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Science · Advanced Physics
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Calculate the Fraunhofer diffraction field and intensity patterns for a rectangular aperture illuminated by a plane wave E_0. The full problem is below, the first thing I did was to expand the integrals but after that I don't know what to do and I don't know if I use the Fourier inverse transform I(r,t) = n(permittivity)c/2(E(r,t))(E*(r,t)).

Calculate the Fraunhofer diffraction field and intensity patterns for a rectangular aperture (dimensions Ax by Ay) illuminated by a plane wave Eo. In other words, derive (10.20). Compute the Fraunhofer diffraction pattern following a rectangular aperture (di- mensions Ax by Ay) illuminated by a uniform plane wave. Solution: According to (10.19), the field downstream is Ay/2 Ax/2 ikz -Ax/2 -Ay/2 It is left as an exercise (see P10.6) to perform the integration and compute the intensity. The result turns out to be Ax2A I (x, y, z) Io (10.20) sinc x sinc az az where sinc (S) E sin IS. Note that lim sinc (&) 1.

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