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### Transcript of Assignment for Lectures

Assignment-1 Gaussian beams1. Calculate the collimation range (confocal beam parameter) for three Gaussian

beams with wo1=3mm, wo2=4cm and wo3=30cm for the case of i) a CO2 laser =10.6 m and b) a frequency doubled Nd: YAG laser =532 nm. Present the results in a table. (1.5 marks) Ans. Collimation Range (2zo) =2 2 w0

Collimation Range (in m) wo (in mm) 3 4 300 CO2, =10.6 m 5.33 9.48 53347.80 Nd:YAG, =.532 m 106.29 188.97 1062944.88

2. Derive analytically the expression for the optimum wo of a monochromatic

Gaussian beam in order to achieve the minimum spot size w(z) at a distance z away from the source. Apply the result to calculate wo for =488 nm and z=1000 km. What is the value for the spot size w(z) at that distance? (2 marks) Ans.2 w( z ) = ( wo +

z 2 2 1/2 ) 2 2 wo

For optimum wo differential of w(z) with respect to wo should be 0.2 w0 wo = ( 2 z 2 2 =0 3 2 wo z 1/2 )

For =488 nm and z=1000 km, minimum wo = 0.394m.3. Calculate the size of the mode on the mirrors of a symmetric (R1=R2=1.5d)

Nd:YAG laser (=1064 nm ) cavity with length d=30 cm. What should be the minimum size of the mirrors in order to have a loss of less than 0.001% per round trip? (2.5 marks) Ans. For stable symmetric resonator minimum spot size should be at centre. Distance of mirror from centre is 0.5d.

4 2 wo Using, R( z ) = z (1 + 2 2 ) for R(z)=1.5d at z=0.5d, d=30cm and =1064 nm we z 2 z 1/2 ) =.268mm get wo = (