PHYS 408 HOMEWORK 5 SOLUTIONS

# 73 cm before the thin lm the divergence angle is 0c

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Unformatted text preview: of the transmitted beam is 8.73 cm before the thin ﬁlm. The divergence angle is θ0,c = 2.2 w0,c = z0,c ￿ λz0,c π z0,c = ￿ (π ·10−6 )(1.345 m) π (1.345 m) ￿1/2 = 0.862 mrad (15) equivalent ABCD matrix 1 1 π · 10−6 m = +i qc qb 2π · 10−6 m2 2.3 ￿1/2 → A B C D = 1 0 (i/2)m−1 1 (16) creation of ﬁlm A pinhole transmits an Airy pattern which, although not gaussian, is approximately gaussian in its larges peak. However, light is still lost in higher-order diﬀraction channels. The pin hole must instead have a gaussian apodization. Physically, one can have a thin ﬁlm that has increasing opacity (increasing absorption) for increasing radius, and the transmitted ﬁeld amplitude at ρ = 0 is 0.8 of the incident ﬁeld amplitude. Photochemical methods invoking a photo-sensitive ﬁlm and applied gaussian beam have been used to create these gaussian apertures; see, for example, http://arxiv.org/abs/astro-ph/0406374, or Paul Nachman, “Fiber-optic based technique for fabricati...
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