# HW7_soln - ECE 455 Optical Electronics Homework 6 Solutions...

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Unformatted text preview: ECE 455: Optical Electronics Homework 6 Solutions 1 HeNe Laser (a) Knowing the net round trip gain must be equal to 1: R left (632 . 8 nm ) Â· R right (632 . 8 nm ) Â· e 2 Î³ th Â· l g e- 2 Î± (632 . 8 nm ) Â· l a = 1 Î³ th = Î±l a l g- 1 2 Â· l g ln ( R left R right ) = Â· 1 cm 30 cm- 1 2 Â· 30 cm ln (0 . 999 Â· . 95) = 8 . 72 Ã— 10- 4 cm- 1 (b) Knowing the net round trip gain must be equal to 1: R left (3 . 39 Î¼m ) Â· R right (3 . 39 Î¼m ) Â· e 2 Î³ th Â· l g e- 2 Î± (3 . 39 Î¼m ) Â· l a = 1 Î³ th = Î±l a l g- 1 2 Â· l g ln ( R left R right ) = . 2 cm- 1 Â· 1 cm 30 cm- 1 2 Â· 30 cm ln (0 . 999 Â· . 98) = 7 . 02 Ã— 10- 3 cm- 1 (c) Looking at the equation sheet for a useful looking equation, we find: Î³ ( Î½ ) = Ïƒ SE ( Î½ ) N 2- g 2 g 1 N 1 ! We should be using Î³ (unsaturated) because we are doing a threshold calculation for which saturation effects can be ignored. From the assumptions of the problem N 1 â†’ 0. Increasing the pumping strength will increase the population of N 2 . The laser will begin oscillation when Î³ = Î³ th . To find which line will begin oscillating first, find the the critical population of N 2 which will cause oscillation on each line. The one with the lower critical population will begin lasing first. Solving: Î³ th = Î³ = Ïƒ...
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HW7_soln - ECE 455 Optical Electronics Homework 6 Solutions...

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