experimental conditions in our model experiments
to be varied readily. We adjusted the paint concentration and thus the diffusivity empirically so
as to obtain good cloaking behavior. We chose this
approach because a reliable quantitative a priori
calculation of the effective photon diffusivities
would be demanding. This approach also automatically compensates for the effect of losses (26).
One side of the tank is illuminated by a liquid-crystal display (LCD) flat screen computer monitor,
which is in direct contact with one of the Plexiglas
walls. The monitor allows us to conveniently vary
the spatial pattern of illumination. We took optical images of the other side of the tank using a
digital camera located at a distance of ~0.5 m,
with its optical axis normal to the LCD screen.
For all cases, we show results for white-light
illumination using either air or the water-paint
mixture, respectively, as surroundings in the tank
(Fig. 2). Homogeneous illumination of the empty
tank, the reference, is shown in Fig. 2A; a shadow
for the obstacle is shown in Fig. 2B; and an even
more pronounced shadow for the cloak is shown
in Fig. 2C. The cloak has not been designed for
air as its surroundings. Both obstacle and cloak
are centered with respect to the tank. The same
sequence is shown in Fig. 2, D to F, but for the
water-paint surrounding. Light emerging from
the reference (Fig. 2D) has been subject to diffu-
sive light scattering. As to be expected, we again
found a nearly homogeneous light distribution.
The yellowish color indicates that blue light is
partially absorbed in the water-paint mixture
(26). For the obstacle (Fig. 2E), a pronounced
diffusive shadow was observed. For the cloak
(Fig. 2F), this shadow disappears, leaving behind
only a small relative modulation of the light in-
tensity within the image. These small imperfections
[(23) for comparison] can be traced back to resid-
ual absorption losses (26). The absence of major
color distortions beyond the overall yellowish ap-
pearance (which occurs for the reference already)
indicates that cloaking works well for the red,
green, and blue components of visible light.
An invisibility cloak should also work for any
other possible illumination condition. An extreme
example is a pointlike or a line-like illumination
(Fig. 2G). Diffusive-light invisibility cloaking remains
very good even under these extremely nonhomogeneous illumination conditions (Fig. 2, J to L).
Figure 3 exhibits the same as Fig. 2, but for a
spherical instead of a cylindrical geometry. By sym-
metry of this cloak, it is clear that the cloak is omni-
directional. It is 2R2/l ≈ five orders of magnitude
larger than the operation wavelength l and works
throughout the entire visible spectrum, qualifying
as a broadband cloak. This is the evidence for our
above claim of having achieved an omnidirectional
passive broadband macroscopic invisibility cloak
in the diffusive regime—attributes that are funda-
mentally impossible in the ballistic regime.
All experimental results (Figs. 2 and 3) agree
well with calculations (26) based on diffusion
theory (figs. S3 and S4). On this basis, we estimate (26) that the used stationary limit of Fick’s
diffusion equation remains applicable down to
time scales of 100 ns, which is equivalent to 107
image frames per second.
Last, as an application of diffusive-light invisibility cloaking, we suggest that one could
insert metal bars, which are almost as thick as
the glass, into a bathroom frosted-glass window
to prevent burglary. Usually, these bars would
immediately be visible via the diffusive shadow
they cast. By adding thin diffusive cloaking shells
around the metal bars, the window would again
appear as a homogeneously bright milky glass.
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We thank A. Naber (KIT) and X. He (visitor at KIT) for
discussions and J. Westhauser (KIT) for technical assistance.
We acknowledge support by the DFG-CFN through subproject
A1.5 and by the Karlsruhe School of Optics & Photonics (KSOP).
We also thank the Hector Fellow Academy for support.
Materials and Methods
Figs. S1 to S4
8 April 2014; accepted 27 May 2014
Published online 5 June 2014;
Fig. 3. Measurement
results for spherical
geometry. (A to L)
Results are as Fig. 2, A to
L, respectively, but for a
spherical rather than a
cylindrical cloak. Obstacle
and cloak are again
centered in the tank.
Here, the concentration
of white paint in
de-ionized water is 0.175%.