A hyperbolic metamaterial with a simultaneous type I/type II behaviour inthe visible range: realization and characterization toward a perfect lens

V. Caligiuri1, R. Dhama1, K. V. Sreekanth2, G. Strangi2,1, and A. De Luca1,∗

1Dept. of Physics and CNR UOS CS - University of Calabria - 87036 - Rende (Italy)2Nanoplasm Laboratory, Department of Physics - Case Western Reserve University - 44106 Cleveland (USA)

*antonio.deluca@fis.unical.it

Abstract— We report on the realization and characterization of a hyperbolic metamaterial with a simul-taneous type I/type II behaviour in the visible range. Spectroscopic ellipsometry is used in comparisonwith a complete scattering and transfer matrix method to show the effective response of the obtained struc-ture. The strong epsilon anisotropy and a transition wavelength around 420nm at which effective epsilonassume contemporarily a near zero and near pole value permits to experience the canalization regime anda perfect lens behaviour.

Since Veselago seminal work made its advent in scientific panorama, metamaterials and perfect lenseshave constituted a sort of inseparable binomial.[1, 2, 3] The possibility of resolving objects in the extremeproximity of a lens fascinated scientists for fifty years but, following the original idea of Veselago, inthe framework of conventional optics, realizing a perfect lens would required a negative refractive indexmedium. More recently, S. A. Ramakrishna et. al. [4] demonstrated the possibility of using an extremelyanisotropic medium to reach what is called the “canalization regime”, a condition under which the mediumshows εx = εy = 0 and εz = ∞ simultaneously. Hyperbolic Metamaterials (HMMs) are a completely newclass of materials constituted by deeply subwavelength sized metallic and dielectric subunits whose prop-erties, together with their aspect ratio, define the macroscopic optical constants of the whole structure.They present a uniaxial form of the dielectric tensor ¯̄ε (⃗r) = diag(εxx,εyy,εzz), where εxx = εyy = ε∥ andεzz = ε⊥. The iso-frequency surface for the extraordinary (TM-polarized) waves propagating in such astrongly anisotropic metamaterial is given by

k2x + k2y

ε⊥+

k2zε∥

=ω2

c2(1)

where: ε∥ = εdLd + εmLm/Ld +Lm and ε⊥ = εdεm(Ld +Lm)/Ldεm +Lmεd . Here εm and εd are the permit-tivities of the two materials chosen as building blocks (m for metal and d for dielectric). As evidenced bythese two last relations, the simultaneous condition of ε∥ ≈ 0 and ε⊥ ≈ ∞ can be fulfilled if Ld = Lm and,contemporarily, εm =−εd .

In this work we show the experimental realization and characterization of a particular HMM showingthe above condition, that we called epsilon near zero and pole (εNZP), in the visible range. We show howit was possible to experimentally achieve the double behaviour of type I and type II HMM, a supercolli-mation effect at the transition wavelength between the two regions, a strong spontaneaous emission rateenhanchement and the possibility to use this system as a near field perfect lens with a resolution down toλ/8. Results are well confirmed by simulations.

As a first step we engineered the metamaterial by means of the widely accepted Effective Medium The-ory (EMT) analysis. The optical constants used in this theoretical step have been extracted directly froma spectroscopic ellipsometrical analysis of each of the deposited layer (fig.1a). Then, the final multilayerstructure has been realized by means of a Physical Vapour Deposition (PVD) technique, by alternating 5bilayers, each of which made of a transparent oxide and a metal. In particular a 20 nm thick layer of IndiumTin Oxide (ITO) has been deposited on a glass substrate by means of a DC Magnetron sputtering system(Edwards Auto 306), with a power of 40W for 2 minutes at a distance of 7.2cm between the substrateand the ITO target. Then, an Ag layer (20 nm thick) has been deposited on the ITO using 10W of powerfor 3 minutes. This constitutes the bilayer. For each deposition session a control sample has been placedside by side with the main one, allowing to check the optical properties of each sputtered layer, as wellas its thickness and uniformity, at the end of each deposition. Spectroscopic ellipsometry has been usedto perform this analysis by means of a V-VASE Ellipsometer (Woollam Co.). By setting up a multistepdeposition procedure we were able to realize the complete multilayered metamaterial (see fig. 1a, inset).

(a)

Re

fle

cta

nce

(b)

355 414

(c)

Figure 1: (a) Real parts of effective dielectric permittivities (ε∥ and ε⊥) determined by means of effective mediumtheory and ellipsometry measurements. Inset: Imaginary parts of ε∥ and ε⊥ and schematic of the fabricated HMM, (b)Comparison between experimental reflectance measured by ellipsometry and SMM simulations at different angles forp- and s- polarized incident beams. (c) Transversal cuts of a FEM analysis of a plane wave propagating from a slit of500nm at the top of a three PMMA nanometric elements through the HMM at two different wavelengths 355nm and414nm. It is evident the superesolution obtained at the transition of type I/type II region (414nm).

Its good morphology has been investigated by means of the scanning electron microscopy analysis (SEM).Indeed, ellipsometry has been used as a powerful tool to perform angular transmission and reflection char-acterizations, as well as the Brewster angle evaluation. Theoretical transmission and reflection behaviorshave been carried out by means of a classic transfer and scattering matrix method (TMM and SMM) codeimplemented in MATLAB. Our code automatically takes into account the contribution of air as the incom-ing medium and glass as the outgoing one. Ellipsometrical measurements made at different angles havebeen compared with simulations, obtaining very good agreement (see fig.1b). It is well evident the almostcomplete reflective behavior of the system above 414nm, whereas the appearing of transmitting modes inthe type I region (below 414nm). Supercollimation and perfect lens simulation have been performed bymeans of a Finite Element Method (FEM) based software. We will show experimental confocal analysis attwo wavelenghts that will emphasize how a transmitted beam can be collimated if it remains in the “canal-ization regime”, that is close to the εNZP transition wavelength. At the same time, FEM simulations of aplane wave propagating from a slit of 500nm at the top of a three PMMA nanometric elements of 150nmwidth, separated by 50nm depth, have been performed to test the multilayer structure. Passing through theHMM, the plane wave can fill the metamaterial or not, depending on the used wavelength. At the εNZP weobserve a collimation behaviour, with a resolution down to λ/8 that permits to resolve the PMMA structureon the top of the HMM.

In conclusion we have realized and characterized a hyperbolic metamaterial made of five Ag/ITO bi-layers with same thickness. Due to the relative dielectric response of the two materials, we have fulfilledthe condition of εNZP that translates into a simultaneous type I/type II HMM. The obtained system hasbeen analyzed by means of spectroscopic ellissometry, from which transmission and reflection spectra atdifferent angles have been acquired and compared with a complete TMM and SMM simulation. A confocalmicroscope analysis with an external laser beam at two impinging wavelengths permitted to demonstratethe “canalization regime”. A FEM analysis has been used to show how this system can be used as a perfectlens and obtain a superesolution down to λ/8.

ACKNOWLEDGMENT

The research leading to these results has received support and funding from the Italian Project ”NanoLase”- PRIN 2012, protocol number 2012JHFYMC, and from the Ohio Third Frontier Project Research Clusteron Surfaces in Advanced Materials (RC-SAM).

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