GeomOpt_Part32 - Gaussian beam example Solutions 1 A laser...

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Gaussian beam example: Solutions 1. A laser beam with a 99% beam diameter of 3 mm must be focused into an optical fibre which has a mode field diameter of 10 µ m. The wavelength is 1.55 µ m. What optical system is required ? Answer: In Gaussian beam questions, it is always worth investigating the possibility of using a telecentric system first. A telecentric system is one in which the input beam waist and the output beam waist are located at the foci of the lens. This is shown below: For such a system we have: 1 2 ωπ λ ω f = Since ω 1 and ω 2 are fixed we can use this to find the necessary focal length f . π 2 1 = f In this example ω 1 =3 mm/3 (remembering that the 99% beam diameter is 3 times the beam waist) and ω 2 =10 µ m/2 (the mode field diameter of a fibre is twice the beam waist radius). This gives is us f =10.1 mm. This is about the shortest practical distance for a lens that we might want to use in the lab, but is quite possible for a commercial system. 2. An optical fibre with a beam waist radius of 5 µ m is used as a source in an experiment. We need to generate a spot 600 µ m (99% radius) and we require at least 20 mm space between the last lens and the spot in order to insert some equipment. The wavelength is again 1.55 nm. What does the optical system look like ? In this case, if we try to do a calculation for a simple telecentric system (where x
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This note was uploaded on 09/28/2010 for the course ECSE ECSE 527 taught by Professor Kirk during the Winter '10 term at McGill.

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GeomOpt_Part32 - Gaussian beam example Solutions 1 A laser...

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