## Abstract

Fraunhofer diffraction by two long, thin, parallel conducting strips in a plane is investigated experimentally using microwaves whose wavelength is of the order of the strip width. The radiation is polarized with the electric field parallel to the axes of the strips. The results are compared with scalar Kirchhoff theory and first and second order Keller theory. It is found that for this polarization each theory yields good agreement with the results obtained in the laboratory.

© 1968 Optical Society of America

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### Equations (9)

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(1)
$$\psi =\frac{1}{4\pi}{\oint}_{s}\left[\frac{\partial \psi}{\partial n}\frac{{e}^{ikr}}{r}-\psi \frac{\partial}{\partial n}\left(\frac{{e}^{ikr}}{r}\right)\right]ds,$$
(2)
$$\psi =\frac{ik}{4\pi}{\int}_{{S}_{1},{S}_{2}}\text{exp}[ik(r+{r}_{0})]\frac{(\text{cos}{\theta}_{i}+\text{cos}\theta )}{{r}_{0}r}ds,$$
(3)
$$\psi =A(\text{cos}{\theta}_{i}+\text{cos}\theta )\left[{\int}_{{S}_{1}}{e}^{i\gamma {y}_{1}}d{y}_{1}+{\int}_{{S}_{2}}{e}^{-i\gamma {y}_{2}}d{y}_{2}\right],$$
(4)
$$I={\psi}^{2}={A}^{2}{(\text{cos}{\theta}_{i}+\text{cos}\theta )}^{2}\left\{\frac{{\text{sin}}^{2}\gamma (w/2)}{{[\gamma (w/2)]}^{2}}{\text{cos}}^{2}\gamma (D/2)\right\},$$
(5)
$$u=\frac{v\hspace{0.17em}\text{exp}[i(\pi /4+kr)]}{2{(2\pi kr)}^{{\scriptstyle \frac{1}{2}}}}\{\text{sec}[(\beta -\alpha )/2\mid \pm \hspace{0.17em}\text{csc}[(\beta +\alpha )/2]\},$$
(6)
$${u}^{(1)}=B\hspace{0.17em}\text{cos}\left(\gamma \frac{D}{2}\right)\left[\text{sec}\left(\frac{{\theta}_{i}+\theta}{2}\right)\text{cos}\gamma \frac{w}{2}-i\hspace{0.17em}\text{csc}\left(\frac{{\theta}_{i}-\theta}{2}\right)\hspace{0.17em}\text{sin}\gamma \frac{w}{2}\right],$$
(7)
$${I}^{(1)}=\mid {u}^{(1)}{\mid}^{2}={B}^{2}\left[\frac{{\text{cos}}^{2}\gamma (w/2)}{{\text{cos}}^{2}[({\theta}_{i}+\theta )/2]}+\frac{{\text{sin}}^{2}\gamma (w/2)}{{\text{sin}}^{2}[({\theta}_{i}-\theta )/2]}\right]\hspace{0.17em}{\text{cos}}^{2}\gamma \frac{D}{2}.$$
(8)
$${u}^{(2)}=\frac{B\hspace{0.17em}\text{exp}\hspace{0.17em}\{i[k(D-w)-\pi /4]\}}{{\{\pi k[(D-w)/2]\}}^{{\scriptstyle \frac{1}{2}}}}\times \left\{\frac{\text{sin}\hspace{0.17em}[({\theta}_{i}+\theta )/2]\hspace{0.17em}\text{sin}\hspace{0.17em}[(D-w){\gamma}^{\prime}/2]+i\hspace{0.17em}\text{cos}[({\theta}_{i}-\theta )/2]\times \text{cos}\hspace{0.17em}[(D-w){\gamma}^{\prime}/2]}{{\text{cos}}^{2}[({\theta}_{i}-\theta )/2]-{\text{sin}}^{2}[({\theta}_{i}+\theta )/2]}\right\}.$$
(9)
$${I}^{(2)}=\mid {u}^{(1)}+{u}^{(2)}{\mid}^{2}.$$