Two branches of Solutions are:
1) k(L1+L2)= 2m*pi + sin^(-1)( \sqrt(r) * cos k(L2-L1)) - sin^(-1)(\sqrt(r)),
and
2) k(L1+L2)= (2m+1)*pi - sin^(-1)( \sqrt(r) * cos k(L2-L1)) - sin^(-1)(\sqrt(r)).
For more detail please check the Eqs.(10)-(12) in the following paper:
W. J. Fader, Theory of two coupled lasers, IEEE J. Quantum Electron. 21, 1838 (1985).
Hi, Anil!
I do not understand, which solution you seek? I suppose that L1 and L2 are parameters, aren't they? Then, you seek to express k as a function of r, or r as a function of k? By the way, what is the physical meaning of k and of r?
Dear Ma'am,
RHS is constant. L1 and L2 are the length of the two cavities and k is wave propagation constant. I have found the solution. That 2m*pi factor is playing a crucial role in the expansion of trigonometric series. Thanks...
Anil, my friend, you are always wellcome. If you found the solution I am glad for you.
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