Operation conditions and stability of a degenerate two-photon laser

Semiclassical stability analysis of a two-photon laser including spatial variation of the cavity field

“…If, on the other hand, Re λ 0 < 0 and, for some value of n, Re λ n > 0, the n th cavity mode will support the growth of a fluctuation whose carrier frequency is different from that of the stationary state. Here, the existence of a one-to-one correspondence between the index n, that appears in equation (20), and the longitudinal cavity modes is suggested. This informal suggestion is founded on physical grounds.…”

“…It can be asserted that the highly excited modes α n such that n >> 10 are stable. This can be seen from looking at the argument of the logarithm in equation (20) in this case with the assumption α n > γ 2 , γ 1 γ 2 F 4 st . However…”

“…Equation (20) predicts that both single and multimode unstable behavior can be established with confidence. We begin our analysis by scaling all the relevant rates of the problem to the linewidth γ 1 of the active medium.…”

“…As instructive example we wish to discuss some limiting cases of the non-linear equation (20) governing the stability of the system.…”

“…(d) iterative state, we can solve equation (20) by substituting the value −iα n for λ n in the right hand side of equation (20). It can be asserted that the highly excited modes α n such that n >> 10 are stable.…”