An Efficient Algorithm for the Computation of the UTD $T$ Transition Function

This paper presents a uniform ray description of electromagnetic wave scattering by locally periodic metasurfaces of polygonal shape. The model is derived by asymptotically evaluating the critical-point contributions of a physical optics scattering integral. It is valid for metasurfaces whose bulk scattering coefficients are periodic functions of a phase parameter which, in turn, is a continuous and smooth function of surface coordinates. The scattered field is expressed in terms of reflected, transmitted and diffracted rays that do not generally obey conventional geometrical constraints (i.e., Snell's law and the Keller cone). An iterative technique is presented to determine the locations of critical points on one or multiple interacting metasurfaces. Numerical results demonstrating the utility and accuracy of the asymptotic physical optics model are also provided.

Section: Appendix C Asymptotic Evaluation Of Corner-diffracted Fieldsmentioning

confidence: 99%

Uniform Ray Description of Physical Optics Scattering by Finite Locally Periodic Metasurfaces

Jong

2022

“…Moreover, for approximation of curved terrains or hills, this approach can be inappropriate. Other approach for estimating diffraction attenuation in different edge setups is to use 2D transition function in the uniform geometrical theory of diffraction (UTD) (see [18], [28], [29] and references therein for more details).…”

Section: A Related Workmentioning

confidence: 99%

A Generalized Recursive Vogler Algorithm for Multiple Bridged Knife-Edge Diffraction

Nguyen

Mansour

Coatanhay

et al. 2022

In this paper, we consider problem of estimating diffraction attenuation from approximation of a terrain using multiple bridged knife-edge model. This model can be considered as a generalization of well-known multiple knife-edge one where spaces between knife-edge are bridged by reflecting surfaces. A series based-standard solution is presented in the literature but suffers from its very high computational complexity. We, thus, propose to generalize the recursive Vogler algorithm developed for multiple knife-edge model to tackle this problem. To reduce complexity, the proposed algorithm exploit the recursive form to avoid repeated calculations of the existing solution. Moreover, we provide a complexity analysis of both the standard algorithm and the proposed algorithm based on number of computed integrals. Both theoretical and numerical results show that our proposed algorithm is faster than the original one while having identical accuracy, hence proving the effectiveness of our solution.

“…The canonical integrals in the uniform geometrical theory of diffraction (UTD) were used in the evaluation of PO integrals. Furthermore, the authors developed the efficient algorithm to calculate the "transition functions" in canonical integrals [11]- [12].…”

Section: Introductionmentioning

confidence: 99%

A Frequency-Independent Method for Computing the Physical Optics-Based Electromagnetic Fields Scattered From a Hyperbolic Surface

Chew

Jin

et al. 2016

In this communication, we propose a frequency independent approach, the numerical steepest descent path method, for computing the physical optics scattered electromagnetic field on the quadratic hyperbolic surface. Due to the highly oscillatory nature of the physical optics integral, the proposed method relies on deforming the integration path of the integral into the numerical steepest descent path on the complex plane. Numerical results for the PO based EM fields from the hyperbolic surface illustrate that the proposed numerical steepest descent path method is frequency independent in computational cost and error controllable in accuracy.