Diffusive-Light Invisibility Cloaking
Robert Schittny1,2, Muamer Kadic1,3, Tiemo Bückmann1,2, Martin Wegener1,2,3
1Institute of Applied Physics, Karlsruhe Institute of Technology (KIT), Germany,
2DFG-Center for Functional Nanostructures (CFN), Karlsruhe Institute of Technology (KIT), Germany,
3Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), Germany.
In an invisibility cloak [1–5], light is guided on a detour around an object such that it emerges behind unchanged, thus making the object invisible to an outside observer. An ideal cloak should be macroscopic and work perfectly for any direction, polarization, and wavelength of the incoming light. To make up for the geometrical detour, light has to travel faster inside the cloak than outside, that is, faster than the vacuum speed of light for cloaking in air or vacuum. Furthermore, the absence of wavelength dependence means that energy velocity and phase velocity are strictly equal. However, general relativity forbids energy velocities higher than the vacuum speed of light. Thus, macroscopic, omnidirectional, and broadband invisibility cloaking is fundamentally impossible in air [4, 5]. Consistently, all experimental demonstrations of optical cloaking so far came with a drawback in terms of operation bandwidth, size, or both [6–10].
In contrast to this, more recently, we have demonstrated  close to ideal macroscopic and broadband invisibility cloaking in diffusive light scattering media at visible wavelengths.
Fig. 1  illustrates the principle and results of invisibility cloaking in diffusive media. In such media, many scattering particles are randomly distributed, causing each photon to travel along a random path (see artistic illustration in the magnifying glass in Fig. 1). This effectively slows down light with respect to the vacuum speed of light, making perfect cloaking possible. In contrast to “ballistic” light propagation in vacuum or air as described by Maxwell’s equations, light propagation in such a medium can be described by diffusion of photons . Figure 1 (Ref.): Principle of diffusive-light cloaking. Computer-generated image of an illuminated cuboid diffusive medium with a zero-diffusivity obstacle (left-hand side) and a core-shell cloak (right-hand side). The magnifying glass shows an artistic illustration of a photon’s random walk inside the diffuse medium. The black streamline arrows are simulation results illustrating the photon current around obstacle and cloak. Corresponding measurement results are projected onto the front side of the cuboid volume, showing a diffuse shadow for the obstacle (left-hand side) and its elimination for the cloak (right-hand side). The euro coin illustrates the macroscopic dimensions of the cloak.
If a diffusive medium is illuminated from one side, any object with a different diffusivity inside this medium will cause perturbations of the photon flow. On the left-hand side of Fig. 1, a hollow cylinder with a diffusivity of exactly zero (the “obstacle”) suppresses any photon flow inside and casts a pronounced shadow, reducing the photon current on the downstream side (see black streamline arrows in Fig. 1). To compensate for this, a thin layer with a higher diffusivity than in the surrounding medium is added to the cylinder on the right-hand side of Fig. 1 (the “cloak”). Intuitively, a higher diffusivity (that is, a lower concentration of scattering particles) leads to an effectively higher light propagation speed and thus makes up for the geometrical detour the light has to take on its way around the obstacle. The black streamline arrows show that the photon current behind the cloak is unchanged. In other words, the shadow cast by the obstacle vanishes.
Such a core-shell cloak design can be thought of as the reduction of more complex multilayer designs based on transformation optics [1–3] to just two layers. It is known theoretically [13, 14] to work perfectly in the static case and for spatially constant gradients of the photon density across the cloak. Core-shell cloaks have been demonstrated before in magnetostatics , thermodynamics [16, 17], and elastostatics , recently even for non-constant gradients [16, 17].
For our experiments, we used a hollow aluminum cylinder as the obstacle, coated with a thin layer of white paint that acted as a diffusive reflector. For the cloaking shell, we coated the cylinder with a thin layer of a transparent silicone doped with dielectric microparticles. Obstacle and cloak are truly macroscopic, as indicated by the euro coin in Fig. 1 for comparison. We realized the diffusive background medium by mixing de-ionized water and white wall-paint. By changing the paint concentration, we could easily vary the surrounding’s diffusivity to find good cloaking performance. Other common examples of diffusive media are clouds, fog, paper or milk.
The samples were submerged in a Plexiglas tank filled with the water-paint mixture. The tank was illuminated from one side with white light coming from a computer monitor; photographs of the other side of the tank were taken with an optical camera. Two of these photographs are projected onto the front side of the cuboid volume shown in Fig. 1. The left-hand side shows the case with just the obstacle inside, exhibiting a pronounced diffuse shadow as expected from the discussion above. This shadow vanishes almost completely on the right-hand side, where the cloak is inside the tank. The yellowish tint of the photographs is caused by partial absorption of blue light in the water-paint mixture. Furthermore, we could trace the small remaining intensity variations for the cloaking case back to a finite absorption of light at the core-shell interface.
While the illustration in Fig. 1 only shows results for homogeneous illumination, we also found excellent cloaking performance using an inhomogeneous line-like illumination pattern (not depicted). Furthermore, we also performed successful experiments with spherical samples (not depicted), proving that our cloak is truly three-dimensional and works for any polarization and any direction of incidence.
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