Fig. 1. (a), (b) Schematics of the metamaterial system. (a) In the absence of an external magnetic field, cobalt nanoparticles are randomly distributed within the ferrofluid, and their magnetic moments (shown by red arrows) have no preferred spatial orientation; (b) application of an external magnetic field leads to formation of nanocolumns (made of nanoparticles), which are aligned along the field direction. (c) Schematic diagram of the experimental geometry. A long wavelength infrared (LWIR) camera (FLIR Systems, USA) is used to study CO2 laser beam propagation through the ferrofluid subjected to the external DC magnetic field. The inset shows the measured beam shape in the absence of the ferrofluid sample. Two orientations of the external magnetic field B used in our experiments are shown by green arrows. The red arrow shows laser light polarization. Note that the z axis is assumed to always point in the direction of the external DC magnetic field.

Fig. 2. (a) Comparison of experimentally measured temporal dependences of the CO2 laser beam shape for the ordinary light (see Video 1) and extraordinary light (see Video 2) after passing through the ferrofluid subjected to an external DC magnetic field (measured at 160 mW laser power). Video 3 shows similar temporal signal dependence for the light passing through the isotropic ferrofluid, which is not subjected to any external DC magnetic field. Filamentation of the extraordinary beam is clearly visible in a single 2.6mm×2.6mm frame taken from the Video 2 and its cross section (see Video 4). The cross section of the ordinary beam (taken from Video 1) measured at the same laser power is shown for comparison. Video 5 shows experimentally measured temporal dependence of the CO2 laser beam profile for the extraordinary light polarization recorded at 22 mW incident CO2 laser power. At this lower power, the beam filamentation virtually disappears, so that the beam shape may be characterized as a slightly perturbed Gaussian profile. (b) The beam filamentation of the extraordinary light is revealed more clearly in the differential image, in which the average Gaussian profile of the laser beam is subtracted from the currently observed beam shape. (c) FFT analysis of image (b) reveals somewhat perturbed hexagonal symmetry in the spatial distribution of the filaments. The corresponding Fourier components are highlighted by white dots. (d) The highly symmetric spatial pattern of filaments is better revealed after high pass filtering of image (b). Video 1, MP4, 2.8 MB [URL: https://doi.org/10.1117/1.AP.2.5.056001.1]; Video 2, MP4, 5.0 MB [URL: https://doi.org/10.1117/1.AP.2.5.056001.2]; Video 3 MP4, 3.4 MB [URL: https://doi.org/10.1117/1.AP.2.5.056001.3]; Video 4, MP4, 1.7 MB [URL: https://doi.org/10.1117/1.AP.2.5.056001.4]; Video 5, MP4, 1.7 MB [URL: https://doi.org/10.1117/1.AP.2.5.056001.5].

Fig. 3. Comparison of gravitational and optical behavior. (a) In the presence of gravity, a simple Newtonian system of dust particles develops progressively more complex structures, so that “the growth-of-complexity arrow” always points away from the unique past. This time evolution is depicted for an example of a planetary system forming from a structureless dust cloud. (b) The observed changes in shape of the extraordinary light beam as a function of the z coordinate exhibit virtually similar behavior. The original structureless Gaussian beam incident onto the cuvette separates into multiple filaments under the action of effective gravity acting in the effective 2+1 dimensional Minkowski spacetime, in which the role of time is played by the spatial z coordinate.

Fig. 4. (a) Four 2.6mm×2.6mm image frames taken from a recorded video of the transmitted extraordinary beam evolution as a function of conventional physical time (the frame number is shown in the corner of each image). These frames show gradual motion of two filaments (indicated by arrows) toward each other, followed by merging of these filaments. (b) An example of an entropic irreversible temporal evolution of the transmitted extraordinary beam following the opening of the CO2 laser shutter. The average temperature of the field of view measured by the LWIR camera increases from frame to frame. The dimensions of all the frames are 2.6mm×2.6mm. All the time frames are recorded in the same physical location. They correspond to the optical field distribution at the output face of the optical cuvette, which is located at a 100μm distance from the input face of the cuvette.