Geometrical Optics Waves Research Articles

Diffraction of quasi-nondiffracting Bessel beam by an impedance disc in an anisotropic plasma

The diffraction of the so-called nondiffracting Bessel beam by an impedance disc immersed in an anisotropic medium is examined. The external uniform magnetic field, which makes the plasma anisotropic, is taken to be rotational as opposed to being parallel to the edge of the problem geometries in the literature. Thus, the appropriate dielectric matrix that models the anisotropic region under the rotational dc external magnetic field is derived for the first time, to the best of our knowledge. Upon considering the geometric optics waves, the total scattered waves are obtained with the diffracted waves by using the definition of high-frequency asymptotic expressions associated with the scattered waves at the transition regions. The results are expressed in terms of the Fresnel functions so that the wave behaviors in the transition regions are uniform. The solutions are compared numerically with existing studies in the literature, including limit values.

Modified theory of physical optics approach to impedance surfaces for skew incidence

A three dimensional modified theory of physical optics integral is constructed for the impedance surfaces, illuminated by a plane wave for skew incidence. The scalar fields are taken into account. The kernel of the physical optics integral is evaluated by using a relation with the geometric optics waves and stationary phase evaluation of the integral. The obtained surface integral is applied to the diffraction problem of waves by an impedance half-plane. The scattered fields are investigated numerically.

The method of transition boundary for the solution of diffraction problems

A new method, which enables one to solve some diffraction problems, is put forth. The technique is based on a relation between the diffracted and scattered geometric optics waves at the transition boundaries. The concept of initial waves is also used instead of the incident field. The general algorithm of the method is outlined and applied to the diffraction problems of waves by perfect electric conductor half-screen, resistive half-plane and impedance sheet junction.

Scattering of electromagnetic waves by a perfectly conducting half-screen at the interface of two different media: E-polarization

The interaction of electromagnetic waves with a perfectly conducting half-screen, which is residing between two media with different electromagnetic properties, is investigated for electric polarization. The diffracted fields, in two regions, are determined by using a relation between diffraction and scattered geometric optics waves. Additional terms are included in the diffracted waves in order to satisfy the boundary conditions in the interface. The behavior of the total field and its components are analyzed numerically.

Wave diffraction by a conductive half-plane between two different media

The scattering of waves by a conductive half-screen, which reflects some portion of the incident energy and transmits the remaining part, between two media with different electromagnetic properties is investigated. First of all the scattered geometric optics waves are obtained. Then the diffracted fields are determined by using a relation between the geometric optics and diffraction waves at the transition boundaries. The behaviors of the total field and its components are studied numerically.

Diffraction of cylindrical waves by an impedance half-plane

The reflection coefficient of an impedance half-screen, illuminated by a line source field, is not the same with the one of a half-screen for plane wave incidence. This process also affects the structure of the diffraction coefficient. A new diffracted field should be obtained for the illumination of cylindrical waves. This paper introduces a new diffraction coefficient for the impedance half-plane, fed by cylindrical waves. The total and total geometric optics waves are also derived. The variation of the fields is studied numerically.

Scattering by a resistive half-plane residing between two dissimilar media

The scattering problem of plane electromagnetic waves by a resistive half-plane, located at the planar interface of two media with different electromagnetic properties, is studied. First of all, the reflection and transmission coefficients of a resistive whole plane, between two different media, are evaluated. The scattered geometrical optics waves are obtained for the problem under consideration. They are used in order to determine the diffracted waves, which are expressed in terms of a split function that arises in the solution of the diffraction problem by a resistive half-plane. The uniform diffraction fields are obtained by using the uniform theory of diffraction. The behavior of the total, total geometric optics and diffracted waves are studied numerically.

General expression of the diffracted waves by a half-screen with generalized impedance boundary conditions

The diffraction process of plane waves by a half-screen with generalized impedance boundary conditions is studied. Firstly, the scattered geometrical optics waves are obtained by subtracting the incident field from the total geometrical optics wave. The diffracted field expressions are derived by taking into account the construction of the scattered geometrical optics wave for first, second and third order impedance half-planes. Then the diffracted field expression is generalized for the Nth order half-screen. The uniform representation of the edge diffracted wave is obtained by considering the exact solution of Sommerfeld. The behaviors of the total, total GO and diffracted fields are analyzed numerically.

Diffraction of electromagnetic waves by a wedge with perfectly absorbing and impedance faces

The scattering process of electromagnetic waves by a wedge with perfectly absorbing and impedance faces is investigated. The scattered geometric optics waves are obtained for two cases, namely the illumination of single and double faces. The geometric optic field is expressed as a sum of two fields, which represent two wedges with different boundary conditions. The diffracted waves are determined for both of the wedge configurations. The behaviours of the total, total geometric optics and diffracted fields are studied numerically.

Edge diffraction in an anomalously reflecting half-plane

A half-plane, formed of anomalously reflecting metasurface, is taken into account. The layer is modeled by an impedance half-screen. In order to obtain the diffracted fields, the geometrical optics waves are evaluated as a sum of equivalent soft, hard and impedance surfaces. The diffracted waves are derived by the superposition of the diffracted fields from the equivalent surfaces. The uniform field expressions are obtained by the method of uniform theory of diffraction. The behaviors of the fields are studied numerically.

Scattering of waves by a planar junction between resistive half-screen and perfectly electric conducting wedge

The diffraction of plane waves by a planar junction between a resistive half-plane and perfectly conducting wedge is investigated. First of all, the relation between the scattered geometrical optics waves and diffracted fields by a wedge is outlined. Then the scattered GO fields of the planar junction are obtained by subtracting the initial fields from the total geometrical optics waves. The diffracted waves by the junction is derived with the aid of the scattered GO waves’ structure. The behaviour of the fields is analysed 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.

Diffraction of waves by a wedge residing between two different media

The scattering problem of plane waves by a perfectly electric conducting wedge, residing at the planar interface of two media with different electromagnetic properties, is investigated. The structure of the scattered geometrical optics waves is used in order to determine the diffracted waves, which are expressed in terms of a split function that arises in the solution of the diffraction problem by a resistive half-plane. The uniform diffraction fields are obtained with the aid of uniform theory of diffraction. The behavior of the total, total geometrical optics and diffracted waves are studied numerically.

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.

Wave diffraction by a right-angled interface between resistive half and whole planes

The interaction phenomenon of electromagnetic plane waves by a right angled interface between whole and half screens with different resistivities is studied. The construction, under examination, is considered in order to model various corner discontinuities between transmissive surfaces for indoor wireless communications. First of all, the initial waves, which occur in the absence of the diffracting edge, are determined. Then the scattered geometrical optics fields are obtained by subtracting the initial waves from the total geometrical optics fields. The diffracted field is constructed directly from the scattered geometrical optics wave by a new method. The resultant field expressions are examined numerically.

Diffraction imaging of high-resolution 3D P-cable data from the Gulf of Mexico using azimuthal plane-wave destruction

We review in historical order the key contributions to the development of the theory of diffractions. The work of Grimaldi, Huygens and Young provides the first part of this story, giving an understanding of diffraction and interference phenomena. Huygens was able to explain the laws of reflection and refraction, but lacked a deeper understanding of interference. This was provided by Young who used it to show how diffraction could arise from the interference of two waves. Fresnel, Helmholtz and Kirchhoff chose a different path and developed a full mathematical expression of Huygens’ principle, incorporating wave phase and interference. Sommerfeld and his students were able to reformulate the Huygens-Helmholtz-Kirchhoff integral as the sum of an incident geometrical-optics wave and a diffraction integral, which is interpretable as the contribution of the diffracted rays from the boundary. From our modern vantage point, this provides a rather pleasing analogy to Young’s early attempts at a theory of diffraction, using just two rays. A full ray-theoretical theory of diffraction, the Geometrical Theory of Diffraction, was given by Keller and extended by Klem-Musatov and Aizenberg to the case of seismic diffraction analysis.

Seismic diffractions: How it all began

We review in historical order the key contributions to the development of the theory of diffractions. The work of Grimaldi, Huygens and Young provides the first part of this story, giving an understanding of diffraction and interference phenomena. Huygens was able to explain the laws of reflection and refraction, but lacked a deeper understanding of interference. This was provided by Young who used it to show how diffraction could arise from the interference of two waves. Fresnel, Helmholtz and Kirchhoff chose a different path and developed a full mathematical expression of Huygens’ principle, incorporating wave phase and interference. Sommerfeld and his students were able to reformulate the Huygens-Helmholtz-Kirchhoff integral as the sum of an incident geometrical-optics wave and a diffraction integral, which is interpretable as the contribution of the diffracted rays from the boundary. From our modern vantage point, this provides a rather pleasing analogy to Young’s early attempts at a theory of diffraction, using just two rays. A full ray-theoretical theory of diffraction, the Geometrical Theory of Diffraction, was given by Keller and extended by Klem-Musatov and Aizenberg to the case of seismic diffraction analysis.

Diffraction of line source field by a resistive half-plane between isorefractive media

The scattering process of cylindrical waves by a resistive half-plane, residing at the interface of isorefractive media, is investigated. The uniform expression of the diffracted cylindrical waves by a resistive half-screen is obtained for a single medium. Then the initial fields are found for an interface between isorefractive media. The scattered geometrical optics waves are derived by subtracting the initial fields from the total geometrical optics waves when the resistive half-plane exists at the interface. The diffracted fields are determined by using the scattered geometrical optics waves. The behavior of the resultant waves is analyzed numerically.

Diffraction of waves by a conductive half-plane

The scattering process of plane waves by a conductive half-plane is investigated. The scattered geometrical optics waves are obtained by subtracting the incident field from the total geometrical optics waves. The physical optics integral is constructed from the scattered geometrical optics fields. The diffracted waves are evaluated by the application of the edge point method to the physical optics integral. A correction field is added to the diffracted waves in order to satisfy the conductive boundary conditions on the surfaces of the half-plane. The uniform diffracted fields are evaluated and the resultant scattered waves are compared with the literature numerically.

Wave diffraction by the junction between resistive and soft-hard half-screens

The scattering process of planes waves by a junction between resistive and soft/hard half-planes is investigated. First of all, the initial and total geometrical optics fields are determined by considering the related geometries. The scattered geometrical optics wave is obtained by subtracting the initial field from the total geometrical optics wave. The diffracted fields are derived by taking into account the behaviour of the geometrical optics wave at the reflection and shadow boundaries. The uniform expressions of the diffracted waves are constructed with the aid of the uniform theory of diffraction. The total field expressions are examined numerically.