PHYS 408 HOMEWORK 6 SOLUTIONS

# 2 46 48 multi wavevector wave f x y u x y z

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Unformatted text preview: = F{f }F{g } 10 10.1 (40) (41) (42) fourier optics, transfer functions, plane waves single-wavevector wave f (x, y ) = U (x, y, z = 0) = A exp(i(αx/4 + αy/3)) (43) g (x, y ) = U (x, y, z = d) = A exp(i(αx/4 + αy/3 + kz d)) (44) ˜ f (x, y ) = Aδ (kx − α/4)δ (ky − α/3) (45) g (x, y ) = Aδ (kx − α/4)δ (ky − α/3) exp(ikz d) ˜ g (x, y ) ˜ Aδ (kx − α/4)δ (ky − α/3) exp(ikz d) = = exp(ikz d) ˜(x, y ) Aδ (kx − α/4)δ (ky − α/3) f (47) g (x, y ) A exp(i(αx/4 + αy/3 + kz d)) = = exp(ikz d) f (x, y ) A exp(i(αx/4 + αy/3)) 10.2 (46) (48) multi-wavevector wave f (x, y ) = U (x, y, z = 0) = A exp(i(αx/4 + αy/3)) + B exp(i(αx/2 + αy/2)) (49) g (x, y ) = U (x, y, z = d) = A exp(i(αx/4 + αy/3 + kz,A d)) + B exp(i(αx/2 + αy/2 + kz,B d)) (50) ˜ f (x, y ) = Aδ (kx − α/4)δ (ky − α/3) + B δ (kx − α/2)δ (ky − α/2) (51) g (x, y ) = Aδ (kx − α/4)δ (ky − α/3) exp(ikz,A d) + B δ (kx − α/2)δ (ky − α/2) exp(ikz,B d) ˜ g (x, y ) ˜ Aδ (kx − α/4)δ (ky − α/3) exp(ikz,A d) + B δ (kx − α/2)δ (ky − α/2) exp(ikz,B d) = ˜(x, y ) Aδ (kx − α/4)δ (ky − α/3) + B δ (kx − α/2)δ (ky − α/2) f (53) g (x, y ) A exp(i(αx/4 + αy/3 + kz,A d)) + B exp(i(αx/2 + αy/2 + kz,B d)) = f (x, y ) exp(i(αx/4 + αy/3)) + B exp(i(αx/...
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