Answer to Question #117318 in Optics for shreevathsa BK

Question

Calculate the reflection coefficient R2 of the output coupler of L cm cavity tube of a laser of wavelength is 632.8nm which has the threshold gain factor and loss factor of 0.15 m-1 and 0.05m-1 respectively with one mirror of R1% reflecting.
L = 0.91 R1% = 98.62

Answer 1

Assume that laser operates in threshold condition $G_L=(G_L)_{th}=1$ , where $G_L$ is the Loop Gain.

$(G_L)_{th}=1=R_1\cdot R_2\cdot exp(2(\beta-\alpha)L)$.

In our case $R_1=0.9862$ , $\alpha=0.05m^{-1}$ , $\beta=0.15m^{-1}$ and $L=0.91m$

So,

$R_2=\frac{1}{R_1\cdot exp(2(\beta-\alpha)L)}=\frac{1}{0.9862\cdot exp(2\cdot(0.15-0.05)\cdot0.91)}=0.8453$ Answer