Laminar flow in fluid systems becomes unstable and turns to turbulent flow when the velocity gradient exceeds the damping of fluctuations due to viscosity. The origin of turbulence lies in nonlinear coupling of fluid elements which is involved in the inertia term in the Navier-Stokes equation. Light propagating in matter also has a similar character. When the light remains weak, the Maxwell equations are nearly linear, so that no peculiar behavior can be seen. As the light intensity is increased, however, nonlinear optical processes via interactions between light and matter generate photons of new frequencies successively, and a transition is finally induced to optical turbulence, a very complicated space-time variation of the electromagnetic field. The present paper is a brief review of recent studies on this phenomenon and its underlying mathematics.
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