Inverse Problems in Turbulent Dynamics of Light

The differential equations underlying the non-linear dynamics of turbulent fluid flow are extended to the transport of optical energy and optical phase in coherent lasers in a new theoretical framework. Since light acts like a pure, incompressible, inviscid fluid, the momentum and mass transport of the NavierStokes equations translate directly to the intensity and phase transport equations in scalar diffraction theory, respectively. The non-linear term in the phase transport equation describes the emergence of turbulent dynamics near cusps and singularities in the optical field, enabling insights into the topology and dynamics of turbulence/speckle in 6D phase space. A better understanding of the mathematical forms of turbulent wave dynamics allows for reformulating the inverse computational problem for the perennial and current problems in the physics and engineering - imaging through turbulent media, understanding stochastic effects in sub 20nm extreme ultraviolet lithography for extending Moore’s law, holographic reconstruction of chaotic diffusion in image processing - but in context of latest computational and sensing capabilities. Turbulence in visible laser light can be easily measured with inexpensive table-top laser sources, scientific cameras, and simple imaging optics, enabling volumetric energy measurements. Combined with the most current mathematical understanding and computational tools for hydrodynamics modeling, we hope to usher in a new understanding of super-linear dynamics in natural flow processes