Multimode intracavity frequency-doubled lasers can reach states of intensity-noise suppression orders of magnitude beyond the predictions of independent-mode partition statistics. I show that the ${\chi }^{\left(2\right)}$ coupled-wave dynamics in the doubling crystal obey a dissipation inequality: a fourth-moment functional of the intracavity intensity decreases monotonically under each forward nonlinear pass, driving the mode ensemble toward a constant-intensity manifold. This per-pass result is a strict Lyapunov inequality, and round-trip simulations show attraction to the same low-$M_4$, nearly constant-intensity state under the full cavity dynamics. I confirm the mechanism in an intracavity frequency-doubled ${\mathrm{Nd}\text{:}\mathrm{YVO}}_4$ laser with a lithium triborate (LBO) doubling crystal, observing a $100\times$ contrast between full and Fabry-Perot-filtered output noise at fixed detector bandwidth, well beyond the $\sqrt{N/N_f}$ statistical-averaging baseline. The argument depends only on the algebraic structure of the coupling: a coherent superposition of oscillators that share a quadratic dissipative channel. It therefore points to a general Lyapunov route to intensity-noise suppression in coupled oscillator systems, beyond the intracavity-doubled laser.

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• Gain properties of lasers
• Lasers
• Nonlinear optics
• Coupled oscillators