This work presents an overview of available uniform asymptotic physical optics solutions for evaluating the plane wave diffraction by some canonical geometries of large interest: dielectric slabs and wedges. Such solutions are based on a physical optics approximation of the electric and magnetic equivalent surface currents in the involved scattering integrals. The resulting diffraction coefficients are expressed in terms of the geometrical optics response of the considered structure and the standard transition function of the Uniform Geometrical Theory of Diffraction. Numerical tests and comparisons make evident the effectiveness and reliability of the presented solutions.

As well-known, the ability to describe and solve electromagnetic scattering problems is highly valued in many areas such as radio planning, remote sensing for monitoring and surveillance of ground, structures and infrastructures, and through-wall building imaging. Numerical techniques represent a possible answer, but they have an inherent drawback: the computation becomes very intensive (if not unmanageable) at high frequencies, where asymptotic methods based on ray-tracing work more efficiently. In this framework, the Geometrical Theory of Diffraction (GTD) [

This paper presents a review of Uniform Asymptotic Physical Optics (UAPO) solutions for diffraction problems concerning some typical canonical structures: dielectric slabs (individually considered or forming junctions) and wedges. Examples of application are relevant to (a) through-wall building imaging [

The starting point for obtaining a UAPO solution is that of considering the scattering integral and using a PO approximation of the electric and magnetic surface currents related to the boundary of the object. A further useful approximation and a uniform asymptotic evaluation of the resulting integrals allow one to obtain the diffraction coefficients in the UTD framework. They result to be expressed in terms of the reflection and transmission coefficients of the structure and the standard transition function of UTD. Note that also the heuristic solutions [

The remainder of this paper is organized as follows. Section

The diffraction problem considered in this Section refers to a linearly polarised plane wave impinging on a thin dielectric slab characterised by thickness

Diffraction by a thin dielectric slab.

The field scattered at the observation point

The expressions of the PO surface currents are obtained in terms of the incident electric field

Formulas (

According to (

Integration path

A set of representative results is reported. They concern a slab characterised by

Dielectric slab. The

Dielectric slab. The

Dielectric slab. The relative magnitude of the total field

Dielectric slab. The relative magnitude of the total field

Accounting for the linearity of the PO radiation integral, the UAPO-based approach for the diffraction problem involving one truncated dielectric slab can be extended to junctions by considering the diffraction contributions of the layers separately. Accordingly, in the case of junctions formed by two slabs, it results:

A two-dimensional scattering scenario involving a lossless nonmagnetic dielectric wedge with obtuse apex angle

Diffraction by an obtuse-angled dielectric wedge.

Note that the two-dimensional diffraction problem involving a right-angled dielectric wedge has been tackled and solved by the authors in [

The methodology adopted for penetrable wedges identifies the inner region (dielectric material) and the surrounding space as separate observation domains and the scattered electric field in each region as originated by electric and magnetic equivalent PO surface currents located on the inner/outer faces of

Both the faces of the wedge are illuminated by the impinging wave, and the GO field presents two reflection boundaries in the space surrounding the wedge and two transmission boundaries in the dielectric material.

Only the external face of

The field transmitted through

The field transmitted through

Figures

Note that the case corresponding to

Dielectric wedge. The relative magnitude of the total field

Dielectric wedge. The relative magnitude of the total field

UAPO solutions have been presented in the UTD context for evaluating the field diffracted by penetrable dielectric slabs and wedges. They are in closed form, simple and easy to handle and yield total field levels in good agreement with data obtained via numerical tools. In addition, the UTD-like formulation of UAPO diffraction coefficients facilitates the analytical evaluation of the time domain counterparts. These characteristics encourage the use of UAPO solutions for diffraction problems of interest in many application areas. Future research activities will be directed towards three-dimensional scenarios involving penetrable wedges with finite conductivity.