HW7_soln - ECE 455: Optical Electronics Homework 6...

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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 ) R right (632 . 8 nm ) e 2 th l g e- 2 (632 . 8 nm ) l a = 1 th = l a l g- 1 2 l g ln ( R left R right ) = 1 cm 30 cm- 1 2 30 cm ln (0 . 999 . 95) = 8 . 72 10- 4 cm- 1 (b) Knowing the net round trip gain must be equal to 1: R left (3 . 39 m ) R right (3 . 39 m ) e 2 th l g e- 2 (3 . 39 m ) l a = 1 th = l a l g- 1 2 l g ln ( R left R right ) = . 2 cm- 1 1 cm 30 cm- 1 2 30 cm ln (0 . 999 . 98) = 7 . 02 10- 3 cm- 1 (c) Looking at the equation sheet for a useful looking equation, we find: ( ) = SE ( ) N 2- g 2 g 1 N 1 ! We should be using (unsaturated) because we are doing a threshold calculation for which saturation effects can be ignored. From the assumptions of the problem N 1 0. Increasing the pumping strength will increase the population of N 2 . The laser will begin oscillation when = 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: th = =...
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HW7_soln - ECE 455: Optical Electronics Homework 6...

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