Electrically controllable soft optical cloak based on ... - OSA Publishing

Electrically controllable soft optical cloak based on gold nanorod fluids with epsilon-near-zero characteristic Zhaoxian Su, Jianbo Yin,* Kun Song, Qi Lei, and Xiaopeng Zhao Smart Materials Laboratory, Department of Applied Physics, Northwestern Polytechnical University, Xi’an, 710129, China * [email protected]

Abstract: We propose an electrically controllable soft optical cloak based on a fluid system containing gold nanorods, which can be transformed from isotropic to anisotropic epsilon-near-zero (ENZ) state at a certain incident optical frequency due to the orientation of gold nanorods under an external electric field stimulus. Both effective medium theory and 3D finite element simulation demonstrate that, at the ENZ point, the scattering from arbitraryshaped objects can be nearly perfect suppressed. The loss and aspect ratio of gold nanorods have an effect on the ENZ point and scattering suppression behavior. When different aspect ratio of gold nanorods is employed, the fluid has multi ENZ points and exhibits perfect suppression of scattering from objects at multiple incident optical frequencies. Because the orientation of gold nanorods depends on the strength of applied external electric field, the permittivity of fluid can be adjusted by external electric field and, as a result, the ENZ state and scattering suppression of objects can be controlled. The flexible, controllable, and multi-frequency responsive characteristics make the optical cloak possess potential use in soft smart metamaterial devices. ©2016 Optical Society of America OCIS codes: (160.3918) Metamaterials; (160.1190) Anisotropic optical materials; (230.3205) Invisibility cloaks.

References and links 1.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010). 2. S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11(5), 426–431 (2012). 3. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008). 4. Z. Su, J. Yin, Y. Guan, and X. Zhao, “Electrically tunable negative refraction in core/shell-structured nanorod fluids,” Soft Matter 10(39), 7696–7704 (2014). 5. H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99(6), 063903 (2007). 6. N. Landy and D. R. Smith, “A full-parameter unidirectional metamaterial cloak for microwaves,” Nat. Mater. 12(1), 25–28 (2012). 7. 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). 8. W. Zhu, M. Premaratne, and Y. Huang, “Hiding inside an arbitrarily shaped metal pit using homogeneous metamaterials,” J. Electromagnet Wave 26(17-18), 2315–2322 (2012). 9. 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). 10. M. G. Silveirinha, A. Alù, and N. Engheta, “Infrared and optical invisibility cloak with plasmonic implants based on scattering cancellation,” Phys. Rev. B 78(7), 075107 (2008). 11. T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010).

#256447 © 2016 OSA

Received 29 Dec 2015; revised 3 Feb 2016; accepted 25 Feb 2016; published 9 Mar 2016 21 Mar 2016 | Vol. 24, No. 6 | DOI:10.1364/OE.24.006021 | OPTICS EXPRESS 6021

12. M. Farhat, S. Mühlig, C. Rockstuhl, and F. Lederer, “Scattering cancellation of the magnetic dipole field from macroscopic spheres,” Opt. Express 20(13), 13896–13906 (2012). 13. A. Monti, A. Alù, A. Toscano, and F. Bilotti, “Optical invisibility through metasurfaces made of plasmonic nanoparticles,” J. Appl. Phys. 117(12), 123103 (2015). 14. A. Monti, F. Bilotti, and A. Toscano, “Optical cloaking of cylindrical objects by using covers made of core-shell nanoparticles,” Opt. Lett. 36(23), 4479–4481 (2011). 15. S. Mühlig, A. Cunningham, J. Dintinger, M. Farhat, S. B. Hasan, T. Scharf, T. Bürgi, F. Lederer, and C. Rockstuhl, “A self-assembled three-dimensional cloak in the visible,” Sci. Rep. 3, 2328 (2013). 16. S. Mühlig, M. Farhat, C. Rockstuhl, and F. Lederer, “Cloaking dielectric spherical objects by a shell of metallic nanoparticles,” Phys. Rev. B 83(19), 195116 (2011). 17. A. Monti, A. Alù, A. Toscano, and F. Bilotti, “Optical Scattering Cancellation through Arrays of Plasmonic Nanoparticles: A Review,” Photonics 2(2), 540–552 (2015). 18. J. Luo, W. Lu, Z. Hang, H. Chen, B. Hou, Y. Lai, and C. T. Chan, “Arbitrary control of electromagnetic flux in inhomogeneous anisotropic media with near-zero index,” Phys. Rev. Lett. 112(7), 073903 (2014). 19. A. S. Shalin, P. Ginzburg, A. A. Orlov, I. Iorsh, P. A. Belov, Y. S. Kivshar, and A. V. Zayats, “Scattering suppression from arbitrary objects in spatially dispersive layered metamaterials,” Phys. Rev. B 91(12), 125426 (2015). 20. A. Monti, F. Bilotti, A. Toscano, and L. Vegni, “Possible implementation of epsilon-near-zero metamaterials working at optical frequencies,” Opt. Commun. 285(16), 3412–3418 (2012). 21. 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). 22. B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-nearzero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100(3), 033903 (2008). 23. A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007). 24. Y. Xu, C. T. Chan, and H. Chen, “Goos-Hänchen effect in epsilon-near-zero metamaterials,” Sci. Rep. 5, 8681 (2015). 25. R. Maas, J. Parsons, N. Engheta, and A. Polman, “Experimental realization of an epsilon-near-zero metamaterial at visible wavelengths,” Nat. Photonics 7(11), 907–912 (2013). 26. 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(12), 14907– 14917 (2013). 27. L. Davis, “The metal particle/insulating oil system: An ideal electrorheological fluid,” J. Appl. Phys. 73(2), 680– 683 (1993). 28. T. Takahashi, T. Murayama, A. Higuchi, H. Awano, and K. Yonetake, “Aligning vapor-grown carbon fibers in polydimethylsiloxane using dc electric or magnetic field,” Carbon 44(7), 1180–1188 (2006). 29. M. Parthasarathy and D. J. Klingenberg, “Electrorheology: mechanisms and models,” Mater. Sci. Eng. Rep. 17(2), 57–103 (1996). 30. A. Sihvola, “Mixing rules with complex dielectric coefficients,” Subsurf. Sens. Technol. Appl. 1(4), 393–415 (2000). 31. M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander, Jr., and C. A. Ward, “Optical properties of the metals al, co, cu, au, fe, pb, ni, pd, pt, ag, ti, and w in the infrared and far infrared,” Appl. Opt. 22(7), 1099–1120 (1983). 32. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004). 33. X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, Jr., and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004). 34. R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004). 35. S. J. Boehm, L. Lin, K. Guzmán Betancourt, R. Emery, J. S. Mayer, T. S. Mayer, and C. D. Keating, “Formation and frequency response of two-dimensional nanowire lattices in an applied electric field,” Langmuir 31(21), 5779–5786 (2015). 36. A.-P. Hynninen and M. Dijkstra, “Phase diagram of dipolar hard and soft spheres: manipulation of colloidal crystal structures by an external field,” Phys. Rev. Lett. 94(13), 138303 (2005). 37. A. S. Potemkin, A. N. Poddubny, P. A. Belov, and Y. S. Kivshar, “Green function for hyperbolic media,” Phys. Rev. A 86(2), 023848 (2012). 38. M. G. Silveirinha, “Nonlocal homogenization model for a periodic array of epsilon-negative rods,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(4), 046612 (2006). 39. T. Geng, S. Zhuang, J. Gao, and X. Yang, “Nonlocal effective medium approximation for metallic nanorod metamaterials,” Phys. Rev. B 91(24), 245128 (2015).

#256447 © 2016 OSA


40. 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). 41. O. D. Miller, W. Qiu, J. D. Joannopoulos, and S. G. Johnson, “Comment on” A self-assembled threedimensional cloak in the visible” in Scientific Reports 3, 2328,” arXiv preprint arXiv:1310.1503 (2013). 42. A. S. Shalin, P. Ginzburg, A. A. Orlov, I. Iorsh, P. A. Belov, Y. S. Kivshar, and A. V. Zayats, “Scattering suppression from arbitrary objects in spatially dispersive layered metamaterials,” Phys. Rev. B 91(12), 125426 (2015). 43. X. Zhang and Y. Wu, “Effective medium theory for anisotropic metamaterials,” Sci. Rep. 5, 7892 (2015). 44. A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013). 45. Y. He, H. Deng, X. Jiao, S. He, J. Gao, and X. Yang, “Infrared perfect absorber based on nanowire metamaterial cavities,” Opt. Lett. 38(7), 1179–1181 (2013). 46. B. M. van der Zande, G. J. Koper, and H. N. Lekkerkerker, “Alignment of rod-shaped gold particles by electric fields,” J. Phys. Chem. B 103(28), 5754–5760 (1999). 47. O. Levy, “Dielectric response and electro-optical effects in suspensions of anisotropic particles,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(1), 011404 (2002).

1. Introduction Electromagnetic metamaterials open a door for people to control the electromagnetic wave as they desired. Up to now, many kinds of metamaterials that can reflect, bend, or absorb wave have been fabricated [1–4]. Metamaterial cloak is one of the most important metamaterial systems because of its unique property, i.e. it can control the scattering from an object illuminated by an external wave to make the object invisible to the external electromagnetic probe [5–8]. Several kinds of metamaterial cloaks based on transformation optics and quasi– conformal mapping techniques have been demonstrated theoretically and experimentally from microwave to optical frequencies [9–11]. However, realization of these cloaks always needs extremely refractive index in some region of the cloak, which makes the cloak very difficult to fabricate. In addition, difficulties in the fabrication of solid metamaterials constantly increase with the decrease of unit sizes in order to be satisfied with higher frequency response. Another interesting method to obtain cloak effect is to cancel the scattering from a sub-wavelength spherical scattering object by coating a shell of metallic nanoparticles onto the object [12–17]. However, it needs to carefully design the radius ratio and the permittivity of the core and shell. Recently, a new kind of metamaterial cloak based on uniaxial epsilonnear-zero (ENZ) medium has been proposed [18–20]. ENZ medium is kind of metamaterial whose real part of permittivity is near zero, and possess many unique transmission properties, such as no phase advancement propagation to a wave with certain polarization, no GoosHänchen effect for p polarized light, squeezing and tunneling effects through a narrow junction area filled with ENZ materials between two waveguides [21–24]. Some ENZ metamaterials have been fabricated either by metal-dielectric layered structure [25] or by vertically aligned array of metal rods [26]. However, the ENZ region in these structures is very narrow. The layered metal-dielectric structure also has a strong dependence on the polarization of incident wave. What’s more, they are all solid matter, and once they have been fabricated, the structure can’t be further changed or adjusted. Thus, the response of the ENZ metaterials is fixed, that is to say the ENZ metamaterials are lack of flexibility and tunability. In this paper, we propose a soft optical cloak based on a fluid system, which can achieve a nearly perfect suppression of scattering from arbitrary-shaped objects in the fluid under an external electric field stimulus. This fluid system is composed of gold nanorods in insulating liquid. Without an external electric field, the gold nanorods are randomly distributed and the permittivity of fluid is isotropic and, as a result, the scattering from objects in the fluid cannot be suppressed. With an external electric field, the gold nanorods orientate along the direction of external electric field and, as a result, the permittivity of the fluid system becomes anisotropic. At a certain frequency range, the real part of the permittivity along the direction of external electric field or the optical axis of the fluid is near zero, i.e. the fluid system becomes an ENZ medium at this frequency. We numerically demonstrate that nearly perfect

#256447 © 2016 OSA


suppression of scattering from arbitrary-shaped objects in the ENZ fluid achieved. The loss and aspect ratio of gold nanorods have an effect on the scattering suppression behavior. In addition, the permittivity of fluid can external electric field strength and, as a result, the ENZ state and scattering objects can be controlled.

system can be ENZ point and be adjusted by suppression for

2. Design and simulation results The proposed soft optical cloak is a fluid system composed of gold nanorods in insulating liquid. Here, the liquid can select silicone oil because it is often used as liquid medium in electro-responsive fluids [27,28]. Silicone oil is not only a good transparent dispersant for gold nanorods due to low surface energy but also a good medium for applying an external electric field to orientate nanorods due to low dielectric constant and high electrically insulating property. Besides electric properties, the viscosity of silicone oil is also important because it has an effect on the rotation rate of nanorods under external electric field [29]. Too high viscosity can enhance the dispersion stability but lead to a longer response time of nanorod orientation. In the realistic design, we can employ silicone oil with an appropriate viscosity to ensure rapid response to electric field and good dispersion stability. Meanwhile, the gold nanorods can also be modified by silicane coupling agent to enhance dispersion stability in silicone oil. Without an external electric field, the gold nanorods are randomly distributed in silicone oil and the fluid is isotropic [as shown in Fig. 1(a)], and its permittivity (ε xx = ε yy = ε zz = ε iso ) can be derived from Maxwell-Garnett type effective medium theory (EMT) [30]:

ε iso

εg − εd p  3 i =⊥ , ⊥, ε d + N i (ε g − ε d ) = ε d [1 + ]. (ε g − ε d ) N i p 1 −  i =⊥ , ⊥, 3 ε d + N i (ε g − ε d )

(1)

where p is the volume fraction of gold nanorods in fluid, N ⊥ and N are the depolarization factors of the gold nanorods in the direction of perpendicular and parallel to long-axis of the nanorods, respectively. N ⊥ and N are related to the aspect ratio of the gold nanorods and satisfy a simple geometric rule, 2 N ⊥ + N = 1 . In our design, we employ sufficiently long

gold nanorods, i.e. the depolarization factor of the gold nanorods along the direction of external electric field is N ~0. ε d is the relative permittivity of silicone oil and it is set as ε d

= 2.13. ε g is the relative permittivity of gold nanorods, which can be approximately obtained from Drude model, ε g = 1 − ωp2 / (ω 2 + iνω ) with plasma frequency ωp = 2π × 2.175 × 1015 s−1

and collision frequency ν = 2π × 6.5 × 1012 s−1 [31]. Owing to the presence of surface scattering and grain boundary, the gold nanorods are likely to have a higher scattering loss than that of bulk gold. Here, to simply describe the loss of gold nanorods, we use a collision frequency value that is three times as large as that in bulk as Ref [32]. did. The calculated effective permittivity ( ε iso ) of fluid system as a function of incident frequency for p = 0.080 are shown in Fig. 1(b). It can be found that the isotropic permittivity is ε iso = 1.73 + 0.03i in wide frequency region, indicating that the optical property of the fluid system in isotropic phase is similar to an ordinary dielectric system. We use COMSOL Multiphysics 4.4 software based on the finite element method to simulate the distribution of electric field component of incident wave (Ex) when a large perfect electric conductor (PEC) with the diameter = 720 nm is placed in the fluid system as model scattering object at 474 THz as shown in Fig. 1(c). In #256447 © 2016 OSA


the simulation, a homogenous medium with calculated permittivity above represents the fluid system and the magnetic field component of the incident optical wave is along y axis. As shown by the distribution of Ex in Fig. 1(c), a strong scattering from PEC object occurs in the case of gold nanorods dispersed in fluid randomly.

Fig. 1. (a) The schematic structure of proposed fluid system containing gold nanorods without an external electric field; (b) The calculated effective permittivity of the fluid system when the gold nanorods is randomly dispersed; (c) The distribution of Ex when a PEC scattering object placed in the fluid at 474 THz based on EMT simulation.

When an external electric field is applied, the long-axis of gold nanorods starts to orientate along the direction of external electric field. Meanwhile, the fluid tends to transform from isotropic medium into anisotropic one as shown by the scheme in Fig. 2(a). We set the direction of external electric field along z axis and, thus, the permittivity of the fluid system can be described as ε xx = ε yy = ε ⊥ , ε zz = ε . The permittivity of the fluid system can be calculated as [30]:

ε ⊥ , = ε d [1 +

p (ε g − ε d )

ε d + N ⊥, (1 − p )(ε g − ε d )

].

(2)

As shown in Fig. 2(b), the real part of ε changes from negative to positive as the incident frequency increases, and the ENZ point is around 474 THz. Thus, for a TM polarized incident optical wave, the isofrequency contour of the system at frequency below the ENZ point has hyperbolic shape. While at higher frequency, the dispersion is elliptic. At the ENZ point, the isofrequency by EMT calculation will be a strongly prolate spheroid due to the finite losses in gold nanorods. Due to the unique dispersion relation at ENZ point, we can manipulate the scattering wave from arbitrary-shaped objects in the orientated fluid system. In order to verify the effectiveness of EMT, we also calculate permittivity through retrieval method applied to realistic geometry of gold nanorod [33]. In the simulation, we simplify the gold nanorod as a cylinder with radius r = 9 nm and length l = 160 nm. The unit cell used in retrieval method is shown in Fig. 2(c), the lattice constant along x and y direction is 50 nm, along z direction is 180 nm. Figure 2(d) shows the typical effective permittivity along z axis through retrieval method applied to realistic geometry of gold nanorods because the ENZ property depends on the permittivity along z axis. It is found that the value of calculated permittivity through

#256447 © 2016 OSA


retrieval method basically agrees with the EMT results. The small ups and downs around 500 THz in Fig. 2(d) may be resulted from the resonance induced by the periodic structure.

Fig. 2. (a) The schematic structure of proposed fluid system containing gold nanorods with an external electric field applied along z axis; (b) The calculated effective permittivity of the fluid system when the gold nanorods orientate along the direction of external electric field; (c) The unit cell used in retrieval method; (d) The calculated effective permittivity along z axis through retrieval method.

Since the scattering pattern from scattering object can be regarded as a dipolar term, to investigate the scattering of electromagnetic wave by an arbitrary object in the orientated fluid system at ENZ point, we first study the dipole radiation in the fluid. We simulate the distribution of Ex when a vertically polarized dipole (x-oriented) is placed inside the fluid at 400 THz, 474 THz and 540 THz. Figures 3(a)-3(c) show the distribution of Ex based on EMT simulation. In the simulation, we take a homogenous medium with permittivity calculated above as the system and perfect matched layers are employed around the simulation domain. It is found that, due to the strong influence of electromagnetic environment on dipole radiation patterns, the wave front is markedly different when the incident frequency is in the hyperbolic, elliptic, and ENZ regimes. The wave front is apparently curved in the hyperbolic regime [shown in Fig. 3(a)] and in the elliptic regime [shown in Fig. 3(c)]. But in the ENZ regime, the dispersion near the ENZ frequency makes the wave front flat [shown in Fig. 3(b)], indicating that the scattering wave from the object in the fluid can be converted to a plane wave. The result also agrees with the theoretical result of a plane-wave from a source placed in an ENZ material in other reports [23,34]. Figures 3(d)-3(f) show the corresponding distribution of Ex based on 3D finite element simulation. Here, we arrange the gold nanorods in rectangular lattice to represent the uniform chain-like structure of gold nanorods in the fluid under external electric field and thus simplify the simulation. In fact, the arranged structure of particle suspension under electric field depends on particle volume fraction. The particles tend to arrange in chain-like structure at low volume fraction, while the particles tend to arrange in body centered tetragonal or hexagonal lattice at high volume fraction [35,36]. When the size and spacing distance of nanorods or the size of position defects are much smaller than the wavelength, however, the effective medium theory will be valid and thus the arranged form of nanorods will not significantly influence the optical property [4,37]. So the cloak effect will still exist when the nanorods are not arranged in a strictly rectangular lattice, only if the size and spacing distance of nanorods are much smaller than the wavelength. In the simulation, the

#256447 © 2016 OSA


small difference in volume fraction is induced by the nonlocal effect, which resulted from dramatically changes of optical properties of systems [38,39]. We set a magnetic current along y axis as wave source to provide a cylindrical wave. As shown in Figs. 3(d)-3(f), the wave front at different incident frequency is identical compared to the result based on EMT simulation. The flat wave front of radiation dipole in ENZ regime implies that the scattering wave of object in the fluid will have the same wave front as the incident wave.

Fig. 3. The distribution of Ex based on EMT simulation when a vertically polarized dipole is placed inside fluid at 400 THz (a), 474 THz (b), and 540 THz (c); The distribution of Ex based on 3D finite element simulation when a vertically polarized dipole is placed inside fluid at 400 THz (d), 474 THz (e), and 540 THz (f). The white cone represents the power flow and both sides of the fluid are set as air.

Based on the analysis above, we further simulate the distribution of Ex when the PEC scattering object with different shape is placed in the orientated fluid system as shown in Fig. 4. In the simulation, the periodic boundary conditions are imposed in x direction and a TM wave is normal incident along z axis at frequency of 474 THz. Figures 4(a), 4(d) and 4(e) are the result based on EMT simulation and Figs. 4(b), 4(d) and 4(f) are the corresponding result of 3D finite element simulation. We can find that the wave front of transmission wave remains flat and uniform for the scattering object with different shape. It indicates that the cloak effect mainly results from the dispersion relation in the ENZ regime of fluid rather than the details of defects. Compared to the distribution of Ex of transmission wave based on EMT simulation, however, the transmission based on 3D finite element simulation is slightly lower. This may be caused by the additional wave due to the nonlocal effect in the composite metamaterial, which is not considered in the homogenous medium based on EMT simulation. But the nonlocal effect has little influence on the plane wave front due to the loss of gold nanorods [40]. To evaluate the cloaking performance, we further calculate the scattering cross-section of the object placed in the fluid system with EMT in the case of cloak off and cloak on [41]. The case of cloak off means the fluid system is in isotropic state without external electric field, while the case of cloak on means the fluid system in anisotropic state with electric field. Due to no heat loss in the PEC object, we ignore the absorption crosssection and only calculate the scattering cross-section. As shown in Figs. 4(c), 4(f) and 4(g), the scattering cross section of the object at ENZ point in the case of cloak on is clearly lower than that in the case of cloak off. But it is also noted that the cloak effect declines when the square object is placed in the fluid system and this may be attributed to the decreased transmittance in the presence of the object with sharp edges [18]. In addition, it is worthy to point out that the distribution of applied external electric field E0 around PEC object is not

#256447 © 2016 OSA


uniform in the real fluid system and, thus, the orientation and distribution of gold nanorods around PEC scattering object are not uniform. In the simulation, however, we ignore the locally non-uniform distribution of gold nanorods around PEC scattering object because the local disorder of the gold nanorods have little influence on the whole effective permittivity of the fluid system and cloak effect.

Fig. 4. The distribution of Ex based on EMT simulation (a, d, g) and 3D finite element simulation (b, e, h) and scattering cross-section (c, f, i) when different shape of PEC object is placed in the fluid: a PEC cycle object with diameter 720 nm (a, b, c), a PEC square object with side length 720 nm (d, e, f), and a PEC equilateral triangle object with side length 720 nm (g, h, i).

In fact, the PEC material is not easy to get at optical frequency. Here, we use it mainly because it is often used as a model scattering object in simulation study [19]. If the PEC object is replaced by a common dielectric object, the cloak effect is not affected as shown in Figs. 5(a) and 5(b). This is attributed to the fact that the cloak effect mainly results from the ENZ property of the fluid system rather than the details of the object. On the other hand, because the cloak effect in our system is resulted from the dispersion of the background, for scattering of a non-electrically small object in anisotropic ENZ medium, the scattering wave in the system is converted into evanescent wave in the forward and backward directions, and only capable of transferring energy flux in the perpendicular direction. Thus, the designed cloak can also hide a non-electrically small object. Figures 5(c) and 5(d) show the distribution of Ex based on EMT simulation and 3D finite element simulation when a non-electrically small object with the diameter d = 360 nm placed in the fluid system. It is found that the cloak effect is well remained. Therefore, the clock effect of the proposed fluid system is not only effective for a PEC object but also effective for a common dielectric object. Besides flexible clock application, the proposed fluid system may be potential for other applications such as smart optical window that can transform from half-transparent to full-transparent by suppressing the scattering of object particles with external electric field stimuli.

#256447 © 2016 OSA


Fig. 5. The distribution of Ex based on EMT simulation (a) and 3D finite element simulation (b) when a common dielectric object with ε = 3.0 placed in the fluid system; The distribution of Ex based on EMT simulation (c) and 3D finite element simulation (d) when a non-electrically small object with the diameter d = 360 nm placed in the fluid system.

In addition, compared to the ENZ medium made of metal-dielectric layered structure [19,25], the present proposed fluid system has a tolerance to the polarization of incident wave due to the symmetry of the distribution of the gold nanorods in x-y plane under external electric field stimuli. Figure 6 shows the EMT simulation result of the electric field distribution in the fluid containing a PEC scattering sphere with diameter 720 nm when the electric field component of incident wave is along x axis and y axis, respectively. It is found that the scattering of the PEC sphere is suppressed and the transmission wave remains flat and uniform, no matter which the incident wave polarization direction is. This tolerance to the polarization of incident wave is favor of designing polarization independent metamaterial cloak.

Fig. 6. The electric field distribution when electric field component of incident wave is along x axis (a) and y axis (b) based on EMT simulation. Coordinate unit is micron.

3. Discussions

3.1 Influence of loss of nanorods It is noted that the gold nanorod fluid system is adequately described by the local dielectric function, since the contribution of nonlocality of permittivity is suppressed by the relatively large losses. When the loss of the fluid system is too high, however, it will not only reduce the transmission but also affect the wave front. According to other reports [18,37,42,43], the effective medium theory is valid when the size and spacing of nanorods are much smaller than the wavelength. Thus, when an electric dipole oriented in the x direction in a uniaxial anisotropic medium, the scattered electric field can be described as [37, 44]

#256447 © 2016 OSA


Ex =

H 0(1) ( k0 re ) x 2ε zz + z 2ε xx [k0 re H 0(1) ( k0 re ) − H1(1) ( k0 re )] k0 re3 ε xx

.

(3)

(1) are the Hankel where re = (z 2ε xx + x 2ε zz )1/ 2 , k0 is the wave number in vacuum, H 0,1

functions of the first kind. When the loss of fluid system is small, both of the real part and imaginary part of ε zz are close to zero in the ENZ regime. Thus, Eq. (3) can be simplified by using asymptotic Hankel functions for large |z| as [19] Ex ≈

i −1

eik0 z

ε xx

ε xxπ (k0 z ε xx )1/ 2

.

(4)

It indicates that the scattering wave is a plane wave. However, when the loss of fluid system is sufficiently large, i.e. the imaginary part of ε zz is sufficiently large, there is an electric field along x axis will be excited according to Eq. (4). The scattered field is no longer a plane wave, and become a cylindrical wave. We simulate the distribution of Ex in the fluid system based on EMT when the imaginary part of ε zz is set as different values at 474 THz. As shown in Fig. 7, the radiation pattern is gradually approach to a cylindrical wave as the imaginary part increases. The scattering wave front is curved even if the incident frequency is at ENZ point. Therefore, the loss of nanorods should be suitable in order to reduce the influence to the wave front. In experiments, the loss of gold nanorods can be controlled by changing the surface roughness of nanorods [45].

Fig. 7. The distribution of Ex based on EMT simulation when a vertically polarized dipole is placed in the fluid at 474 THz and the imaginary part of ε zz is set as 0.5i (a), 1i (b), 2.5i (c), and 5i (d).

3.2 Realization of ENZ cloak at multi-frequency According to Eq. (2), the permittivity in the fluid system under external electric field stimuli has a dependence on the depolarization factor of the gold nanorods, i.e. the aspect ratio of gold nanorods. This gives us a chance to realize an ENZ metamaterial with multi frequency response when different aspect ratio of gold nanorods is employed. The effective permittivity along the optical axis for the orientated fluid containing nanorods with different aspect ratio can be calculated by Eq. (5) [30]: #256447 © 2016 OSA


ε = ε d [1 +



4

pi (ε g − ε d )

ε d + N i (ε g − ε d ) ]. pi (ε g − ε d ) N i 4 1 −  i =1 ε d + N i (ε g − ε d ) i =1

(5)

where pi is the corresponding volume fraction of each kind of nanorods. Figure 8(a) shows the calculated effective permittivity along the optical axis ( ε ) for the fluid containing gold nanorods with depolarization factors of 0, 0.05, 0.10 and 0.20. The corresponding volume fraction of each kind of gold nanorods is 0.07, 0.01, 0.01, 0.01, respectively. As shown in Fig. 7(a), in the fluid containing different of aspect ratio of gold nanorods, there are three ENZ points located at 409 THz, 482 THz and 538 THz, respectively. The distributions of Ex when a PEC object placed in the fluid system are depicted in Figs. 8(b)-8(d). We can find that the suppression of scattering from PEC object can be well realized at 408 THz and 538 THz. But the scattering suppression or cloak effect failures at 482 THz. According to the calculated ε in Fig. 7(a), this can be attributed to the fact that the imaginary part of becomes too large due to the longitudinal plasmon resonance of gold nanorods [40].

Fig. 8. (a) The calculated effective permittivity of the fluid system containing gold nanorods with different depolarization factors; (b-d) The distribution of Ex when a PEC object placed in the fluid system containing gold nanorods with different depolarization factors at 409 THz (b), 482 THz (c), and 538 THz (d).

3.3 Influence of applied external electric field The orientation of gold nanorods in the fluid depends on the strength of applied external electric field. As the strength of applied electric field increases, the gold nanorods will gradually orient along the direction of applied electric fields and become order [46,47]. The order parameter of the gold nanorods can be defined as: S=

1 (3 < cos 2 θ > −1). 2

(6)

where θ is the orientation angle between the principal axis of gold nanorods and the direction of applied external electric fields. When the applied external electric field is zero, the orientation of gold nanorods is random. In this case, < cos 2 θ >= 1 / 3 and the order parameter S = 0. When a sufficiently large external electric field is applied, all the nanorods are oriented with their principal axis parallel to the direction of external electric field. In this case, < cos 2 θ >= 1 and the order parameter S = 1. At intermediate situations, S is determined by a thermal average of the electrostatic energy that seeks to orient the particles in the direction of applied external electric field. The electrostatic energy of a single gold nanorod is

#256447 © 2016 OSA


1 U = − Δα E 2 cos 2 θ . 2

(7)

where Δα is the anisotropy in electric polarizability, E is applied external electric field. Because the conductivity and permittivity of gold nanorods are much higher than those of the insulating liquid medium at a low-frequency external electrical field, we can regard Δα as Δα = ε 0ε dπ lr 2 ( N ⊥ − N ) / ( N ⊥ N ) , where ε 0 is the permittivity of vacuum. Then we can obtain U

< cos θ >= 2

exp(− k T ) cos

2

θ dΩ

B

exp(−

U )dΩ kBT

.

(8)

where kB is the Boltzmann constant, T is the ambient temperature and Ω is solid angle. With parameters T = 300 K , N = 0.02 , r = 9 nm and l = 160 nm, we can get the order parameter S as a function of the strength of applied external electric field, as shown in Fig. 9(a). At intermediate situations, the polarization of the nanorods is anisotropic and can be expressed by 1 2

α xx = α yy = [α + α ⊥ − (α − α ⊥ < cos 2 θ > )].

(9a)

α zz = α ⊥ + (α − α ⊥ ) < cos 2 θ > .

(9b)

1 2

κ xx = κ yy = [κ + κ ⊥ − (κ − κ ⊥ < cos 2 θ >)].

(9c)

κ zz = κ ⊥ + (κ − κ ⊥ ) < cos 2 θ > .

(9d)

where κ , ⊥ = ε d / [ε d + N, ⊥ ( ε g − ε d )] and α , ⊥ = κ , ⊥ ( ε g − ε d ) . Thus, the permittivity of fluid at intermediate situations can be expressed by the following Eq. (10) based on the orientation angle dependent EMT [47]:

ε zz,xx = ε d +

pα xx,zz

1 − p + pκ zz,xx

.

(10)

According to Eq. (10), we can predict the permittivity of the fluid as a function of the strength of applied external electric field, as shown in Fig. 9(b). It can be found that the permittivity of fluid gradually changes from isotropic to anisotropic as the strength of applied external electric field increases. Finally, the fluid becomes a uniaxial ENZ medium when the applied electric field strength exceeds about 4V / μm . Thus, the permittivity of the fluid system can be adjusted by tuning the strength of applied electric field. Based on the calculated permittivity under different applied electric strength, we further simulate the distribution of Ex of incident wave at 474 THz when a PEC object placed in the fluid when it is subjected to 0, 1.5, and 4 V / μm of external electric fields. As shown in Figs. 9(d)-9(f), the transmission wave front gradually change flat and uniform as the strength of applied electric field increases, in other words, the scattering object gradually becomes invisible and clock effect is achieved.

#256447 © 2016 OSA


Fig. 9. (a) The dependence of order parameter S on the strength of external electric field; (b) The dependence of effective permittivity of fluid system on the strength of external electric field; (c-e) The distribution of Ex at 474 THz when a PEC object placed in the fluid system which is subjected to different strength of external electric field: 0 V/μm (c), 1.5 V/μm (d), and 4 V/μm (e).

4. Conclusions

In conclusion, we have designed a soft optical cloak based on gold nanorods dispersed in insulating liquid. Under an external electric field stimulus, the fluid can transform from isotropic to anisotropic epsilon-near-zero state at a certain incident optical frequency due to the orientation of gold nanorods. Both effective medium theory and 3D finite element simulations demonstrate that, at the epsilon-near-zero point, the scattering from arbitraryshaped objects can be nearly perfect suppressed. The loss of gold nanorods has an effect on the epsilon-near-zero point and scattering suppression behavior. The loss of nanorods should be suitable because too large loss easily makes the scattering field transform from a plane wave into a cylindrical wave. The aspect ratio of gold nanorods also has an effect on the epsilon-near-zero point and scattering suppression behavior due to the difference of depolarization factor of different aspect ratio of gold nanorods. When the fluid contains different aspect ratio of gold nanorods, it has multi epsilon-near-zero points and exhibits perfect suppression of scattering from arbitrary-shaped objects at multiple optical frequencies. The orientation of gold nanorods in the fluid depends on the strength of the applied external electric field and, as a result, the permittivity and the optical property of the system can be adjusted by external electric field. Thus, the epsilon-near-zero state and scattering suppression for object can be controlled by adjusting external electric field strength. The flexible, switchable, and multi-frequency responsive characteristics make the fluid-based optical cloak be a good candidate for the development of soft smart clock applications. Acknowledgments

This work is supported by the National Natural Science Foundation of China (no. 51272214), Program for New Century Excellent Talents in University of China (no. NCET-10–0081).

#256447 © 2016 OSA
