The blueprint for our light-diffusion invisibility cloaks (Fig. 1A) contains either a cylindrical or
a spherical core with zero light diffusivity D1 = 0
and radius R1, which effectively suppresses the
flow of photons within. Thus, we can carve out
the core’s interior, opening up a space for objects
to be hidden within. When illuminated from one
side, the bare zero-diffusivity core reduces the
photon current on the downstream side; this
obstacle casts a diffusive shadow. To compensate for this reduced photon current, the core is
surrounded by a layer with diffusivity D2 and
radius R2 > R1. Given the photon diffusivity of
the homogeneous surrounding D0, a mathematical connection of D2 and R2 and the other parameters can be obtained (24, 26). For example,
for the cylindrical geometry in our experiments
with R2/R1 = 1.24, we calculate a moderate, hence
feasible, diffusivity contrast of D2/D0 = 4.72—and
for the spherical geometry in our experiments
with R2/R1 = 1.20, we calculate a similar diffusivity contrast of D2/D0 = 3.06—for negligible
losses (26). This core-shell structure is the cloak.
The cloak also restores the photon flux in the
backward and sideward directions (Fig. 1A).
In the experimental setup (Fig. 1B), the three
light diffusivities are realized in rather different
ways. For the core, we used a hollow stainless-steel cylinder (or sphere) that is coated with a
thin layer of acrylic white paint (26), which serves
as a diffusive reflector. The metal guarantees that
no light can enter the inside of the cloak. The shell
is composed of polydimethylsiloxane (PDMS),
doped with dielectric 10-mm-diameter melamine-resin particles at a concentration of 1 mg/ml (26).
For the surrounding diffusive medium within
which the cloak is placed, we used a cuboid tank
with an inner volume 35.5 by 16 by 6 cm filled
with de-ionized water to which white wall dispersion paint (26) is added (in Fig. 1B, the tank is only
partially filled for illustration). This allows for the
L
R1 R1
R2
R1 R1
R2
AB
R1
R2
Monitor screen
Fig. 1. Cloaking principle and experimental setup. (A) Illustration of
the cylindrical and spherical core-shell invisibility cloaks for diffusive
light. The outer radii for core R1 and shell R2 are indicated. The corresponding light diffusivities are D1 and D2, and that of the surrounding is
D0. The streamlines visualize the photon-current-density vector field
→
j
(the analog of the Poynting vector for ballistic light transport) as cal-
culated from Fick’s diffusion equation for homogeneous illumination for
obstacle (left) and cloak (right). Parameters are R2/R1 = 1.24, D1 = 0, and
D2/D0 = 4.72. The magnifying glass exhibits an artistic microscopic view
of light transport in diffusive media containing many randomly distrib-
uted scatterers. (B) Photograph of the experimental setup. The diam-
eters of the cylinders used in Fig. 2 (spheres in Fig. 3) are 2R1 = 32.1 mm
and 2R2 = 39.8 mm (2R1 = 33.2 mm and 2R2 = 39.9 mm), and the tank
thickness is L = 60 mm.
Fig. 2. Measurement
results for cylindrical
geometry. (A to F)
True-color photographs
of light emerging from
the setup (Fig. 1B)
for homogeneous
illumination with white
light. The first row is
the plain surrounding
(“reference”); in the
second row, the cylindrical
core (“obstacle”) is
added; and in the third
row, the cylindrical core-shell structure (“cloak”)
is added. In (A) to (C),
the surrounding is the
empty tank (“air”). In
(D) to (F), the tank is
filled with de-ionized
water and 0.35% white
paint (“water-paint”).
Obstacle and cloak are
centered in the tank,
with their cylinder axes
oriented along the
vertical direction. The
curves superimposed
onto the photographs
are horizontal cuts
of the normalized
intensity along the
gray dashed line. All
images and cuts
within one column are
shown on the identical
intensity scale. Obstacle and cloak cast a pronounced shadow in air. In the water-paint surrounding,
the obstacle still casts a pronounced diffusive shadow (center is four times darker), whereas the
intensity variation around a mean is less than T10% for the cloak. (G to L) As (A) to (F), but for line-like illumination (G).
