 #1
CptXray
 23
 3
 Homework Statement:
 I have a laser cavity with one flat mirror ##R_{1} = \infty,## one positive lens with the focal length ##f_{lens}=50 \, mm## and curved mirror on the end of curvature ##R_{2}=100 \, mm.## The total length of the resonator is fixed and is equal to ##L = 1000 \, mm.## For what values of ##d## is the resonator stable? What is the distance d for which the waist size between the lens and mirror is the smallest? What is the size of the beam waist in this case? Assume ##TEM_{00}## mode.
 Relevant Equations:

Focal length of curved mirror:
$$f_{curved} = \frac{R_{2}}{2}.$$
I guess the resonator will be stable when both focal lengths of lens and curved mirror meet. The curved mirror is fixed and it's focal length:
$$f_{curved} = \frac{R_{2}}{2} = 50 \, mm.$$ Then the d should be: $$d=f_{lens}+f_{curved} = 100 \, mm.$$ I think that's also the distance for which the waist size is the smallest, but I don't really know how to get it's exact size. If someone who knows what's going on here could give me a hint or textbook where this is explained I'd be really grateful.