All-optical event horizon in an optical analog of a Laval nozzle

Exploiting the fact that light propagation in defocusing nonlinear media can mimic the transonic flow of an equivalent fluid, we demonstrate experimentally the formation of an all-optical event horizon in a waveguide structure akin to a hydrodynamic Laval nozzle. The analog event horizon which forms at the nozzle throat is suggested as a platform for analogous gravity experiments.

Figure 1

An illustration of a laser beam propagating inside the optical Laval nozzle. The beam, with a small initial angle relative to the $z$ axis, bends more toward the $x$ direction as it propagates along the $z$ direction (“time”). The bend in the illustration is strongly exaggerated. A fluctuation is schematically shown near the Mach horizon as it is cut in two parts which propagate in opposite directions.

Figure 2

Images of the waveguide structures. (a) The input plane, with six circular openings of light pipes of different dimensions. (b) The exit plane, with grooves of triangular cross section, cut half-way along the sides of the channels, and forming the divergent sections of the nozzles.

Figure 3

Waveguide exit plane images and corresponding power density cross sections along the nozzle axis for an input power of 2 W and an iodine concentration of $\sim$40 ppm. (a) and (b) Data for a 2-mm-diam waveguide, (c) and (d) data for a 3-mm-diam waveguide, and (e) the free expansion of the beam outside the waveguide structure. Part (f) is a reference image of the 3-mm-diam waveguide.

Figure 4

The measured jet velocities as a function of input power for an iodine concentration of $\sim$40 ppm. Data are shown for two waveguides and for free expansion of the beam outside the waveguide structure. The calculation of velocities is explained in the text. The lines are guides to the eye.

Figure 5

Acceleration of supersonic flow. (a) An image of the exit plane of the 3 mm waveguide. (b) The corresponding power density cross section along the nozzle axis. (c) The jet velocity as a function of the distance between the beam axis and the nozzle throat, for four input powers (the curves are guides to the eye). The iodine concentration is $\sim$20 ppm.