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# Download Tutorial for Chapter 8

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Tutorial for Chapter 8 1. Understand and memorize (8.9) for a Gaussian beam, (8.11) for its beam radius, (8.12) for its radius of curved wave front, and (8.13) for its Rayleigh range. 2. Understand and memorize the ABCD law in (8.15) for converting a Gaussian A beam to another by an optical system whose matrix is given by C B . D 3. Show that (8.22) is consistent with (8.20) and (8.21). 4. Show that the matrix (6.46) for a thick window obeys the ABCD law. 5. (a) Confirm that (8.9) reduces to (8.1) when z = 0. (b) Take the limit z >> z0 to find the field far from the laser focus. (c) Define the ratio of z to the (far-away) beam diameter as the f-number: z f number Lim z 2 ( z ) 6. A Gaussian beam of Rayleigh range z0 = 50 cm and wavelength = 488 nm is converted into another Gaussian beam with using a lens of focal length f = 5 cm at a distance z = 75 cm. Find the beam waist and location (from the lens) for the new Gaussian beam.