Geometrical Optics Field Research Articles

Plane wave diffraction by an interface of anomalously transmitting and impedance half planes

Diffraction of E-polarized plane waves by a junction of anomalously transmitting and impedance half planes is examined by employing the method of transition boundary (MTB). Firstly, initial fields that exist in space independent of the geometry are determined. In that situation, the scatterers causing diffraction are excluded. Secondly, total geometrical optics (GO) fields are written. Then, subtraction of initial fields from the total geometrical field will yield the scattered GO fields. Lastly, diffracted fields are found by using the scattered GO fields expression at the transition boundaries. The diffracted fields expression contains the diffracted fields of both half planes. The diffracted fields are examined for some parameters of the problem.

Designing Freeform Optical Surfaces by the Monge-Ampère Equations: A Review

Background: The equations of Monge-Ampère type which arise in geometric optics are used to design illumination lenses and mirrors. The optical design problem can be formulated as an inverse problem: determine an optical system consisting of a reflector and/or refractor that converts a given light distribution of the source into a desired target light distribution. For two decades, the development of fast and reliable numerical design algorithms for the calculation of freeform surfaces for irradiance control in the geometrical optics limit is of great interest in current research. Objective: The objective of this paper is to summarize the types, algorithms, and applications of Monge-Ampère equations. It helps scholars better grasp the research status of Monge-Ampère equations and further explore the theory of Monge-Ampère equations. Methods: This paper reviews the theory and applications of Monge–Ampère equations from four aspects. We first discuss the concept and development of Monge–Ampère equations. Then we derive two different cases of Monge–Ampère equations. We also list the numerical methods of Monge–Ampère equation in actual scenes. Finally, the paper gives a brief summary and an expectation. Results: This paper reviews the theory and applications of Monge-Ampère equations from four aspects. We first discuss the concept and development of Monge-Ampère equations. Then we derive two different cases of Monge-Ampère equations. We also list the numerical methods of the Monge-Ampère equation in actual scenes. Finally, the paper gives a brief summary and an expectation. Conclusion: Monge-Ampère equation has been widely applied in the geometric optics field since the predetermined energy distribution and the boundary condition creation can be well satisfied. Although the freeform surfaces designed by the Monge-Ampère equations is developing rapidly, there is still plenty of room for development in the design of the algorithms.

Uniform solution for the diffraction by an impedance and reflectionless metasurface planar junction.

The scattering process of waves by a planar junction of two half-planes, one of which is impedance and the other a reflectionless metasurface, is studied. The transition boundary method is considered. The scattered geometric optics field is obtained by subtracting the initial fields from the total geometric optics field. The diffracted field is obtained by considering the relation between diffracted and scattered geometric optics field expressions in the transition boundary. The ultimate expressions of the fields are examined numerically for different parameter groups.

Physical optics approximation of electromagnetic field scattered from large PEC objects covered with chiral metamaterials

Electromagnetic scattering analysis from conducting objects comparable in size with the incident wavelength, using exact numerical approaches, always suffers from high computational complexity, especially when covered with composite penetrable materials. In this paper the asymptotic method of the physical optics (PO) is developed to predict the scattering patterns from conducting objects coated by chiral metamaterials (CMMs) as an absorber. In first stage, the backward ray-tracing is used to determine the lit region on the outer surface of the objects represented by flat elementary facets. Simple closed-form expressions are derived for the co- and cross-polarized reflection coefficients from a metal-backed CMM layer to approximate the equivalent currents on lit facets in terms of the geometrical-optics fields. Then, for stealth applications, a CMM layer with appropriate electromagnetic properties is suggested with reflected power lower than −20 dB in a wide aspect angle of incident ray from 0 to 57 degrees. Finally, the scattering patterns are calculated via the PO approximation and the equivalent currents. In order to check the accuracy of the proposed solutions, the simulation results of several objects will be compared with the experimental data and the results of the exact Mie theory and method of moment (MoM).

Modified Theory of Physical Optics Approach to Diffraction by an Interface between PEMC and Absorbing Half-Planes

The scattering of electromagnetic plane waves by an interface, located between perfect electromagnetic conductor and absorbing half-planes is investigated. The perfect electromagnetic conductor half-plane is divided into perfect electric conductor and perfect magnetic conductor half-screens. The same decomposition is done for the absorbing surface. Then four separate geometries are defined according to this approach. The scattered fields by the four sub-problems are obtained with the aid of the modified theory of physical optics. The resultant scattering integrals are combined in a single expression by using key formulas, defined for the perfect electromagnetic conductor and absorbing surfaces. The scattering integral is asymptotically evaluated for large values of the wave-number and the diffracted and geometric optics fields are obtained. The behaviors of the derived field expressions are analyzed numerically.

On the Complete Radiation Pattern of a Vertical Hertzian Dipole Above a Low-Loss Ground

The complete radiation field pattern of a vertical Hertzian dipole antenna on or above a lossless or low-loss dielectric half-space is studied using a rigorous Sommerfeld formalism. The reflected fields in the air above the interface and the subsurface fields transmitted into the dielectric are computed by numerical integration of the Sommerfeld integrals. Furthermore, to facilitate the physical interpretation of these results, a detailed asymptotic saddle-point integration method analysis is presented, which includes terms that vary in magnitude with the second power of the inverse distance from the dipole. It is shown that the second-order field constituents are dominant at the interface, where the first-order geometrical fields vanish. These second-order terms comprise an evanescent wave propagating along the interface in the upper half-space and a lateral wave, also known as the head wave, which propagates in the subsurface along the direction of the critical angle. The two waves only exist between two cones whose half-angles are equal to the critical angle, and their interference with the geometrical-optics fields determines the radiation pattern for elevation angles near the horizon. The far zone surface fields on either side of the interface comprise two second order waves that propagate along the interface, one with the phase velocity in the air, and the other with the phase velocity in the dielectric. Away from the interface, the leading field components vary with the first power of the inverse distance, which explains the sharp dip in the field pattern at the interface-a phenomenon known as the interface pattern extinction. Another distinctive phenomenon, observed in the subsurface field pattern, is the rippling that occurs in the angular range between the critical angle cone and the interface. The asymptotic analysis has shown that this pattern scalloping results from the interference of the lateral wave with the geometrical-optics spherical wave.

Diffraction of Gauss beam by a resistive half-plane in an anisotropic plasma

The theoretical investigation of Gauss beam diffraction by a resistive half-plane surrounded by an anisotropic plasma is presented. For this purpose, an integral theory which yields the scattered fields in terms of the Fresnel function is considered. The kernel of the scattering integral is arranged, according to the relation between scattered geometric optics (GO) fields and the transition boundaries, to obtain the scattered fields. The magnetic line source illumination is considered since a single magnetic field component is affected by the anisotropy. Later, complex point source method is used for evaluation of Gauss beam diffraction. The resultant waves are plotted and discussed for the limiting cases of anisotropic medium and resistive half-plane.

Heuristic UTD Diffraction Coefficient for Three-Dimensional Dielectric Wedges

This article presents a heuristic diffraction coefficient for 3-D dielectric wedges of arbitrary angles. First, the proposed diffraction coefficient is derived for 2-D wedges with soft and hard polarization, by enforcing continuity of the total field at every shadow boundary associated with the multiply reflected fields inside the wedge. The accuracy of the proposed heuristic 2-D solution is verified comparing with the UTD solution derived from Maliuzhinets' exact integration. Then, it is extended to 3-D wedges for arbitrary polarizations and incident/scattered directions by transforming ray-fixed to edge-fixed coordinate systems. The total field predicted using the proposed heuristic diffraction coefficient is continuous for arbitrary angle 3-D dielectric wedges, including interior wedges, and is close to the geometrical optics field far from the shadow boundaries. The proposed method is validated against a Method-of-Moment solution. Finally, we show the method can significantly improve the accuracy of ray-tracing modeling of wave propagation in arched tunnels.

High-frequency diffraction contribution by planar metallic–DNG metamaterial junctions

AbstractThe plane wave diffraction by a planar junction consisting of a thick metallic sheet and a lossy double-negative metamaterial slab is studied by using the Uniform Asymptotic Physical Optics approach. This approach assumes the radiation integral as a starting point and uses the physical optics surface currents as sources to be integrated. The integral is manipulated by taking advantage of useful approximations and evaluations, and re-formulated in order to apply an asymptotic procedure able to generate a closed-form approximate solution in the framework of the Uniform Geometrical Theory of Diffraction. Accordingly, advantages and drawbacks result from the application of the proposed solution. The jumps of the geometrical optics field are compensated. Implementation and handling of the computer code are facilitated by the evaluation of well-known functions and parameters. No differential/integral equations or special functions must be computed.

Gaussian source beam diffraction by a perfect electromagnetic half-plane.

In the present work, diffraction of a Gaussian source beam by a perfect electromagnetic conductor (PEMC) semi-screen is investigated. Due to the special property of the PEMC sheet, which is a combination of perfect electric conductor and perfect magnetic conductor surfaces, the reflected wave from the PEMC surface has a cross-polarized component in addition to the co-polarized component. For an electric line source illumination, the diffracted fields are derived by considering the analogy between the transition boundaries and scattered geometric optics fields. Later, the complex point source technique is applied for evaluation of Gaussian beam diffraction. The finite magnitude values of fields are derived with the aid of an improved version of the well-known uniform theory of diffraction for evanescent plane waves. Also, the resultant waves are plotted and discussed for different groups of parameters.

Diffraction by a right angle impedance wedge between left- and right-handed media

ABSTRACTAn analytical solution for the diffraction of plane waves by a right angle impedance wedge which is lying between double negative and positive materials is investigated. In order to satisfy the boundary conditions and shifted shadow boundary, the diffracted fields are divided to subfields. As a result, an anomalous shift of shadow boundary is observed towards to lower surface of the wedge. In addition, geometric optics fields are determined by using the geometry of the problem. Also, the behavior of the fields is investigated numerically.

Diffraction of waves by a perfect electromagnetic conductor half-plane between isorefractive media

In this study, diffraction of waves by a perfectly electromagnetic conductor half-plane which is lying at the boundary of isorefractive media is investigated. The diffracted field expressions are constructed by using the relation between scattered geometrical optics fields and the transition boundaries. The high frequency asymptotic expressions of diffracted fields reach infinite magnitude values at the transition boundaries. The uniform expressions of fields are obtained by using the uniform theory of diffraction method in order to obtain the finite magnitude values at the transition boundaries and the results are analyzed numerically for different set of parameters.

Wave interaction with a perfect electromagnetic conductor half-plane between two dissimilar media

The interaction of electromagnetic plane wave by a perfect electromagnetic conductor half-plane, located between two media with different electromagnetic properties, is investigated. The diffracted waves, related with the z components of the electric and magnetic fields are obtained by considering the structures of the geometric optics fields, which are expressed in terms of the waves excited by soft and hard surfaces. The diffraction fields are extended in order to satisfy the boundary conditions on the interface between two media. Some numerical results are also given.

Diffraction by a planar junction between resistive and perfect electromagnetic conductor half-screens

The interaction of plane electromagnetic waves by a planar junction between resistive and perfect electromagnetic conductor half-planes is investigated. First of all the initial waves for a whole resistive plane is evaluated. Then the scattered geometric optics fields are obtained from the difference of the total geometric optics and initial waves. The diffracted fields are evaluated with the aid of a relation between the scattered geometric optics and diffraction fields at the transition boundaries. It is found that the interaction between the two half-screens occur only for the z-polarized electric fields.

Scattering of electromagnetic waves by a perfect electromagnetic conductor half-screen

The diffraction of plane electromagnetic waves by a perfect electromagnetic conductor half-screen is investigated. The total geometrical optics fields are obtained by using the boundary conditions of a perfect electromagnetic conductor surface. A general relation is defined for the scattered fields in terms of waves by soft and hard surfaces. The total scattered field is derived by using this relation. Some numerical simulations are also given.

Diffraction of electromagnetic waves by a planar interface between perfectly absorbing and anomalously transmitting metasurface half-planes

The interaction process of electromagnetic waves by a planar interface between perfectly absorbing and anomalously refracting metasurface half-planes is investigated. First of all, the scattered geometric optics field is obtained from the difference of the total geometric optics and initial waves. The diffracted fields are determined by using a relation between the scattered geometric optics and diffraction waves at the transition boundaries. It consists of the diffraction fields of perfectly absorbing and anomalously refracting metasurface half-screens. The behaviors of the total, total geometric optics and diffracted waves are studied numerically.

Scattering of plane waves by a rational half-plane between DNG media

Scattering of plane waves by a hard-soft half-plane which is lying between double negative material is investigated. The diffracted fields are determined by dividing the diffraction coefficient to four subfields for satisfying the boundary conditions. It is observed that the shadow boundary shifts towards to lower surface of the half-plane. Also geometric optics fields are determined by using the geometry of the problem. As a result, the behavior of the fields is investigated numerically.

Wave diffraction by a half-screen with Nth order generalized sheet transition conditions

The scattering of plane waves by a half-plane with Nth order transition conditions is investigated. First of all, the reflection and transmission conditions of the transmissive surface are evaluated by using the generalized sheet transmission boundary conditions. The scattered geometrical optics fields are determined from the total geometrical optics and incident waves. The diffracted field is obtained by using a relation between the scattered geometrical optics and diffracted waves. The behaviors of the total, total geometric optics and diffracted fields are analyzed numerically.

Physical optics-based diffraction coefficient for a wedge with different face impedances.

A new diffraction field expression is introduced with the aid of the modified theory of physical optics for a wedge with different face impedances. First, the scattered geometrical optics fields are determined when both faces of the wedge are illuminated by the incident wave. The geometrical optics waves are then expressed in terms of the sum of two different fields that occur for different impedance wedges. The diffracted fields are determined for the two cases separately, and the total diffracted field is obtained as a sum of these waves. Lastly, the uniform field expressions are obtained, and the resultant fields are numerically compared with the solution of Maliuzhinets.

Interaction of plane waves by a half-screen between two different media

The diffraction process of plane waves by a perfectly electric conducting half-screen, residing at a planar junction between two different media, is investigated. The scattered geometrical optics waves are evaluated by subtracting the initial fields from the total geometrical optics waves. The diffracted waves are obtained from the scattered geometrical optics fields by using a relation at the transition boundaries. The diffracted waves are expressed separately for both of the media. The uniform representations of the diffracted fields are obtained by using the uniform theory of diffraction. The scattered fields are analyzed numerically.