Towards Optical Hydrodynamics

Jason
W. Fleischer, Assistant Professor of Electrical Engineering,
Princeton

It is well-known, but
underappreciated, that the basic equations of nonlinear optics can be
mapped to
equations from condensed matter physics.
For example, the nonlinear Schrödinger description of
paraxial beam
propagation is identical to the Gross-Pitaevskii treatment of coherent
matter
waves, e.g. for Bose-Einstein Condensates.
In turn, these equations can be mapped to Euler-like fluid
dynamics
using the Madelung transformation. Here,
we exploit these relations to develop an optical hydrodynamics. Using coherent laser light in a nonlinear
crystal, we directly observe ideal (inviscid) fluid behavior, including
dispersive
shock waves, peakon/cuspon formation, and vortex flow. Using
spatially-incoherent light, we
demonstrate all-optical plasma dynamics, including Landau damping,
bump-on-tail
instabilities, and weak and strong regimes of speckle turbulence. Theory is developed and shown to match very
well with experiment. The results
establish optical systems as an analog simulator for fluid behavior and
hold
potential for the design of new photonic devices.