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Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 8, Iss. 7 — Aug. 1, 2013
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Manipulating polarization of light with ultrathin epsilon-near-zero metamaterials

P. Ginzburg, F. J. Rodríguez Fortuño, G. A. Wurtz, W. Dickson, A. Murphy, F. Morgan, R. J. Pollard, I. Iorsh, A. Atrashchenko, P. A. Belov, Y. S. Kivshar, A. Nevet, G. Ankonina, M. Orenstein, and A. V. Zayats  »View Author Affiliations


Optics Express, Vol. 21, Issue 12, pp. 14907-14917 (2013)
http://dx.doi.org/10.1364/OE.21.014907


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Abstract

One of the basic functionalities of photonic devices is the ability to manipulate the polarization state of light. Polarization components are usually implemented using the retardation effect in natural birefringent crystals and, thus, have a bulky design. Here, we have demonstrated the polarization manipulation of light by employing a thin subwavelength slab of metamaterial with an extremely anisotropic effective permittivity tensor. Polarization properties of light incident on the metamaterial in the regime of hyperbolic, epsilon-near-zero, and conventional elliptic dispersions were compared. We have shown that both reflection from and transmission through λ/20 thick slab of the metamaterial may provide nearly complete linear-to-circular polarization conversion or 90° linear polarization rotation, not achievable with natural materials. Using ellipsometric measurements, we experimentally studied the polarization conversion properties of the metamaterial slab made of the plasmonic nanorod arrays in different dispersion regimes. We have also suggested all-optical ultrafast control of reflected or transmitted light polarization by employing metal nonlinearities.

© 2013 OSA

1. Introduction

The ability to manipulate the polarization of light is essential for numerous applications spanning tele- and data communications, spectroscopy and microscopy, to name a few. The most commonly used approach for polarization rotation and conversion is based on either half- and quarter-wave plates utilizing retardation effects in anisotropic crystals [1

1. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 2000).

]. However, almost all natural birefringent materials have a small ratio between refractive indices associated with the different crystallographic directions, resulting in relatively thick retardation plates, typically more than tens of microns (dozens of wavelengths).

On the other hand, metamaterials provide an unprecedented opportunity to manipulate light in previously impossible ways and achieve peculiar refractive index properties [2

2. A. K. Sarychev and V. M. Shalaev, Electrodynamics of Metamaterials, (World Scientific, 2007).

]. In terms of polarization manipulation, optically active artificially structured media have been demonstrated in several configurations, e.g., planar arrays of subwavelength gammadions [3

3. A. Papakostas, A. Potts, D. M. Bagnall, S. L. Prosvirnin, H. J. Coles, and N. I. Zheludev, “Optical manifestations of planar chirality,” Phys. Rev. Lett. 90(10), 107404 (2003). [CrossRef] [PubMed]

], chiral plasmonic structures [4

4. M. Hentschel, M. Schäferling, T. Weiss, N. Liu, and H. Giessen, “Three-Dimensional chiral plasmonic oligomers,” Nano Lett. 12(5), 2542–2547 (2012). [CrossRef] [PubMed]

, 5

5. C. Helgert, E. Pshenay-Severin, M. Falkner, C. Menzel, C. Rockstuhl, E. B. Kley, A. Tünnermann, F. Lederer, and T. Pertsch, “Chiral metamaterial composed of three-dimensional plasmonic nanostructures,” Nano Lett. 11(10), 4400–4404 (2011). [CrossRef] [PubMed]

], spiral bull-eye grooves [6

6. A. Drezet, C. Genet, J. Y. Laluet, and T. W. Ebbesen, “Optical chirality without optical activity: How surface plasmons give a twist to light,” Opt. Express 16(17), 12559–12570 (2008). [CrossRef] [PubMed]

], chromatic plasmonic polarizers [7

7. T. Ellenbogen, K. Seo, and K. B. Crozier, “Chromatic plasmonic polarizers for active visible color filtering and polarimetry,” Nano Lett. 12(2), 1026–1031 (2012). [CrossRef] [PubMed]

], and twisted nanorods stacks [8

8. Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat. Commun. 3, 870 (2012). [CrossRef] [PubMed]

]. Efficient broadband [9

9. J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009). [CrossRef] [PubMed]

] and narrowband polarizers [10

10. N. I. Zheludev, E. Plum, and V. A. Fedotov, “Metamaterial polarization spectral filter: isolated transmission line at any prescribed wavelength,” Appl. Phys. Lett. 99(17), 171915 (2011). [CrossRef]

] have also been demonstrated. Other novel approaches such as Faraday rotators based on single confined spin excitations [11

11. M. Atatüre, J. Dreiser, A. Badolato, and A. Imamoglu, “Observation of Faraday rotation from a single confined spin,” Nat. Phys. 3(2), 101–106 (2007). [CrossRef]

] or graphene sheets [12

12. I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. Marel, and A. B. Kuzmenko, “Giant Faraday rotation in single- and multilayer graphene,” Nat. Phys. 7(1), 48–51 (2011). [CrossRef]

], require either macroscopic designs or challenging technological efforts to achieve acceptable levels of reliability and repeatability.

In this paper, we demonstrate efficient manipulation of polarization properties of light using a metamaterial slab based on plasmonic nanorods. We compare polarization properties of reflected and transmitted light in the regimes of hyperbolic, ENZ and conventional dispersion and show the experimental proof of concept for a functional polarization converter based on a plasmonic nanorod metamaterial slab. Wavelength-dependent control over polarization was demonstrated in passive regime, and an active device has been proposed by employing the intrinsic nonlinearities of metal.

2. Results and discussion

A plasmonic metamaterial consisting of arrays of vertically aligned and electromagnetically coupled Au nanorods is an example of a highly anisotropic artificial medium [Fig. 1(a)
Fig. 1 (a) Schematic view of the plasmonic nanorod metamaterial layer for polarization control in reflection or transmission. (b) Geometry and definitions for elipsometric parameters. (c) Real (red) and imaginary (blue) parts of the effective permittivity tensor components ε and ε|| of the metamaterial. The metamaterial consists of Au nanorods deposited within aluminium oxide matrix, nanorod height and diameter are 350 nm and 30 nm, respectively, nanorod spacing is 60 nm. Spectral ranges of elliptic and hyperbolic dispersions are also indicated.
]. Having properties different of those of isolated rods [25

25. P. Ginzburg, A. Nevet, N. Berkovitch, A. Normatov, G. M. Lerman, A. Yanai, U. Levy, and M. Orenstein, “Plasmonic resonance effects for tandem receiving-transmitting nano-antennas,” Nano Lett. 11(1), 220–224 (2011). [CrossRef] [PubMed]

, 26

26. A. Normatov, P. Ginzburg, N. Berkovitch, G. M. Lerman, A. Yanai, U. Levy, and M. Orenstein, “Efficient coupling and field enhancement for the nano-scale: plasmonic needle,” Opt. Express 18(13), 14079–14086 (2010). [CrossRef] [PubMed]

], it can be described by the diagonal permittivity tensor in the effective medium approximation (see Methods):
ε=(εεε),
(1)
where εis the permittivity for the electric field perpendicular to the nanorod axes (parallel to the metamaterial layer), whileε is the permittivity for the electric field parallel to the nanorod axes (normal to the metamaterial layer) [27

27. R. Atkinson, W. R. Hendren, G. A. Wurtz, W. Dickson, A. V. Zayats, P. Evans, and R. J. Pollard, “Anisotropic optical properties of arrays of gold nanorods embedded in alumina,” Phys. Rev. B 73(23), 235402 (2006). [CrossRef]

]. Due to the plasmonic nature of the optical response of metal, the ε component may become negative in the long wavelength range of the spectrum for certain geometrical parameters of the nanorod array. Anisotropic metamaterials with permittivity components having opposite signs, namely, εε<0, are called hyperbolic metamaterials, since they have hyperbolic isofrequency contours. The elliptic dispersion requires εε>0, while the ENZ regime is achieved for εε0with, as a rule of thumb, neff,<1. The advanced fabrication techniques enable control over the length, diameter and periodicity of the nanorods and, hence, allow tuning of the ENZ frequency to the desired values required for a particular application [27

27. R. Atkinson, W. R. Hendren, G. A. Wurtz, W. Dickson, A. V. Zayats, P. Evans, and R. J. Pollard, “Anisotropic optical properties of arrays of gold nanorods embedded in alumina,” Phys. Rev. B 73(23), 235402 (2006). [CrossRef]

]. By engineering the anisotropy of the artificial metamaterial, precise control over the polarization of light can be achieved using simple reflection or transmission configurations with a sub-wavelength thick metamaterial slab [Fig. 1(b)].

To illustrate anisotropic properties of nanorod metamaterial, we first consider a typical nanorod metamaterial, which will be used in the subsequent ellipsometric measurements. The metamaterial consisting of 350 nm height Au nanorods with 30 nm diameter and 60 nm average spacing between nanorods, embedded in alumina, can be attributed the real and imaginary parts of the effective permittivity componentsεandε shown in Fig. 1(c). The effective permittivities were derived using the effective medium theory (see Methods for details), neglecting nonlocal spatial dispersion effects. The hyperbolic dispersion regime interfaces the conventional elliptical one at a wavelength of around 735 nm at which the ENZ regime occurs. In the elliptical regime (wavelengths shorter 735 nm), the anisotropy of metamaterial is very strong with the ordinary and extraordinary refraction index difference Re(n)Re(n)0.25 atλ=500 nm, comparable to the anisotropy achievable with naturally available anisotropic crystals such as rutile (Δn=0.3). At the same time, losses are significant in this spectral range, also introducing significant dichroism (Δk=0.04). In the hyperbolic regime, the index difference is Re(n)Re(n)1.44atλ=1 μm which exceeds the anisotropy of all naturally occurring crystals. With the remarkable reduction of the losses for the field component perpendicular to the nanorod axes, the linear dichroism effect is further increased (Δk=1.7). Thus, the metamaterials provide record values for anisotropy and birefringence, which can be engineered by controlling structural parameters or indeed dynamically with active control of the optical properties of metamaterial constituents by external stimuli.

2.1. Polarization conversion in a nanorod metamaterial

The metamaterial parameters required to achieve specific polarization conversion of the linearly (p-) polarized incident light can be inferred from Fig. 2
Fig. 2 Parametric plots for polarization conversion of p-polarized incident light in (a,b) reflection and (c,d) transmission configurations: red-dashed curves correspond Δ = π/2, blue-doted curves to Δ = π, green-solid curves to |ξ| = 1. The linearly polarized light is incident from the air side. (a,c) The angle of incidence is φ = 60°. (b,d) The thickness is d = λ/20. Metamaterial parameters are: ε|| = 4 + 0.1i and Im(ε) = 0.1. Black crosses are the intersections corresponding to conversion to circular polarization (red-green lines intersection) and to 90° linear polarization rotation (blue-green lines intersection). (e,f) 3D plots of Ψ and Δ ellipsometric parameters (in degrees) for reflected light as the function of layer thickness d/λ and Re(ε). The incident light is p-polarized. The angle of incidence is 60°. Spectral ranges of elliptic and hyperbolic dispersions are also indicated.
where red-dashed curves correspond to the phase shift of Δ = π/2 between the TE and TM components of the electric field [Fig. 1(b)], demanded for circular polarization, while blue-doted curves satisfies the phase of Δ = π, required for rotation of polarization plane, and green-solid curves for the amplitude ratios of 1. The intersections (marked with black crosses) of red and green curves satisfy the conditions of the complete conversion of the linear polarization into circular one, the blue and green curves intersections correspond to 90° rotation of the incident linear polarization – both upon reflection [Figs. 2(a), 2(b)] or transmission [Figs. 2(c), 2(d)]. All other points on these parametric maps lead to elliptical polarization. As can be seen from Fig. 2, polarization conversion occurs in the vicinity of the ENZ point, even with very thin metamaterial layers of a fraction ofλthickness. In all considered cases, ‘half-waveplate’ and ‘quarter-waveplate’ effects occur for refractive indexes much less than 1, emphasizing the role of the ENZ regime. Comparable performance may only be achieved with much thicker components based on natural materials. For example, rutile (TiO2) crystal has an extremely high natural anisotropy of about 10%, resulting in a quarter-wave plate of 514 nm thickness at the wavelength of 590 nm.

Generally, strong rotation capability is observed close to ENZ point in both cases of weak hyperbolic and elliptic dispersions, providing huge polarization rotations angles – as high as 1000-3000 [°/λ], while for natural crystals (e.g., rutile) this value does not exceed 100 [°/λ]. The benefit of operating close to the ENZ regime relies on the fact that certain field components (perpendicular to the layer) are not accumulating propagation phase, while others do. In this scenario, it is easy to obtain sufficient phase differences over thin metamaterial layers. Subsequent increase of the layer thickness will introduce unequal losses in TE and TM components and break the balance between their amplitudes due to dichroism effects.

Beyond the parameters shown on the parametric maps in Fig. 2(a-d), the rest of the amplitude-phase space of the reflection scheme is presented in the 3D plots in Fig. 2(e,f) showing the dependences of ellipsometric angles [Eq. (4)] on the metamaterial layer thickness d/λ and Re(ε) at the angle of incidence of 60°. As expected, maximal phase accumulation occurs near the ENZ point, and a wide dynamic range of phase angles can be accumulated with deep-subwavelength metamaterial layers.

The discussed manipulation of light polarization with a plasmonic nanorod metamaterial has several advantages over others recently demonstrated, both in performance and fabrication simplicity. Other proposed approaches for polarization control with metamaterials include the use of stereometamaterials [29

29. N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3(3), 157–162 (2009). [CrossRef]

] and twisted [8

8. Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat. Commun. 3, 870 (2012). [CrossRef] [PubMed]

] metamaterial that serve as very efficient polarizers but require much more complicated layer-by-layer fabrication and hundreds of nanometers separation between the layers. Helix metamaterial based devices are also of micron thickness [9

9. J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009). [CrossRef] [PubMed]

]. ‘Nonhermitian’ metamaterials promise remarkable performances even with very thin single layers [30

30. P. Ginzburg, F. J. Rodríguez-Fortuño, A. Martínez, and A. V. Zayats, “Analogue of the quantum Hanle effect and polarization conversion in non-Hermitian plasmonic metamaterials,” Nano Lett. 12(12), 6309–6314 (2012). [CrossRef] [PubMed]

]. Nonlinear optical activity in metamaterials could be millions times higher than in natural crystals but, being power dependent, is small compared with linear polarization changes [31

31. M. Ren, E. Plum, J. Xu, and N. I. Zheludev, “Giant nonlinear optical activity in a plasmonic metamaterial,” Nat. Commun. 3, 833 (2012). [CrossRef] [PubMed]

]. It has to be noted that nanorods-based ENZ metamaterials have been shown to act as polarizers and narrowband angular transmittance filters [32

32. L. V. Alekseyev, E. E. Narimanov, T. Tumkur, H. Li, Yu. A. Barnakov, and M. A. Noginov, “Uniaxial epsilon-near-zero metamaterial for angular filtering and polarization control,” Appl. Phys. Lett. 97(13), 131107 (2010). [CrossRef]

] but not as polarization converters. Arrays of gold nanorods were also tested in terms of polarization state change in the transmission regime, but they have not been considered as a platform for on demand polarization control [33

33. R. Kullock, W. R. Hendren, A. Hille, S. Grafström, P. R. Evans, R. J. Pollard, R. Atkinson, and L. M. Eng, “Polarization conversion through collective surface plasmons in metallic nanorod arrays,” Opt. Express 16(26), 21671–21681 (2008). [CrossRef] [PubMed]

]. Similarly, L-shaped hole arrays in a metal film can be used for efficient polarization rotation in transmission [34

34. T. Li, S. M. Wang, J. X. Cao, H. Liu, and S. N. Zhu, “Cavity-involved plasmonic metamaterial for optical polarization conversion,” Appl. Phys. Lett. 97(26), 261113 (2010). [CrossRef]

, 35

35. T. Li, H. Liu, S. Wang, X. Yin, F. Wang, S. N. Zhu, and X. Zhang, “Manipulating optical rotation in extraordinary transmission by hybrid plasmonic excitations,” Appl. Phys. Lett. 93(2), 021110 (2008). [CrossRef]

]. Metamaterials have been also proposed to design polarization control functionalities in microwave spectral range [36

36. J. Hao, Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett. 99(6), 063908 (2007). [CrossRef] [PubMed]

].

2.2. Experimental realization

The spectral dependence of extinction, reflection and ellipsometric angles Ψ and Δ, extracted from measurements described in ‘Methods’, provide confirmation of the predicted strong polarization effects [Figs. 3(a)
Fig. 3 (a,c,e) Experimental and (b,d,f) theoretical spectra of (a,b) extinction and (c,d) reflection for p-polarized (solid lines) and s-polarized (dashed lines) light for different incidence angles. (e,f) The spectra of ellipsometric parameters Δ (solid lines) and Ψ (dashed lines) for different incidence angles. Metamaterial parameters are as in Fig. 1(c). Spectral ranges of elliptic and hyperbolic dispersions are also indicated.
-3(f)]. The experiments were performed for five different angles of incidence in the range from 35° to 55°. The extinction spectra [Fig. 3(a)] extracted from the transmission measurements, are typical of the plasmonic nanorod metamaterials with the transverse resonance at around 520 nm excited with light having an electric field component normal to the nanorod axes and the longitudinal resonance at around 700 nm excited by light polarized parallel to the nanorod axes. With the increase of the angle of incidence, the longitudinal resonance become more pronounced as the component of the electric field along the nanorod axes increases. The longitudinal peak is situated near the ENZ wavelength as has been observed previously [27

27. R. Atkinson, W. R. Hendren, G. A. Wurtz, W. Dickson, A. V. Zayats, P. Evans, and R. J. Pollard, “Anisotropic optical properties of arrays of gold nanorods embedded in alumina,” Phys. Rev. B 73(23), 235402 (2006). [CrossRef]

]. The reflection spectra have complex structure with less pronounced angular dependencies [Fig. 3(c)]. The longitudinal resonance of the extinction spectra can be correlated to the reduced reflection.

The measured parameter Δ which describes polarization plane rotation, varies significantly when the transition from conventional to hyperbolic dispersion regime occurs [Figs. 3(e), 3(f)]. It can be seen that there exists a set of frequencies for which Δ is equal to 90° indicating full conversion from linear to circular polarization in reflection. The 90° point is very sensitive to the angle of incidence and could be obtained in the vicinity of the ENZ regime. On the other hand, ψ, the measure of amplitude change, is close to 45° throughout the whole spectral range showing that the linear dichroism of the structure plays a minor role for the thin structures under investigation.

The experimental data have been modelled using analytical expressions obtained from the transfer matrix technique [37

37. P. Yeh, “Optics of anisotropic layered media: a new 4x4 matrix algebra,” Surf. Sci. 96(1-3), 41–53 (1980). [CrossRef]

] with the effective permittivities shown in Fig. 1(c). For these metamaterial parameters, the absolute value of ratio of ε and ε|| does not exceed 1, which is similar to the conditions assumed for the dependences in Fig. 2. It can be seen that the spectral dependences, as well as the absolute values of all parameters in Fig. 3 are well described by the theoretical model. The optimal geometrical parameters for the fitting are within 5% of those directly measured from the fabricated structure (see Methods).

2.3. All-optical control of polarization

Figure 4
Fig. 4 All-optical control of polarization conversion in the metamaterial upon reflection for different wavelengths: the dependences of (blue lines) rotation angle Δ and (red lines) amplitude angle ψ on the electron temperature in Au nanorods. Metamaterial parameters are as in Fig. 1(c). The metamaterial layer thickness is d/λ = 1/20 and the angle of incidence is φ = 60°
shows the modelled changes of Ψ and Δ parameters in the reflection configuration as the function of the electron temperature in the nanorods, induced by the pump beam. The results show that the polarization can be modulated very substantially on the sub-picosecond time scale. The considered signal wavelengths of 635, 735, and 835 nm were chosen to be in the region of elliptic, ENZ, and hyperbolic dispersion, respectively. The most pronounced modulation is observed close to the ENZ and weak hyperbolic regimes where the phase changes manifest themselves in the most pronounced way.

3. Conclusions

We have proposed and experimentally demonstrated ultrathin nanorod metamaterial based components for manipulation of light polarization. Both reflection and transmission configurations have been experimentally shown to provide linear-to-circular polarization conversion in a 350 nm thick slab at oblique incidence, which cannot be achieved by employing any naturally existing material in geometries of similar simplicity and which typically require components of tens of microns thickness, based on natural uniaxial crystals. Theoretically, complete linear-to-circular polarization conversion or 90° linear polarization rotation in both reflection from and transmission through a λ/20 thick slab of metamaterial can be achieved. Moreover, ultrafast all-optical phase modulation of the reflected and transmitted light can be achieved leading to significant (about 40° rotation) changes of polarization state of the signal light. This is an important step towards ultrasensitive polarization devices for free-space and integrated photonics as well as active devices for ultrafast, low-power, all-optical information processing on the deep-subwavelength scale utilizing electron nonlinearities of metamaterial components.

4. Methods

Polarization properties modeling. Considering a slab of a uniaxial anisotropic material with a principal axis oriented perpendicularly to a transparent isotropic substrate and bounded by vacuum [Fig. 1(b)], the reflection coefficients for p-polarized (TM) and s-polarized (TE) modes can be expressed as
rp=(1kz,sub/(εsubk0z))itan(kzpd)(εkz,sub/(εsubkzp)kzp/(εkzp))(1+kz,sub/(εsubk0z))itan(kzpd)(εkz,sub/(εsubkzp)+kzp/(εkzp))
(2)
and
rs=(1kz,sub/(εsubk0z))itan(kzsd)(εkz,sub/(εsubkzs)kzs/(εkzp))(1+kz,sub/(εsubk0z))itan(kzsd)(εkz,sub/(εsubkzs)+kzs/(εkzp)),
(3)
respectively. Here, kzp2=εk02β2ε/ε,kzs2=εk02β2, kz,sub2=εsubk02β2, and k0z2=k02β2; β is the in-plane (xy) component of the wavevector of the incident light, dis the thickness of the metamaterial slab; εand εare the components of the metamaterial dielectric permittivity tensor (Eq. (1), respectively, εsubis the dielectric permittivity of the substrate, while the superstrate was assumed to be vacuum εsup=1.

The polarization changes experienced by a plane wave reflected from a planar surface are derived from the ratio of the reflection coefficients (rp/rs) for its p- (TM) and s- (TE) polarized components (Fig. 1) and in general is a complex number [1

1. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 2000).

]:
ξ=rprs=tan(ψ)eiΔ,
(4)
whereψ is the measure of the amplitude ratio and Δ represents the phase rotation. The polarization conversion of the incident beam from linear polarization into circular one corresponds to ξ=i (ψ=45,Δ=90), while ξ=1 (ψ=45,Δ=180) corresponds to the polarization rotation by 90°.

Effective medium model. In order to model the optical properties of the metamaterial, the experimental parameters of the nanorods were used to calculate the dielectric permittivity of the layer by applying the standard Maxwell-Garnett effective medium model presented in [40

40. J. Elser, R. Wangberg, V. A. Podolskiy, and E. Narimanov, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett. 89(26), 261102 (2006). [CrossRef]

] with a modified intra-rod interaction tensor γ.

Sample fabrication. The metamaterial sample fabrication sequence, similar to the one described in [14

14. G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, “Designed ultrafast optical nonlinearity in a plasmonic nanorod metamaterial enhanced by nonlocality,” Nat. Nanotechnol. 6(2), 107–111 (2011). [CrossRef] [PubMed]

], involves the reactive magnetron sputter deposition of a 10 nm thick Tantalum pentoxide adhesion layer on a 1 mm thick glass substrate, followed by the deposition of a 5 nm thick gold electrode with a 350 nm thick aluminum layer on top. The latter is then anodized in sulphuric acid (20 V) to obtain a nanoporous alumina template in which gold nanorods are electrochemically grown. The metamaterials studied here is made of rods with 350 nm height, 30 nm diameter, and 60 nm average interrod spacing.

Experimental measurements. The ellipsometric measurements have been performed using J. A. Woollam Co. commercial instrument. The reflection and transmission spectra in the range of angle of incidence and in the various polarization configurations (s-s, s-p, p-p, p-s) were recorded with both amplitude and phase information. The amplitude ratio and phase rotation have then been derived.

Acknowledgments

This work has been supported in part by EPSRC (UK) and ERC. P. G. acknowledges support from the Royal Society via the Newton International Fellowship.

References and links

1.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 2000).

2.

A. K. Sarychev and V. M. Shalaev, Electrodynamics of Metamaterials, (World Scientific, 2007).

3.

A. Papakostas, A. Potts, D. M. Bagnall, S. L. Prosvirnin, H. J. Coles, and N. I. Zheludev, “Optical manifestations of planar chirality,” Phys. Rev. Lett. 90(10), 107404 (2003). [CrossRef] [PubMed]

4.

M. Hentschel, M. Schäferling, T. Weiss, N. Liu, and H. Giessen, “Three-Dimensional chiral plasmonic oligomers,” Nano Lett. 12(5), 2542–2547 (2012). [CrossRef] [PubMed]

5.

C. Helgert, E. Pshenay-Severin, M. Falkner, C. Menzel, C. Rockstuhl, E. B. Kley, A. Tünnermann, F. Lederer, and T. Pertsch, “Chiral metamaterial composed of three-dimensional plasmonic nanostructures,” Nano Lett. 11(10), 4400–4404 (2011). [CrossRef] [PubMed]

6.

A. Drezet, C. Genet, J. Y. Laluet, and T. W. Ebbesen, “Optical chirality without optical activity: How surface plasmons give a twist to light,” Opt. Express 16(17), 12559–12570 (2008). [CrossRef] [PubMed]

7.

T. Ellenbogen, K. Seo, and K. B. Crozier, “Chromatic plasmonic polarizers for active visible color filtering and polarimetry,” Nano Lett. 12(2), 1026–1031 (2012). [CrossRef] [PubMed]

8.

Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat. Commun. 3, 870 (2012). [CrossRef] [PubMed]

9.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009). [CrossRef] [PubMed]

10.

N. I. Zheludev, E. Plum, and V. A. Fedotov, “Metamaterial polarization spectral filter: isolated transmission line at any prescribed wavelength,” Appl. Phys. Lett. 99(17), 171915 (2011). [CrossRef]

11.

M. Atatüre, J. Dreiser, A. Badolato, and A. Imamoglu, “Observation of Faraday rotation from a single confined spin,” Nat. Phys. 3(2), 101–106 (2007). [CrossRef]

12.

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. Marel, and A. B. Kuzmenko, “Giant Faraday rotation in single- and multilayer graphene,” Nat. Phys. 7(1), 48–51 (2011). [CrossRef]

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14.

G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, “Designed ultrafast optical nonlinearity in a plasmonic nanorod metamaterial enhanced by nonlocality,” Nat. Nanotechnol. 6(2), 107–111 (2011). [CrossRef] [PubMed]

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A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009). [CrossRef] [PubMed]

16.

V. A. Podolskiy and E. E. Narimanov, “Strongly anisotropic waveguide as a nonmagnetic left-handed system,” Phys. Rev. B 71(20), 201101 (2005). [CrossRef]

17.

P. Ginzburg and M. Orenstein, “Nonmetallic left-handed material based on negative-positive anisotropy in low-dimensional quantum structures,” J. Appl. Phys. 103(8), 083105 (2008). [CrossRef]

18.

P. Ginzburg and M. Orenstein, “Metal-free quantum-based metamaterial for surface plasmon polariton guiding with amplification,” J. Appl. Phys. 104(6), 063513 (2008). [CrossRef]

19.

C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. 14(6), 063001 (2012). [CrossRef]

20.

A. N. Poddubny, P. A. Belov, P. Ginzburg, A. V. Zayats, and Y. S. Kivshar, “Microscopic model of Purcell enhancement in hyperbolic metamaterials,” Phys. Rev. B 86(3), 035148 (2012). [CrossRef]

21.

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E. 70(4), 046608 (2004). [CrossRef] [PubMed]

22.

M. G. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using epsilon-near-zero materials,” Phys. Rev. Lett. 97(15), 157403 (2006). [CrossRef] [PubMed]

23.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of ε-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100(3), 033903 (2008). [CrossRef] [PubMed]

24.

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100(2), 023903 (2008). [CrossRef] [PubMed]

25.

P. Ginzburg, A. Nevet, N. Berkovitch, A. Normatov, G. M. Lerman, A. Yanai, U. Levy, and M. Orenstein, “Plasmonic resonance effects for tandem receiving-transmitting nano-antennas,” Nano Lett. 11(1), 220–224 (2011). [CrossRef] [PubMed]

26.

A. Normatov, P. Ginzburg, N. Berkovitch, G. M. Lerman, A. Yanai, U. Levy, and M. Orenstein, “Efficient coupling and field enhancement for the nano-scale: plasmonic needle,” Opt. Express 18(13), 14079–14086 (2010). [CrossRef] [PubMed]

27.

R. Atkinson, W. R. Hendren, G. A. Wurtz, W. Dickson, A. V. Zayats, P. Evans, and R. J. Pollard, “Anisotropic optical properties of arrays of gold nanorods embedded in alumina,” Phys. Rev. B 73(23), 235402 (2006). [CrossRef]

28.

R. J. Pollard, A. Murphy, W. R. Hendren, P. R. Evans, R. Atkinson, G. A. Wurtz, A. V. Zayats, and V. A. Podolskiy, “Optical nonlocalities and additional waves in epsilon-near-zero metamaterials,” Phys. Rev. Lett. 102(12), 127405 (2009). [CrossRef] [PubMed]

29.

N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3(3), 157–162 (2009). [CrossRef]

30.

P. Ginzburg, F. J. Rodríguez-Fortuño, A. Martínez, and A. V. Zayats, “Analogue of the quantum Hanle effect and polarization conversion in non-Hermitian plasmonic metamaterials,” Nano Lett. 12(12), 6309–6314 (2012). [CrossRef] [PubMed]

31.

M. Ren, E. Plum, J. Xu, and N. I. Zheludev, “Giant nonlinear optical activity in a plasmonic metamaterial,” Nat. Commun. 3, 833 (2012). [CrossRef] [PubMed]

32.

L. V. Alekseyev, E. E. Narimanov, T. Tumkur, H. Li, Yu. A. Barnakov, and M. A. Noginov, “Uniaxial epsilon-near-zero metamaterial for angular filtering and polarization control,” Appl. Phys. Lett. 97(13), 131107 (2010). [CrossRef]

33.

R. Kullock, W. R. Hendren, A. Hille, S. Grafström, P. R. Evans, R. J. Pollard, R. Atkinson, and L. M. Eng, “Polarization conversion through collective surface plasmons in metallic nanorod arrays,” Opt. Express 16(26), 21671–21681 (2008). [CrossRef] [PubMed]

34.

T. Li, S. M. Wang, J. X. Cao, H. Liu, and S. N. Zhu, “Cavity-involved plasmonic metamaterial for optical polarization conversion,” Appl. Phys. Lett. 97(26), 261113 (2010). [CrossRef]

35.

T. Li, H. Liu, S. Wang, X. Yin, F. Wang, S. N. Zhu, and X. Zhang, “Manipulating optical rotation in extraordinary transmission by hybrid plasmonic excitations,” Appl. Phys. Lett. 93(2), 021110 (2008). [CrossRef]

36.

J. Hao, Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett. 99(6), 063908 (2007). [CrossRef] [PubMed]

37.

P. Yeh, “Optics of anisotropic layered media: a new 4x4 matrix algebra,” Surf. Sci. 96(1-3), 41–53 (1980). [CrossRef]

38.

W. S. Chang, J. B. Lassiter, P. Swanglap, H. Sobhani, S. Khatua, P. Nordlander, N. J. Halas, and S. Link, “A plasmonic fano switch,” Nano Lett. 12(9), 4977–4982 (2012). [CrossRef] [PubMed]

39.

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012). [CrossRef]

40.

J. Elser, R. Wangberg, V. A. Podolskiy, and E. Narimanov, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett. 89(26), 261102 (2006). [CrossRef]

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(350.4238) Other areas of optics : Nanophotonics and photonic crystals

ToC Category:
Metamaterials

History
Original Manuscript: January 28, 2013
Revised Manuscript: March 19, 2013
Manuscript Accepted: March 21, 2013
Published: June 17, 2013

Virtual Issues
Vol. 8, Iss. 7 Virtual Journal for Biomedical Optics
Hyperbolic Metamaterials (2013) Optics Express

Citation
P. Ginzburg, F. J. Rodríguez Fortuño, G. A. Wurtz, W. Dickson, A. Murphy, F. Morgan, R. J. Pollard, I. Iorsh, A. Atrashchenko, P. A. Belov, Y. S. Kivshar, A. Nevet, G. Ankonina, M. Orenstein, and A. V. Zayats, "Manipulating polarization of light with ultrathin epsilon-near-zero metamaterials," Opt. Express 21, 14907-14917 (2013)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-21-12-14907


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References

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  13. C. R. Simovski, P. A. Belov, A. V. Atrashchenko, and Y. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mater.24(31), 4229–4248 (2012). [CrossRef] [PubMed]
  14. G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, “Designed ultrafast optical nonlinearity in a plasmonic nanorod metamaterial enhanced by nonlocality,” Nat. Nanotechnol.6(2), 107–111 (2011). [CrossRef] [PubMed]
  15. A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater.8(11), 867–871 (2009). [CrossRef] [PubMed]
  16. V. A. Podolskiy and E. E. Narimanov, “Strongly anisotropic waveguide as a nonmagnetic left-handed system,” Phys. Rev. B71(20), 201101 (2005). [CrossRef]
  17. P. Ginzburg and M. Orenstein, “Nonmetallic left-handed material based on negative-positive anisotropy in low-dimensional quantum structures,” J. Appl. Phys.103(8), 083105 (2008). [CrossRef]
  18. P. Ginzburg and M. Orenstein, “Metal-free quantum-based metamaterial for surface plasmon polariton guiding with amplification,” J. Appl. Phys.104(6), 063513 (2008). [CrossRef]
  19. C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt.14(6), 063001 (2012). [CrossRef]
  20. A. N. Poddubny, P. A. Belov, P. Ginzburg, A. V. Zayats, and Y. S. Kivshar, “Microscopic model of Purcell enhancement in hyperbolic metamaterials,” Phys. Rev. B86(3), 035148 (2012). [CrossRef]
  21. R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E.70(4), 046608 (2004). [CrossRef] [PubMed]
  22. M. G. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using epsilon-near-zero materials,” Phys. Rev. Lett.97(15), 157403 (2006). [CrossRef] [PubMed]
  23. B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of ε-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett.100(3), 033903 (2008). [CrossRef] [PubMed]
  24. R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett.100(2), 023903 (2008). [CrossRef] [PubMed]
  25. P. Ginzburg, A. Nevet, N. Berkovitch, A. Normatov, G. M. Lerman, A. Yanai, U. Levy, and M. Orenstein, “Plasmonic resonance effects for tandem receiving-transmitting nano-antennas,” Nano Lett.11(1), 220–224 (2011). [CrossRef] [PubMed]
  26. A. Normatov, P. Ginzburg, N. Berkovitch, G. M. Lerman, A. Yanai, U. Levy, and M. Orenstein, “Efficient coupling and field enhancement for the nano-scale: plasmonic needle,” Opt. Express18(13), 14079–14086 (2010). [CrossRef] [PubMed]
  27. R. Atkinson, W. R. Hendren, G. A. Wurtz, W. Dickson, A. V. Zayats, P. Evans, and R. J. Pollard, “Anisotropic optical properties of arrays of gold nanorods embedded in alumina,” Phys. Rev. B73(23), 235402 (2006). [CrossRef]
  28. R. J. Pollard, A. Murphy, W. R. Hendren, P. R. Evans, R. Atkinson, G. A. Wurtz, A. V. Zayats, and V. A. Podolskiy, “Optical nonlocalities and additional waves in epsilon-near-zero metamaterials,” Phys. Rev. Lett.102(12), 127405 (2009). [CrossRef] [PubMed]
  29. N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics3(3), 157–162 (2009). [CrossRef]
  30. P. Ginzburg, F. J. Rodríguez-Fortuño, A. Martínez, and A. V. Zayats, “Analogue of the quantum Hanle effect and polarization conversion in non-Hermitian plasmonic metamaterials,” Nano Lett.12(12), 6309–6314 (2012). [CrossRef] [PubMed]
  31. M. Ren, E. Plum, J. Xu, and N. I. Zheludev, “Giant nonlinear optical activity in a plasmonic metamaterial,” Nat. Commun.3, 833 (2012). [CrossRef] [PubMed]
  32. L. V. Alekseyev, E. E. Narimanov, T. Tumkur, H. Li, Yu. A. Barnakov, and M. A. Noginov, “Uniaxial epsilon-near-zero metamaterial for angular filtering and polarization control,” Appl. Phys. Lett.97(13), 131107 (2010). [CrossRef]
  33. R. Kullock, W. R. Hendren, A. Hille, S. Grafström, P. R. Evans, R. J. Pollard, R. Atkinson, and L. M. Eng, “Polarization conversion through collective surface plasmons in metallic nanorod arrays,” Opt. Express16(26), 21671–21681 (2008). [CrossRef] [PubMed]
  34. T. Li, S. M. Wang, J. X. Cao, H. Liu, and S. N. Zhu, “Cavity-involved plasmonic metamaterial for optical polarization conversion,” Appl. Phys. Lett.97(26), 261113 (2010). [CrossRef]
  35. T. Li, H. Liu, S. Wang, X. Yin, F. Wang, S. N. Zhu, and X. Zhang, “Manipulating optical rotation in extraordinary transmission by hybrid plasmonic excitations,” Appl. Phys. Lett.93(2), 021110 (2008). [CrossRef]
  36. J. Hao, Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett.99(6), 063908 (2007). [CrossRef] [PubMed]
  37. P. Yeh, “Optics of anisotropic layered media: a new 4x4 matrix algebra,” Surf. Sci.96(1-3), 41–53 (1980). [CrossRef]
  38. W. S. Chang, J. B. Lassiter, P. Swanglap, H. Sobhani, S. Khatua, P. Nordlander, N. J. Halas, and S. Link, “A plasmonic fano switch,” Nano Lett.12(9), 4977–4982 (2012). [CrossRef] [PubMed]
  39. M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics6(11), 737–748 (2012). [CrossRef]
  40. J. Elser, R. Wangberg, V. A. Podolskiy, and E. Narimanov, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett.89(26), 261102 (2006). [CrossRef]

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