In metamaterials, sub-wavelength-scale features are used to produce desired macroscopic optical constants, which may reach exotic values unattainable in natural materials, such as negative refractive index [1
See, for reviewW. Park and J. Kim, “Negative-Index Materials: Optics by Design,” MRS Bull.
33, 907–911 (2008). [CrossRef]
]. The ability to freely engineer optical constants has spawned a new field of transformation optics whose hallmark application is the invisibility cloak, a structure containing an electromagnetically inaccessible region [2
J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science
312(5781), 1780–1782 (2006). [CrossRef]
]. Experimental demonstration of invisibility remains a challenge partly because many cloaks require extreme values of optical constants difficult to achieve even with state-of-the-art metamaterials. Recently, a new cloak was proposed to hide objects in front of a mirror plane [3
J. Li and J. B. Pendry, “Hiding under the Carpet: A New Strategy for Cloaking,” Phys. Rev. Lett.
101(20), 203901 (2008). [CrossRef]
] and was experimentally demonstrated in the microwave region [4
R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science
323(5912), 366–369 (2009). [CrossRef]
]. This structure does not require extreme values for optical constants and is therefore an ideal candidate for optical frequency operation.
In transformation optics, an invisibility cloak is designed by a coordinate transformation that opens up an electromagnetically inaccessible region in the transformed space [2
J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science
312(5781), 1780–1782 (2006). [CrossRef]
D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express
14(21), 9794–9804 (2006). [CrossRef]
]. Ideally, one must be able to achieve extreme values of permittivity and permeability to realize this structure, which makes the actual implementation of invisibility cloak very difficult. Many schemes have therefore been proposed to mitigate these requirements [6
S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.
74(3), 036621 (2006). [CrossRef]
M. Farhat, S. Guenneau, A. B. Movchan, and S. Enoch, “Achieving invisibility over a finite range of frequencies,” Opt. Express
16(8), 5656–5661 (2008). [CrossRef]
]. Most reduction schemes aim to demonstrate the same wave behavior as the ideal cloak but sacrifice the scattering properties. A reduced cloak has been experimentally demonstrated in the microwave region [13
D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science
314(5801), 977–980 (2006). [CrossRef]
]. While theoretical research in designing invisibility cloaks is rapidly progressing and expanding, experimental demonstrations of cloaking structures, particularly in the optical frequency region, remain scarce. Even a reduced cloak is highly challenging at optical frequencies for several reasons. First, metamaterial requires deep sub-wavelength-scale elements, which fall in the nanoscale regime for optical frequency operation. Demonstrating optical metamaterials therefore needs access to high-precision nanofabrication technologies. In addition, many optical metamaterials involve metallic nanostructures which become highly lossy at optical frequencies, severely degrading, if not completely masking off, the desired effects. Furthermore, losses are greatly amplified when the metamaterial structure comprise resonators, which is usually the case in most cloak designs. Managing and minimizing loss is therefore one of the most significant challenges in metamaterial research. The new ground plane invisibility cloak, however, requires only a modest range of permittivity with minimal anisotropy and can thus be implemented with non-resonant dielectric materials. This significantly relieves the issue of loss, thus making this system an ideal candidate for optical frequency operation. Very recently, this new cloak structures were implemented in a silicon-on-insulator wafer and the cloaking effect was observed experimentally by monitoring the scattered light or out-coupled light [14
J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, Nature Mater. , Advanced Online Publication, DOI: .
]. In this paper, we report an invisibility cloak based on a silicon nanorod array fabricated by the electron-beam lithography. Unlike the two other reports, the light propagation inside the device plane was imaged by the near-field optical microscopy (NSOM). This represents the first direct visualization of cloaking effect in the optical frequency region.
2. Cloak design and fabrication
The ground plane cloak was designed using a silicon nanorod array fabricated on a single-crystalline silicon-on-insulator (SOI) wafer. We first calculated the effective permittivity for the fundamental transverse-magnetic (TM, electric field perpendicular to the device layer) mode for the air-silicon-oxide slab waveguide, which was found to be εSOI-TM = 6.50 at λο = 1500 nm. When the nanorods are small, the effective permittivity of the nanorod array is given by the simple volume average of the silicon slab and air, εeff = AεSOI-TM + (1 – A)εair where A is the total cross-sectional area encompassed by nanorods, εSOI-TM = 6.50 and εair = 1. Thus, the range of permittivity values required for the cloak can be realized by progressively varying the nanorod diameter throughout the structure. The validity of this simple averaging rule was also confirmed by rigorous 3D photonic band structure calculations.
The cloak consists of a 215x80 array of nanorods whose diameters vary from 0.35a to 0.87a, where the array periodicity, a, is set to be 150 nm for this specific implementation. Ideally the reflecting interface should be a perfect reflecting mirror but in our structure the high reflectivity at the nanorod-air interface is used to mimic the mirror plane, greatly simplifying the fabrication process. As discussed later, the simulations show the reflectivity is high enough to exhibit cloaking behavior. Also, in the small area in the middle, both the nanorod size and periodicity are doubled in order to avoid extremely small gaps (~20 nm) between the nanorods which are difficult to fabricate accurately with our electron-beam facility. After this modification, the smallest gap dimension was 57 nm. Finally, the background medium with permittivity 2.25 was produced by a uniform array of nanorods with a diameter 0.53a.
The silicon nanorod based cloak structure was fabricated using an electron-beam lithography process on a silicon-on-insulator (SOI) wafer consisting of a 340 nm thick single crystalline silicon device layer on top of a 1 μm thick silicon oxide (SiO2
) over a bulk silicon substrate. The device region is comprised of a silicon nanorod array over a 39.6 μm x 39.6 μm area, connected to a 10 μm wide input waveguide and a 36.9 μm wide unpatterned silicon output region, as schematically shown in Fig. 1(a)
. The input waveguide is designed to make an incident angle of 45° with the curved reflecting interface of the cloak. The device region contains a 32 μm x 12 μm cloaking structure made of nanorods with diameters ranging from 90.75 nm to 52.18 nm and a uniform spacing of 150 nm. As explained earlier, the cloaking structure also contains a secondary array of 300 nm spaced nanorods with larger diameters in the range of 184.05 nm to 256.18 nm. The modified spacing of the center nanorods in the secondary region increased the minimum gap between adjacent structures, which reduced the spacing requirements and therefore the difficulties in defining the nanorods accurately using the electron-beam lithography tool.
Fig. 1 Schematic of (a) the ground plane cloak implemented with a silicon nanorod array and (b) reference sample made of unpatterned silicon with identical shape. The cloak structure consists of a square array of nanorods with a periodicity of 150 nm. The nanorod diameter is varied to produce the required index profile of ground plane cloak. In a small section in the middle, the periodicity and nanorod diameter were doubled to avoid feature sizes too small to fabricate. (c) SEM image of a silicon nanorod array fabricated by electron-beam lithography and reactive ion etching. Only the area near the curved reflecting interface is shown. Not shown are input and output waveguides positioned at 45° with respect to the reflecting interface.
The structure design was first entered into a CAD format, and then converted to a .v30 format that could be read by the electron-beam lithography system. Proximity correction was necessary during the file conversion process to allow for dose adjustments across the structure, most importantly at the device edges and near the large waveguide areas. A negative resist was chosen for the nanorod mask and applied to the wafer to provide a patterning medium for the subsequent electron-beam writing process. The resist was then patterned across the wafer using the electron-beam lithography tool. Once the pattern had been written, a developing process was used to remove the resist areas on the device that were to be etched. This process was repeated multiple times, as several test runs were required to finalize the electron beam dose that most accurately patterned the correct nanorod sizes and spacing. The etch process was performed on an inductively-coupled plasma (ICP) system that etched through the silicon layer while leaving the oxide layer unetched. Once the devices had been successfully fabricated, the wafer was manually cleaved to provide a clean edge for launching light into the edge of the input waveguide. In addition to the cloak device, we also fabricated an unpatterned reference sample that has identical shape and size to the cloak device, as schematically shown in Fig. 1(b)
, for comparisons. Figure 1(c)
shows a scanning electron micrograph (SEM) of the fabricated cloak structure near the curved reflecting interface.
3. Near-field visualization of cloaking effect
The performance of this cloak design was investigated by finite-difference time-domain (FDTD) simulations. As shown in Fig. 2(a)
, the cloak produced a well-defined reflected beam exactly analogous to the specular reflection from a flat mirror plane. There is some scattering due to the discretization of the curved interface which is inevitable in the metamaterial implementation. If we decrease the periodicity and nanorod size, the scattering is reduced significantly due both to the more accurately defined reflecting interface and the more precise representation of the required index profile of the cloak. Also, the design exhibits some light leakage through the reflecting interface due to the less than 100% reflectivity at the interface. The cloak performance will be compromised if the reflectivity becomes too low, however, despite these imperfections, the cloak performs very well. Considering that the middle part of the cloak has nanorod sizes as large as 256 nm, the performance of the current implementation is quite remarkable, showing the robustness of this ground plane cloak design.
Fig. 2 (a) FDTD simulation showing the performance of the silicon nanorod array cloak. The frequency was set to ωa/2πc = 0.1 which corresponds to a = 150 nm for an operating wavelength of λ = 1500 nm. (b) NSOM image of silicon nanorod array cloak for λ = 1500 nm. The input beam was fed into the structure vertically through the substrate. The reflected beam propagating to the left is circled for clarity.
The fabricated cloak structures were investigated by NSOM. Three fiber-coupled tunable lasers each of which covers 1410 - 1520 nm, 1528 - 1565 nm, and 1570-1603 nm, respectively, were used as light source. Proper polarization was set by the polarization controlling paddle and the laser output was butt-coupled into the input waveguide. The NSOM scanning process consisted of three steps. First, the tip oscillation amplitude and phase were set. Then, a section of the 10 μm input waveguide very close to the nanorod array was scanned. During this scan the parameters of the feedback controller were optimized so that a sharp topology scan may be obtained. Also, the NSOM scanning of the input waveguide section verified the proper alignment between the fiber and input waveguide. In the final step, the desired scan area was established via a topology scan, which was used to verify the feedback control set earlier. Finally, the near-field optical image was obtained by scanning the area again.
shows an NSOM image for a wavelength at 1500 nm. A well-defined input beam was observed propagating vertically from the bottom of the figure into the cloaking structure. A spot of intense scattering is visible at the reflecting interface. The out-of-plane scattering at the reflecting interface significantly reduces the reflected beam intensity, but is unavoidable in a 2D implementation, such as the current design, in which the guiding condition is compromised due to the abrupt interface. Despite losses at the reflecting interface, a clearly defined reflected beam was observed at a reflection angle of 45° with respect to the reflecting interface, as indicated in Fig. 2(b)
. The reflected light beam does not reach the output waveguide, however, due to the propagation loss within the nanorod array and also because of scattering losses at the reflecting interface. Similar patterns were measured at other wavelengths within the wavelength range accessible with the tunable laser system. This cloak is an all-dielectric cloak made of non-resonant elements and is expected to operate well over a broad range of frequencies. In the current implementation, however, the bandwidth is limited by the waveguide dispersion of the silicon slab.
In Fig. 3
, we compare the simulation and experimental results of laser light reflection in an unpatterned silicon reference sample. All device dimensions in the reference sample were the same as in the cloak, except that the nanorod array was replaced with an unpatterned silicon film. Naturally the curved interface generates a complex reflection pattern. Additionally, multiple reflections around the boundaries of the structure make the pattern even more complex. In the NSOM image shown in Fig. 3(b)
, we were able to identify at least two major reflected beams, creating two bright scattering areas along the top boundary of the device with a dark region in between. This is consistent with the intensity map generated by the FDTD simulation in Fig. 3(a)
, which also shows two high intensity spots along the top interface. The exact positions of the bright spots along the top interface were slightly shifted in the NSOM image compared to the FDTD intensity map. This is attributed to the slight misalignment of input laser beam. The brightest reflected beam is reflected again at the top interface, subsequently strikes the left interface above the input waveguide, and then is reflected again onto the bottom interface. Again, this pattern agrees very well with the FDTD simulation. The fact that the entire boundary of the reference structure lights up in the NSOM image indicates that there are many stray light paths created by random reflections at the curved interface. This is in clear contrast to the cloak structure measured and shown in Fig. 2
(a) The FDTD simulation and (b) NSOM image taken at λ = 1520 nm for the reference sample fabricated with identical dimensions as the cloak in Fig. 2
expect that the nanorod array is replaced with unpatterned silicon.
In summary, we present an experimental demonstration of a ground plane cloak made purely of dielectric materials and therefore capable of low-loss, broad-band operation at optical frequencies. Electron-beam lithography and reactive ion etching processes were used to fabricate silicon nanorod arrays whose size profile mimics the index profile of the ground plane cloak. The implementation reported in this paper exhibits good cloaking performance despite the fact that, for fabrication purposes, some of the feature sizes were made relatively large compared to the operating wavelength (~λ/6). NSOM was used to directly visualize light propagation inside the cloaking structure. A well-defined specularly reflected beam was observed, clearly confirming the cloaking effect. In contrast, a reference sample made of unpatterned silicon exhibited a complex reflection pattern that is naturally expected from a curved reflecting surface. This work represents the first direct visualization of cloaking effect in the optical frequency region. While the present report concerns 2D implementation, the structure can be readily extended to 3D structures, potentially enabling more practical applications. The low loss and modest index requirements make this all-dielectric ground plane cloak one of the most promising cloak designs for optical frequency operation.