4500PF02-1 - Fraunhofer Diffraction by Four Slits A metal...

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Unformatted text preview: Fraunhofer Diffraction by Four Slits A metal plate in air contains four parallel slits, each of width a. The distance between the slits is d with d = 4a. The metal slit plate is illuminated at normal incidence by a plane wave of freespace wavelength . The transmittance of the slit plate is given by f4 as shown in the figure. The transmittance is 100% (t = 1) within the slits and 0% (t = 0) elsewhere. Derive, showing all work, the amplitude of the far-field (Fraunhofer) diffraction pattern resulting from the diffraction of the plane wave by this amplitude transmittance function, f4 . Express your answer as A(kx ) where A(kx ) is a function of a and kx only, where kx is the x-component of the diffracted wavevector. Derive, showing all work, the radiant intensity of the far-field (Fraunhofer) diffraction pattern resulting from the diffraction of the plane wave by this amplitude transmittance function, f4 . Express your answer as I(kx ) where I(kx ) is a function of I0 , a, and kx only, where I0 is the far-field radiant intensity at kx = 0. Also express your answer as I() where I() is a function of I0 , a, , and only, where is the angle of propagation in the far-field (as measured from the normal to the surface of the spatial light modulator) and I0 is the far-field radiant intensity at = 0. Put your final answers in the spaces provided. A(kx ) = I(kx ) = I() = Make an accurate (computer-based, not hand-drawn) plot of the diffracted amplitude. On the y-axis, plot A(kx )/a from -4 to +4. On the x-axis, plot kx a/ from -6 to +6. Also, make an accurate (computer-based, not hand-drawn) plot of the diffracted radiant intensity. On the y-axis, plot I(kx )/I0 from 0 to 1. On the x-axis, plot kx a/ from -6 to +6. Be sure that the resolutions that you select for your plots are sufficient to show all variations that occur in these functions. Attach your plots to your solution. ...
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This note was uploaded on 04/29/2008 for the course ECE 4500 taught by Professor Gaylord during the Spring '08 term at Georgia Institute of Technology.

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4500PF02-1 - Fraunhofer Diffraction by Four Slits A metal...

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