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Unformatted text preview: MASSACHUSETTS INSTITUTE OF TECHNOLOGY 2.710 Optics Spring ’09 Problem Set #6 Posted Monday, Apr. 6, 2009 — Due Wednesday, Apr. 15, 2009 1. Grating with tilted plane wave illumination Consider a sinusoidal phase grating of the surface relief type with complex amplitude transmission function g t ( x ) = exp n i m 2 sin 2 π x Λ o . The grating is placed at the plane z = 0 and illuminated by an off–axis plane wave g- ( x,z = 0) = exp n i 2 π x λ sin θ + i 2 π z λ cos θ o z =0 ≈ exp i 2 π θx λ propagating at angle θ 1 with respect to the optical axis z . 1.a) Describe, in as much detail as possible, the Fresnel diffraction pattern g + ( x,z = 0). 1.b) Describe, in as much detail as possible, the Fraunhofer diffraction pattern. 1.c) Compare with the on–axis illuminated phase grating that we analyzed in class. 2. Grating with spherical wave illumination Consider a sinusoidal amplitude grating with complex amplitude transmission function g t ( x ) = 1 2 h 1 + m cos 2 π x Λ i . The grating is placed at the plane z = 0 and illuminated by a spherical wave originating on–axis at location z =- z (where z > . ) Using the paraxial approximation for the spherical wave,...
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- Spring '09
- Diffraction, Fraunhofer diffraction, Fresnel diffraction, Binary amplitude grating