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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 farfield (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 xcomponent of the diffracted wavevector. Derive, showing all work, the radiant intensity of the farfield (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 farfield 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 farfield (as measured from the normal to the surface of the spatial light modulator) and I0 is the farfield radiant intensity at = 0. Put your final answers in the spaces provided. A(kx ) = I(kx ) = I() = Make an accurate (computerbased, not handdrawn) plot of the diffracted amplitude. On the yaxis, plot A(kx )/a from 4 to +4. On the xaxis, plot kx a/ from 6 to +6. Also, make an accurate (computerbased, not handdrawn) plot of the diffracted radiant intensity. On the yaxis, plot I(kx )/I0 from 0 to 1. On the xaxis, 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.
 Spring '08
 Gaylord

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