Experimental demonstration of a broadband array of invisibility cloaks in the visible frequency range

Very recently Farhat et al (2011, Phys. Rev. B 84 235105) suggested that arrays of invisibility cloaks may find important applications in low-interference communication, noninvasive probing, sensing and communication networks and so on. We report on the first experimental realization of such an array of broadband invisibility cloaks that operates in the visible frequency range. The wavelength and angular dependences of the cloak array performance have been studied.

performance.Here we report on the first experimental realization of such an array of broadband invisibility cloaks, which operates in the visible frequency range.
Our experimental geometry is based on the 2D broadband invisibility cloak design which utilizes an adiabatically tapered gold-coated waveguide emulating anisotropic dielectric permittivity and magnetic permeability distributions required for realization of the transformation optics-based invisibility cloak [4] (see Fig. 1(a)).This approach leads to low-loss, broadband performance in the visible frequency range, which is difficult to achieve by other means.This simple design has been extended to 3D cylindrical geometry and its broadband performance was independently verified in 3D [5].The basic idea of this design may be easily understood in the ray-optics approximation based on the semi-classical 2D cloaking Hamiltonian (dispersion law) introduced in [6]: where m is the transverse mode number.It appears that the cloaking Hamiltonian (1) can be emulated by an adiabatically changing d(r).Moreover, the required waveguide shape is very close to a gap between a sphere and a plane surface [4].The cloak radius for a mode number m is then given as where R is the sphere radius and λ is the wavelength of light.This cloaking geometry appears to be broadband with the cloaked areas for different light wavelengths nested inside each other [4].As demonstrated in Fig. 1(a), the described geometry is easy do transform into an array of broadband invisibility cloaks using commercially available microlens arrays.In the ideal case scenario light would propagate through such an array without scattering, as demonstrated in Fig. 1(b).
Our invisibility cloak arrays were fabricated as follows.As a first fabrication step, a commercially available microlens array [7] was coated on the microlens side with a 30-nm gold film (Fig. 2a).The array was placed with the gold-coated side down on top of a flat glass slide coated with a 30-nm gold film.Two gold coated surfaces were pressed against each other using a mechanical arrangement with set screws.Argon ion laser light with different wavelengths λ was coupled into the waveguide from the side.Periodic array of adiabatically tapered gaps between the gold-coated surfaces has been used as a 2D array of invisibility cloaks similar to the ones described in refs.[4,5].Similar to ref. [4], cloaked areas appear as dark circles surrounded by concentric rings in the experimental images.According to eq.( 3), roughly 20% of the surface area is cloaked in this experiment, which is consistent with the experimental image in Fig. 2(c).
While such images clearly demonstrate that an array of cloaks have been created in the experiment, cloak separation appears to be too large to study individual cloak interaction.
In order to clearly demonstrate the effects of cloak interaction, we have used smaller array parameters (30 μm pitch, 42 μm lens radius) in the next set of experiments.These results are presented in Figs.3-5.From the basic symmetry considerations the hexagonal dense cloak array shown in these figures is supposed to work best while illuminated along its three main symmetry axis, as shown in Fig. 3.
Indeed, microscope image of 514 nm light propagation through the cloak array is consistent with the "idealized" cloaking behaviour as shown in the inset.Similar to ref. [4], cloaked areas appear as dark circles.The inset in Fig. 3 demonstrated that for such a cylindrically symmetric Hamiltonian, the rays of light would flow smoothly without scattering around a cylindrical cloaked region of radius b.Such a cloaking Hamiltonian may be emulated by a gold-coated tapered waveguide, which thickness d in the z-direction changes adiabatically with radius r.The dispersion law (Hamiltonian) of light in such As a first experimental step, we have studied 514 nm light propagation through a cloak array formed by an array of large microlenses (500 μm pitch, 56 mm lens radius) as shown in Fig.2.As clearly visible in Fig.2(b), laser beam diameter in this experiment is comparable with the distance between the individual cloaks in the array.Dashed line in Fig.2(b) indicates the waveguide edge (the top and bottom gold-coated surfaces did not overlap precisely), while light propagation direction is indicated by the arrow.
(b) illustrates light propagation through the array.We were also able to confirm broadband cloaking behaviour of the cloak array illuminated along one of the main symmetry axis.Images of the array taken using 514 nm (Fig.4(a)) and 488 nm (Fig.4(b)) laser light coupled into the waveguide from the side illustrate similar cloaking performance.On the other hand, angular performance of the dense hexagonal cloak array clearly shows signs of deterioration.As illustrated in Fig. 5(d), cloak array illumination along the direction which does not coincide with one of the three main symmetry axis of the array leads to reduction of symmetry of the problem.This must lead to enhanced light scattering inside the array.Comparison of images in Fig.5(a) and Fig.5(c) indeed demonstrates such an enhanced light scattering inside the rotated cloak array.In conclusion, we have reported the first experimental realization of an array of broadband invisibility cloaks, which operates in the visible frequency range.Such an array is able of cloaking ~20% of an unlimited surface area.We have studied wavelength and angular dependencies of the cloak array performance.While the broadband performance appears to be similar to the performance of individual cloaks in the array, angular performance of a dense array shows sign of deterioration due to reduction of symmetry of the cloaking arrangement.

Figure Captions Figure 1 .
Figure Captions

Figure 2 .
Figure 2. Light propagation through a rectangular cloak array formed by the gap between gold coated surfaces of a large microlens array (500 μm pitch, 56 mm lens

Figure 3 .
Figure 3.Light propagation through a hexagonal cloak array formed by the gap between gold coated surfaces of a microlens array (30 μm pitch, 42 μm lens radius) and

Figure 4 .
Figure 4. Broadband performance of the cloak array is illustrated by two images of

Figure 5 .
Figure 5.Light propagation through the rotated cloak array indicates reduction in cloak Fig.1