest is that diffraction and external reflection are separable in the SIM, whereas they are combined in the VIM. A feature of zero forward reflection is noticed in the SIM. The applicability of the DPR method is restricted to particles with random orientations. In the manner of van de Hulst, we develop a new technique to compute the reflection pattern of randomly oriented convex particles using spheres with the same refractive index, resulting in an improvement in the precision of the reflection calculation in near-forward and near-backward directions. The accuracy of the aforementioned three methods is investigated by comparing their results with those from the discrete-dipole-approximation (DDA) method for hexagonal particles at the refractive index of 1.3+i1.0. For particles with fixed orientations, it is found that the SIM and the VIM are comparable in accuracy and applicable when the size parameter is on the order of 20. The ray-spreading effect on the phase function is evident from the results of various size parameters. For randomly oriented particles, the DPR is more efficient than the SIM and the VIM.

High Frequency Techniques: the Physical Optics Approximation and the Modified Equivalent Current Approximation (MECA)

Abstract: In most of the electromagnetic problems, the number of unknowns to evaluate the scattered fields grows whenever the size of the antenna, device or scenario increases or the working frequency becomes higher In this context, the rigorous full-wave methods –eg Method of Moments (MoM), Fast Multipole Method (FMM) (Engheta et al, 1992), Finite-Difference Time-Domain (FDTD) (Taflove & Umashankar, 1987) or Finite-Difference FrequencyDomain (FDFD) (Rappaport & McCartin, 1991), Finite Element Method (FEM) (Kempel et al, 1998) – can not tackle the analysis of such problems beyond an upper limit determined by the computational requirements in terms of time and memory High frequency techniques consist in the asymptotic evaluation of the Maxwell’s equations As a consequence, they provide good accuracy when dealing with electrically large geometries meanwhile the computational needs diminish with respect to the aforementioned methods Within the high frequency techniques, the Geometrical Optics (GO) and the Physical Optics (PO) approximation are the most extended methods due to the successful results obtained in various fields such as Radar Cross Section (RCS), design of reflector antennas or radioelectric coverage calculation Since the Physical Optics approximation is detailed in the following section, the Geometrical Optics is briefly summarised The main interest in the GO lies in the fact that incident, reflected and transmitted electromagnetic waves are studied based on the conservation of the energy flux along a ray tube between a source and an observation point Therefore, the Geometrical Optics is usually referred to as Ray Optics The GO comprises two different methodologies (Rossi & Gabillet, 2002): Ray Tracing (Glassner, 1989) – the starting point is the receiver or observation point and a path to the source is sought analysing the reflections on walls, buildings, mountains – and Ray Launching – multiple rays are launched from the source, so they are independently followed until an observation point or the receiver is reached One of the common applications of the GO is the evaluation of radio electric coverage or the channel characterization in urban scenarios Both the GO and the PO techniques require of an additional method to compute the contribution due to the diffraction phenomenon The GO can be complemented by means of the Geometrical Theory of Diffraction (GTD) (Keller, 1962) or the Uniform Theory of

Boundary Diffracted Wave and Incremental Geometrical Optics: A Numerically Efficient and Physically Appealing Line-Integral Representation of Radiation Integrals. Aperture Scalar Case

Abstract: This paper presents a novel formulation to reduce radiation integrals to line integrals. Such a reduction is exact for Kirchhoff aperture radiation integrals and physical optics (PO) scattering from flat soft/hard (perfectly conducting) plates, illuminated by a spherical source, but can be effectively extended in an approximate version to more general configurations. The advantage of our approach is that the integrand of the line integral along the rim of the radiating surface is free from singularities and can be easily integrated at all the observation aspects, including geometrical optics shadow boundaries. Conversely, at those aspects, existing formulations exhibit, in the integrand, a pole singularity that renders the numerical integration inaccurate or time consuming, since it requires adaptive integration routines. This was a main concern in the use of this kind of approach for the time reduction in the numerical calculation of aperture/scattering radiation integrals, which is overcome by our approach. Also, the novel result presents a neat ray interpretation which is physically appealing and allows for the heuristic extension of the approach to non-exact cases (e.g., arbitrary impedance boundary conditions or curved surfaces) using standard ray approximations. Beside the already known boundary diffraction wave (BDW), which is an incremental wave excited by the incident field and arising from the rim of the surface, a further term called incremental geometrical optics (IGO) is introduced. This novel term is an elementary portion of the direct field arising from the source and impinging at the observation point; it is able to cancel the BDW singularity thus rendering the whole integrand smooth. For the sake of simplicity, the BDW+IGO theory is here presented with reference to the simplest scalar case of aperture radiation.

A Fast Hybrid Method for Scattering From a Large Object With Dihedral Effects Above a Large Rough Surface

Abstract: A new hybrid numerical method is described for scattering from an electrically large perfectly-conducting object with dihedral effects above a very long one-dimensional rough surface (two-dimensional problem). Such a problem involves a large number of unknowns and cannot be solved easily with a conventional method of moments by using a direct LU inversion. Thus, to solve this issue, the Extended-PILE method is combined with the forward-backward spectral acceleration (FBSA) for the local interactions on the rough surface and with the second-order physical optics (PO2) approximation for the local interactions on the object. Classically objects under test do not present dihedral effects and in the high frequency domain the first-order PO (PO1) provides the main contribution. In opposite, in this paper since a cross is considered, the second-order inner reflections contribute significantly and the PO2 must be included. By assuming a Gaussian process with a Gaussian height spectrum, this new hybrid method, E-PILE+FBSA+PO2, is tested against the rigorous E-PILE+ FBSA method (direct LU inversion on the object) as functions of the object inclination, the polarization and the incidence angle.