## Abstract

A comparison is made between approximations using the geometrical theory of diffraction (GTD) and Kirchhoff theory and the exact solution using Maxwell’s equations for the case of Fraunhofer diffraction of electromagnetic radiation incident upon a long, thin, perfectly conducting strip with the electric field vector polarized perpendicular to the strip axis. Strip widths from approximately 0.3λ to 3λ are considered. Glancing angles of incidence are taken from 4° to 90°. Irradiances are compared as a function of diffraction angle in the region on the same side of the strip as the incident radiation.

© 1976 Optical Society of America

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### Equations (5)

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(1)
$${I}_{E}=B(r)\hspace{0.17em}\left[{\left(\sum _{m}\frac{Q{o}_{m}}{1+{f}_{0,m}^{2}}\right)}^{2}+{\left(\sum _{m}\frac{Q{o}_{m}{f}_{0,m}}{1+{f}_{0,m}^{2}}\right)}^{2}\right],$$
(2)
$$Q{o}_{m}(u,\theta )=\frac{S{o}_{m}(u)S{o}_{m}(\theta )}{{{M}_{m}}^{0}},$$
(3)
$${f}_{0,m}={\frac{N{{o}_{m}}^{\prime}(\mu )}{J{{o}_{m}}^{\prime}\hspace{0.17em}(\mu )}|}_{\mu =0}.$$
(4)
$${I}_{\text{KI}}=A{(kw)}^{2}{(\text{sin}u+\text{sin}\theta )}^{2}\hspace{0.17em}{\text{sin}}^{2}(\gamma w/2)/{(\gamma w/2)}^{2},$$
(5)
$${I}_{\text{GTD}}=B\hspace{0.17em}\left\{\frac{{\text{cos}}^{2}(\gamma w/2)}{{\text{sin}}^{2}[(u+\theta )/2]}+\frac{{\text{sin}}^{2}(\gamma w/2)}{{\text{sin}}^{2}[(u-\theta )/2]}\right\},$$