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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. 8 — Sep. 4, 2013
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Nanoscale dielectric-graphene-dielectric tunable infrared waveguide with ultrahigh refractive indices

Bofeng Zhu, Guobin Ren, Siwen Zheng, Zhen Lin, and Shuisheng Jian  »View Author Affiliations


Optics Express, Vol. 21, Issue 14, pp. 17089-17096 (2013)
http://dx.doi.org/10.1364/OE.21.017089


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Abstract

We propose in this paper a dielectric-graphene-dielectric tunable infrared waveguide based on multilayer metamaterials with ultrahigh refractive indices. The waveguide modes with different orders are systematically analyzed with numerical simulations based on both multilayer structures and effective medium approach. The waveguide shows hyperbolic dispersion properties from mid-infrared to far-infrared wavelength, which means the modes with ultrahigh mode indices could be supported in the waveguide. Furthermore, the optical properties of the waveguide modes could be tuned by the biased voltages on graphene layers. The waveguide may have various promising applications in the quantum cascade lasers and bio-sensing.

© 2013 OSA

1. Introduction

Metamaterials are artificially structured materials that can be composed of dielectric elements or structured metallic with unconventional electromagnetic properties, which have demonstrated potential in various applications, such as left-handed behavior [1

1. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004). [CrossRef] [PubMed]

] and the cloaking [2

2. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [CrossRef] [PubMed]

]. In recent years, indefinite metamaterial with hyperbolic dispersion has been proposed [3

3. Y. Liu, G. Bartal, and X. Zhang, “All-angle negative refraction and imaging in a bulk medium made of metallic nanowires in the visible region,” Opt. Express 16(20), 15439–15448 (2008). [CrossRef] [PubMed]

]. The hyperbolic dispersion eliminates the cut off of large wave vectors, modes with ultrahigh refractive indices could propagate along the waveguide. The capability has been applied on the nanoscale waveguides [4

4. Y. He, S. He, J. Gao, and X. Yang, “Nanoscale metamaterial optical waveguides with ultrahigh refractive indices,” J. Opt. Soc. Am. B 29(9), 2559–2566 (2012). [CrossRef]

, 5

5. F. Y. Meng, Q. Wu, and L. W. Li, “Transmission characteristics of wave modes in a rectangular waveguide filled with anisotropic metamaterial,” Appl. Phys., A Mater. Sci. Process. 94(4), 747–753 (2009). [CrossRef]

] and optical cavities [6

6. X. Yang, J. Yao, J. Rho, X. Yin, and X. Zhang, “Experimental realization of three-dimensional indefinite cavities at the nanoscale with anomalous scaling laws,” Nat. Photonics 6(7), 450–454 (2012). [CrossRef]

].

Graphene, a two-dimensional form of carbon in which the atoms are arranged in a honeycomb lattice [7

7. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004). [CrossRef] [PubMed]

, 8

8. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005). [CrossRef] [PubMed]

], which has been emerged as an alternative material in optical devices and optical optoelectronic applications [9

9. A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012). [CrossRef]

]. Recently, the hyperbolic metamaterial with graphene-dielectric multilayers has been studied by I. V. Iorsh et al. [10

10. F. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B 87(7), 075416 (2013). [CrossRef]

] and M. K. Othman et al. [11

11. M. A. K. Othman, C. Guclu, and F. Capolino, “Graphene-based tunable hyperbolic metamaterials and enhanced near-field absorption,” Opt. Express 21(6), 7614–7632 (2013). [CrossRef] [PubMed]

]. The hyperbolic dispersion characteristics of this stacked structure are investigated at a temperature of 4 K and 300 K, respectively.

In principle, any inductive infinitesimally-thin layer with negative permittivity could be fabricated between dielectric layers to realize hyperbolic metamaterial. However, thin metal layers would suffer from high metallic losses and the spatial and frequency dispersion introduced by periodically patterned conductive layers [11

11. M. A. K. Othman, C. Guclu, and F. Capolino, “Graphene-based tunable hyperbolic metamaterials and enhanced near-field absorption,” Opt. Express 21(6), 7614–7632 (2013). [CrossRef] [PubMed]

], which may greatly restrict the application of the hyperbolic metamaterials. Recently, heavily doped oxide semiconductors have been shown to exhibit both negative real permittivity and relatively small losses at near- and mid-infrared frequencies. G. V. Naik et al. have shown a high-performance hyperbolic metamaterial formed by Al:ZnO and ZnO as the metallic and dielectric components [12

12. G. V. Naik, J. Liu, A. V. Kildishev, V. M. Shalaev, and A. Boltasseva, “Demonstration of Al:ZnO as a plasmonic component for near-infrared metamaterials,” Proc. Natl. Acad. Sci. U.S.A. 109(23), 8834–8838 (2012). [CrossRef] [PubMed]

]. And the transparent conducting oxides (TCOs) could outperform conventional metals in hyperbolic metamaterials in near-infrared frequencies [13

13. G. V. Naik and A. Boltasseva, “A comparative study of semiconductor-based plasmonic metamaterials,” Metamaterials (Amst.) 5(1), 1–7 (2011). [CrossRef]

]. C. Rizza et al. have proposed a hyperbolic metamaterial made of alternating semiconductor and dielectric layers [14

14. C. Rizza, A. Ciattoni, E. Spinozzi, and L. Columbo, “Terahertz active spatial filtering through optically tunable hyperbolic metamaterials,” Opt. Lett. 37(16), 3345–3347 (2012). [CrossRef] [PubMed]

].

The graphene could be treated as a layer of thin metal at THz frequencies. Since the real part of the conductivity (determining the attenuation) of graphene is remarkably small compared with noble metal (e.g. Gold and Silver), which may possess desirable performance on the waveguide modes losses at THz frequencies. What is more, the conductivity of the graphene could be tuned by varying the chemical potential of the graphene sheets via electrostatic biasing, which may provide a robust and flexible method to tune the dispersion characteristics of the waveguide and the optical properties of the waveguide modes. All of these make graphene a good candidate for realizing the hyperbolic metamaterial designs in the THz range.

Recently, the hyperbolic metamaterials have been investigated to achieve high refractive indices at infrared spectroscopy. M. Choi et al. have investigated a terahertz metamaterial with unnaturally high refractive index [15

15. M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K. Y. Kang, Y. H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011). [CrossRef] [PubMed]

], which could achieve highest index of refraction of 33.22 at a frequency of 0.851 THz. J. Shin et al. have designed three-dimensional isotropic metamaterials which possess an enhanced refractive index between 5.5~7 in the wavelength range from 3 um~6 um [16

16. J. Shin, J. T. Shen, and S. H. Fan, “Three-Dimensional Metamaterials with an Ultrahigh Effective Refractive Index over a Broad Bandwidth,” Phys. Rev. Lett. 102(9), 093903 (2009). [CrossRef] [PubMed]

].

Since nanosacle waveguides are critical devices in many fundamental studies of optical physics and integrate optics, waveguides based on hyperbolic metamaterials have been recently investigated [4

4. Y. He, S. He, J. Gao, and X. Yang, “Nanoscale metamaterial optical waveguides with ultrahigh refractive indices,” J. Opt. Soc. Am. B 29(9), 2559–2566 (2012). [CrossRef]

, 5

5. F. Y. Meng, Q. Wu, and L. W. Li, “Transmission characteristics of wave modes in a rectangular waveguide filled with anisotropic metamaterial,” Appl. Phys., A Mater. Sci. Process. 94(4), 747–753 (2009). [CrossRef]

]. Y. He et al. have demonstrated that a hyperbolic metamaterial waveguide could achieve ultrahigh effective refractive index up to 62.0 at near-infrared region [4

4. Y. He, S. He, J. Gao, and X. Yang, “Nanoscale metamaterial optical waveguides with ultrahigh refractive indices,” J. Opt. Soc. Am. B 29(9), 2559–2566 (2012). [CrossRef]

].

In this paper, we propose deep-subwavelength waveguides composed of dielectric-graphene-dielectric multilayer indefinite metamaterials, which support waveguide modes with ultrahigh refractive indices in the mid-infrared and far-infrared frequencies. The optical properties of the modes are investigated by both multilayer structures and the effective medium approach. The dependences of waveguide mode indices and propagation lengths on different mode orders, free-space wavelengths, sizes of waveguide cross and biased voltages on graphene layers are also investigated. Moreover, the mode indices and the propagation lengths could be further adjusted by the biased voltages on graphene layers. The waveguide which supports modes with ultrahigh refractive indices and thus the strong field confinement effect could enhance the light-matter interactions, such as the quantum cascade lasers [17

17. R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002). [CrossRef] [PubMed]

19

19. M. Beck, D. Hofstetter, T. Aellen, J. Faist, U. Oesterle, M. Ilegems, E. Gini, and H. Melchior, “Continuous Wave Operation of a Mid-Infrared Semiconductor Laser at Room Temperature,” Science 295(5553), 301–305 (2002). [CrossRef] [PubMed]

], nonlinear optics and bio-sensing [20

20. R. Soref, “Mid-infrared photonics in silicon and germanium,” Nat. Photonics 4(8), 495–497 (2010). [CrossRef]

].

2. The hyperbolic dielectric-graphene-dielectric multilayer metamaterial

Graphene's complex conductivity (σg=σintra+σinter) could be determined from the Kubo formalisms, the Eq. (1) and Eq. (2) are due to intraband and interband contributions [21

21. C. Xu, Y. Jin, L. Yang, J. Yang, and X. Jiang, “Characteristics of electro-refractive modulating based on Graphene-Oxide-Silicon waveguide,” Opt. Express 20(20), 22398–22405 (2012). [CrossRef] [PubMed]

,22

22. G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008). [CrossRef]

], respectively:
σintra(ω,T,τ,μc)=je2kTBπ2(ωjτ1)[μckBT+2ln(eμc/kBT+1)]
(1)
σinter(ω,T,τ,μc)=je24πln(2|μc|(ωjτ1)2|μc|+(ωjτ1)),
(2)
where ω is the angular frequency, τ is the relaxation time which represents the loss mechanism, e is the charge of the electron, kB is the reduced Planck's constant, T is the temperature and μc is the chemical potential, which can be defined as [21

21. C. Xu, Y. Jin, L. Yang, J. Yang, and X. Jiang, “Characteristics of electro-refractive modulating based on Graphene-Oxide-Silicon waveguide,” Opt. Express 20(20), 22398–22405 (2012). [CrossRef] [PubMed]

]:
|μc|=νFπ|a0(VgVDirac)|,
(3)
where a0 ≈9 × 1016m−1V−1,VDirac and νF represent the voltage offset and the Fermi velocity of Dirac fermions in Graphene, respectively. Expression τ=5×1013scan be considered as the biased voltage Vbiased, which could modify the chemical potential. Moreover, the chemical potential could also be tuned by electric field, magnetic field and chemical doping [23

23. A. Vakil and N. Engheta, “Transformation Optics Using Graphene,” Science 332(6035), 1291–1294 (2011). [CrossRef] [PubMed]

]. It should be noted that, since a factor ρ(E) which represents the density of states per spin per unit cell, has been introduced in the deriving process of Eq. (1) and Eq. (2) [24

24. T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78(8), 085432 (2008). [CrossRef]

], the effect caused by the finite size of the graphene layer has been neglected in our conductivity model, which has also been applied in the design of graphene optical devices, such as the terahertz gate-controlled metamaterials [25

25. S. H. Lee, M. Choi, T. T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012). [CrossRef] [PubMed]

] and the graphene-based modulator [21

21. C. Xu, Y. Jin, L. Yang, J. Yang, and X. Jiang, “Characteristics of electro-refractive modulating based on Graphene-Oxide-Silicon waveguide,” Opt. Express 20(20), 22398–22405 (2012). [CrossRef] [PubMed]

].

In this work, we assume that the environment temperature is fixed at τ=5×1013s, the relaxation time is τ=5×1013s.The conductivity of graphene as functions of free-space wavelength λ0 and the biased voltage Vbiasedare plotted in Figs. 1(a)
Fig. 1 The conductivity of graphene as a function of free-space wavelength λ0 (a) and the biased voltage Vbiased (c). The dependences of the effective permittivity εx, εy and εz. of the multilayer metamaterial on the wavelength λ0 (b) and biased voltage Vbiased (d).
and 1(c), respectively. In Fig. 1(a), the voltages are Vbiased = 1.6 volt and 2.5 volt with the corresponding chemical potentials μc = 0.4 eV and 0.5 eV. And the free-space wavelength is fixed at λ0 = 15 um in Fig. 1(c). As shown in Fig. 1(a), with a fixed Vbiased, the real part of graphene conductivity stays near the universal value, σ0 = πe2/2ћ≈6.085x10−5S/m, and the absolute value of the imaginary part increases with the wavelength. The real part of the conductivity is insensitive to the biased voltage, and the imaginary part decreases as the voltage increases. In Fig. 1(c), the real part stays relative high when the biased voltage is below a well-defined threshold, whereas over this threshold the real part recovers the universal value. For the imaginary part, a positive peak value appears at the threshold voltage.

The multilayer metamaterial waveguide is composed of alternative layers of graphene and dielectric. We choose SiO2 as the dielectric material in our subsequent simulation. The permittivity of the dielectric is εd = 2.2 and the refractive index is nd = 1.48. The period of the structure is a = 20 nm. Each period is constructed with a layer of graphene with thickness ag = 1 nm and the layer of dielectric with thickness ad = 19 nm. The schematic of the waveguide is sketched in Figs. 2(a)
Fig. 2 The schematic of the waveguide. The Lx and Ly represents horizontal and vertical dimensions of the cross section of the waveguide, while Lz is the length of the waveguide.
and 2(b). The Lx and Ly represents horizontal and vertical dimensions of the cross section of the waveguide, while the Lz is the length of the waveguide.

Since the period a is much less than the incident wavelength, the multilayer metamaterial could be treated as a homogeneous effective medium and the anisotropic permittivity sensor could be defined as [4

4. Y. He, S. He, J. Gao, and X. Yang, “Nanoscale metamaterial optical waveguides with ultrahigh refractive indices,” J. Opt. Soc. Am. B 29(9), 2559–2566 (2012). [CrossRef]

,26

26. C. A. Foss, G. L. Hornyak, J. A. Stockert, and C. R. Martin, “Template-synthesized nanoscopic gold Particles: optical spectra and the effects of particle size and shape,” J. Phys. Chem. 98(11), 2963–2971 (1994). [CrossRef]

],
εx=εz=fgεg,t+(1fg)εd,εy=εg,nεdfgεd+(1fg)εg,n,
(4)
where filling factor fg = 0.05, which is the fraction of the multilayer structure period occupied by graphene. The εx, εy and εz represents the permittivity along x, y and z directions. The εd is the permittivity of the dielectric. And the εg,t and εg,n represent the tangential and normal components of the permittivity of the graphene layer, respectively. The εg,t could be derived from the relationship between the relative permittivity and the conductivity [27

27. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007), Chap. 1.

],
εg,t(K,ω)=1iσg(K,ω)ωε0d,
(5)
where d is the thickness of graphene layer. Since the wavelength λ in the metamaterial is significantly longer than all characteristic dimensions, the general formula thus could be simplified as ε(K = 0,ω) = ε(ω). Moreover, it should be considered that the normal electric field cannot excite any current in the graphene sheet, so the normal component of the permittivity of graphene should be εg,n = 1. So in our multilayer metamaterial, the normal component of the effective permittivity εy, which could be derived from Eq. (4), is only depending on the filling factor fg. The calculated real parts of permittivity εx, εy and εz as functions of free-space wavelength λ0 and the biased voltage kx2+kz2εy+ky2εx=k02, are sketched in Figs. 1(b) and 1(d), respectively. In Fig. 1(b), the voltages are kx2+kz2εy+ky2εx=k02, = 1.6 volt and 2.5 volt and the free-space wavelength is fixed at λ0 = 15 um in Fig. 1(d). As shown in Fig. 1(b), when the biased voltage is fixed, the real part of εy stays positive, while the real parts of εx and εz decrease as the wavelength increases. In Fig. 1(d), the curve represents the tangential component of the permittivity shows a similar trend with the imaginary part of conductivity under fixed wavelength, which is shown in Fig. 1(c). It has been shown that the multilayer metamaterial with anisotropic permittivity sensor is equivalent to a uniaxial anisotropic material with dispersion [28

28. J. Yao, X. Yang, X. Yin, G. Bartal, and X. Zhang, “Three-dimensional nanometer-scale optical cavities of indefinite medium,” Proc. Natl. Acad. Sci. U.S.A. 108(28), 11327–11331 (2011). [CrossRef] [PubMed]

]:
kx2+kz2εy+ky2εx=k02,
(6)
where k0 is the free-space wave vector, kx, ky and kz are the wave factors along x, y and z direction, respectively. The corresponding effective refractive indices along different directions thus could be achieved through ki/k0, where ki is one of the three wave factors. As is shown in Figs. 1(b) and 1(d), with capable biased voltage, the permittivity component εx could be negative while the normal component εy is positive, which implies that the dispersion characteristic is hyperbolic type. Furthermore, since the effective permittivity appears as functions of the biased voltages, the dispersion properties of the waveguide could be tuned by adjusting the biased voltages on graphene layers.

For the hyperbolic metamaterial, the permittivity sensor is anisotropic, which means that one component of the permittivity need to be negative. Therefore, the working wavelength of the proposed metamaterial could span from mid-infrared to far-infrared wavelength region, which could be found in Fig. 1(b). What is more, the working wavelength could be pushed to a shorter wavelength simply by adjusting the biased voltages on graphene layers.

3. Dielectric-graphene-dielectric waveguides

The proposed multilayer indefinite waveguide is numerically analyzed with COMSOL MULTIPHYSICS based on finite element method. All materials are nonmagnetic (μr = 1) and the environment is free of external magnetic fields. The biased voltage is Vbiased = 1.6 volt, equivalent to the chemical potential μc = 0.4 eV. We calculate the waveguide mode profiles of different mode orders under the dimensions Lx = 200 nm and Ly = 200 nm with free-space wavelength λ0 = 30 μm. The distribution of field components Ey and Hx for the mode orders (1,my), which are derived from the effective medium approach and the multilayer structures, are illustrated in Figs. 3(a)
Fig. 3 The field distributions of modes with order (1,my), which are calculated from the effective medium approach (a) and the multilayer structure (b). Effective refractive indices along the propagation direction neff,z (c) and the propagation lengths Lm (d) as functions of free-space wavelength λ0. The solid and the dot-dashed lines represent the results calculated from the effective medium approach and the multilayer structure, respectively.
and 3(b).

We could note that, for a specific waveguide mode with order (mx,my), the mx and my represent the distributions of the resonant peaks along x direction and y direction on the cross section. Based on the two methods, we also calculate the effective refractive indices along the propagation direction neff,z and the propagation lengths Lm as functions of free-space wavelength λ0, which are plotted in Figs. 3(c) and 3(d). The solid and the dot-dashed lines represent the results calculated from the effective medium approach and the multilayer structure, respectively. The propagation length Lm is defined as Lm = 1/2Im(kz) = λ0/4πIm(neff,z). As is shown in Fig. 3(c), the modes with a higher my may have larger mode indices. And each mode tends to have a smaller indice at longer wavelength. In Fig. 3(d), we could find that the modes with higher indices tend to have less propagation lengths, and the propagation lengths would increase with the wavelength.

As illustrated in Fig. 3(d), the mode indices derived from the multilayer structure and the effective medium approach agree well for the propagation lengths. While in Fig. 3(c), the differences are obviously concerned with mode orders of the waveguide modes. For higher order modes, there would be more resonant periods of electric (or magnetic) field on the cross section of the waveguide, which are shown in Figs. 3(a) and 3(b). The more periods on the cross section means the less of the graphene-dielectric unit layers in one period, and the effective medium theory would be less precise.

The higher order modes tend to have larger mode indices, while more loss as a consequence of the stronger field confinement effect, we thus only consider the modes with orders (1,my) in the subsequent investigations. Then we calculate the dependences of mode indices and propagation lengths on Lx and Ly. The free-space wavelength is λ0 = 30 um. The Lx or Ly spans from 150 nm to 250 nm, while the other is fixed at 200 nm. The result calculated from the multilayer structure and effective medium approach is shown in Fig. 4
Fig. 4 The dependences of mode indices real(neff,z) (a),(c) and the propagation lengths Lm (b),(d) on the waveguide transparent dimensions Lx and Ly are calculated. The results are calculated from the multilayer structure (a-b) and effective medium approach (c-d), respectively.
.

As shown in Figs. 4(a) and 4(c), the mode indices decrease as Lx or Ly increases. The propagation lengths of all the modes are insensitive to the change of horizontal dimension Lx, while they all increase with the vertical dimension Ly, which are presented in Figs. 4(b) and 4(d). Finally, we demonstrate the optical properties of the waveguide modes could be tuned by adjusting the biased voltages on graphene layers. The dependences of the mode indices of (1,my) modes on the biased voltage are shown in Fig. 5(a)
Fig. 5 The dependences of the mode indices of modes (1, my) (a) and propagation lengths (b) on the biased voltage.
. The propagation lengths as functions of the biased voltage are shown in Fig. 5(b). Here we assume the waveguide cross section is square with L = Lx = Ly = 200 nm and the wavelength is λ0 = 30 um. The biased voltage spans from 0.1 volt to 1.6 volt.

As shown in Fig. 5(a), all the modes tend to have lower mode indices at higher biased voltages. And higher biased voltages lead to less losses, and thus larger propagation lengths, which are shown in Fig. 5(b). Therefore, in our proposed hyperbolic waveguide, the biased voltages on graphene layers could tune not only the dispersion properties of the waveguide, but also the optical properties of the waveguide modes, such as the mode indices and the propagation lengths. The graphene layers could be deposited by chemical vapor deposition (CVD) or by epitaxial growth [29

29. Y. Zou, P. Tassin, T. Koschny, and C. M. Soukoulis, “Interaction between graphene and metamaterials: split rings vs. wire pairs,” Opt. Express 20(11), 12198–12204 (2012). [CrossRef] [PubMed]

]. The dielectric layers (SiO2) could be fabricated by plasma-enhanced chemical vapor deposition (PECVD) [30

30. A. Satta, E. Simoen, T. Clarysse, T. Janssens, A. Benedetti, B. De Jaeger, M. Meuris, and W. Vandervorst, “Diffusion, activation, and recrystallization of boron implanted in preamorphized and crystalline germanium,” Appl. Phys. Lett. 87(17), 172109 (2005). [CrossRef]

, 31

31. M. Björk, J. Knoch, H. Schmid, H. Riel, and W. Riess, “Silicon nanowire tunneling field-effect transistors,” Appl. Phys. Lett. 92(19), 193504 (2008). [CrossRef]

].

4. Conclusion

In this paper, we have proposed a dielectric-graphene-dielectric waveguide based on multilayer metamaterials. The waveguide mode characteristics have been described through the effective medium approach, which agree with the results calculated from the multilayer structure. Numerical simulation has shown that the multilayer metamaterial waveguide, which appears hyperbolic dispersion characteristics in the mid-infrared and far-infrared wavelength region, could support waveguide modes with ultrahigh refractive indices. The waveguide modes indices and the propagation lengths could be further adjusted by the biased voltages on the graphene layers. The dielectric-graphene-dielectric metamaterial waveguide provides a robust and simple method to achieve strong field confinement and ultrahigh mode indices, which has a promising application in the quantum cascade lasers, nonlinear optics and bio-sensing.

Acknowledgment

This work is supported in part by the Major State Basic Research Development Program of China (Grant No. 2010CB328206), the National Natural Science Foundation of China (NSFC) (Grant Nos. 61178008, 61275092), and the Fundamental Research Funds for the Central Universities, China.

References and links

1.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004). [CrossRef] [PubMed]

2.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [CrossRef] [PubMed]

3.

Y. Liu, G. Bartal, and X. Zhang, “All-angle negative refraction and imaging in a bulk medium made of metallic nanowires in the visible region,” Opt. Express 16(20), 15439–15448 (2008). [CrossRef] [PubMed]

4.

Y. He, S. He, J. Gao, and X. Yang, “Nanoscale metamaterial optical waveguides with ultrahigh refractive indices,” J. Opt. Soc. Am. B 29(9), 2559–2566 (2012). [CrossRef]

5.

F. Y. Meng, Q. Wu, and L. W. Li, “Transmission characteristics of wave modes in a rectangular waveguide filled with anisotropic metamaterial,” Appl. Phys., A Mater. Sci. Process. 94(4), 747–753 (2009). [CrossRef]

6.

X. Yang, J. Yao, J. Rho, X. Yin, and X. Zhang, “Experimental realization of three-dimensional indefinite cavities at the nanoscale with anomalous scaling laws,” Nat. Photonics 6(7), 450–454 (2012). [CrossRef]

7.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004). [CrossRef] [PubMed]

8.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005). [CrossRef] [PubMed]

9.

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012). [CrossRef]

10.

F. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B 87(7), 075416 (2013). [CrossRef]

11.

M. A. K. Othman, C. Guclu, and F. Capolino, “Graphene-based tunable hyperbolic metamaterials and enhanced near-field absorption,” Opt. Express 21(6), 7614–7632 (2013). [CrossRef] [PubMed]

12.

G. V. Naik, J. Liu, A. V. Kildishev, V. M. Shalaev, and A. Boltasseva, “Demonstration of Al:ZnO as a plasmonic component for near-infrared metamaterials,” Proc. Natl. Acad. Sci. U.S.A. 109(23), 8834–8838 (2012). [CrossRef] [PubMed]

13.

G. V. Naik and A. Boltasseva, “A comparative study of semiconductor-based plasmonic metamaterials,” Metamaterials (Amst.) 5(1), 1–7 (2011). [CrossRef]

14.

C. Rizza, A. Ciattoni, E. Spinozzi, and L. Columbo, “Terahertz active spatial filtering through optically tunable hyperbolic metamaterials,” Opt. Lett. 37(16), 3345–3347 (2012). [CrossRef] [PubMed]

15.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K. Y. Kang, Y. H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011). [CrossRef] [PubMed]

16.

J. Shin, J. T. Shen, and S. H. Fan, “Three-Dimensional Metamaterials with an Ultrahigh Effective Refractive Index over a Broad Bandwidth,” Phys. Rev. Lett. 102(9), 093903 (2009). [CrossRef] [PubMed]

17.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002). [CrossRef] [PubMed]

18.

R. Colombelli, F. Capasso, C. Gmachl, A. L. Hutchinson, D. L. Sivco, A. Tredicucci, M. C. Wanke, A. M. Sergent, and A. Y. Cho, “Far-infrared surface-plasmon quantum-cascade lasers at 21.5 μm and 24 μm wavelengths,” Appl. Phys. Lett. 78(18), 2620 (2001). [CrossRef]

19.

M. Beck, D. Hofstetter, T. Aellen, J. Faist, U. Oesterle, M. Ilegems, E. Gini, and H. Melchior, “Continuous Wave Operation of a Mid-Infrared Semiconductor Laser at Room Temperature,” Science 295(5553), 301–305 (2002). [CrossRef] [PubMed]

20.

R. Soref, “Mid-infrared photonics in silicon and germanium,” Nat. Photonics 4(8), 495–497 (2010). [CrossRef]

21.

C. Xu, Y. Jin, L. Yang, J. Yang, and X. Jiang, “Characteristics of electro-refractive modulating based on Graphene-Oxide-Silicon waveguide,” Opt. Express 20(20), 22398–22405 (2012). [CrossRef] [PubMed]

22.

G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008). [CrossRef]

23.

A. Vakil and N. Engheta, “Transformation Optics Using Graphene,” Science 332(6035), 1291–1294 (2011). [CrossRef] [PubMed]

24.

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78(8), 085432 (2008). [CrossRef]

25.

S. H. Lee, M. Choi, T. T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012). [CrossRef] [PubMed]

26.

C. A. Foss, G. L. Hornyak, J. A. Stockert, and C. R. Martin, “Template-synthesized nanoscopic gold Particles: optical spectra and the effects of particle size and shape,” J. Phys. Chem. 98(11), 2963–2971 (1994). [CrossRef]

27.

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007), Chap. 1.

28.

J. Yao, X. Yang, X. Yin, G. Bartal, and X. Zhang, “Three-dimensional nanometer-scale optical cavities of indefinite medium,” Proc. Natl. Acad. Sci. U.S.A. 108(28), 11327–11331 (2011). [CrossRef] [PubMed]

29.

Y. Zou, P. Tassin, T. Koschny, and C. M. Soukoulis, “Interaction between graphene and metamaterials: split rings vs. wire pairs,” Opt. Express 20(11), 12198–12204 (2012). [CrossRef] [PubMed]

30.

A. Satta, E. Simoen, T. Clarysse, T. Janssens, A. Benedetti, B. De Jaeger, M. Meuris, and W. Vandervorst, “Diffusion, activation, and recrystallization of boron implanted in preamorphized and crystalline germanium,” Appl. Phys. Lett. 87(17), 172109 (2005). [CrossRef]

31.

M. Björk, J. Knoch, H. Schmid, H. Riel, and W. Riess, “Silicon nanowire tunneling field-effect transistors,” Appl. Phys. Lett. 92(19), 193504 (2008). [CrossRef]

OCIS Codes
(230.7370) Optical devices : Waveguides
(160.3918) Materials : Metamaterials
(310.4165) Thin films : Multilayer design
(310.6628) Thin films : Subwavelength structures, nanostructures

ToC Category:
Metamaterials

History
Original Manuscript: May 14, 2013
Revised Manuscript: June 15, 2013
Manuscript Accepted: June 28, 2013
Published: July 10, 2013

Virtual Issues
Vol. 8, Iss. 8 Virtual Journal for Biomedical Optics

Citation
Bofeng Zhu, Guobin Ren, Siwen Zheng, Zhen Lin, and Shuisheng Jian, "Nanoscale dielectric-graphene-dielectric tunable infrared waveguide with ultrahigh refractive indices," Opt. Express 21, 17089-17096 (2013)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-21-14-17089


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References

  1. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science305(5685), 788–792 (2004). [CrossRef] [PubMed]
  2. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006). [CrossRef] [PubMed]
  3. Y. Liu, G. Bartal, and X. Zhang, “All-angle negative refraction and imaging in a bulk medium made of metallic nanowires in the visible region,” Opt. Express16(20), 15439–15448 (2008). [CrossRef] [PubMed]
  4. Y. He, S. He, J. Gao, and X. Yang, “Nanoscale metamaterial optical waveguides with ultrahigh refractive indices,” J. Opt. Soc. Am. B29(9), 2559–2566 (2012). [CrossRef]
  5. F. Y. Meng, Q. Wu, and L. W. Li, “Transmission characteristics of wave modes in a rectangular waveguide filled with anisotropic metamaterial,” Appl. Phys., A Mater. Sci. Process.94(4), 747–753 (2009). [CrossRef]
  6. X. Yang, J. Yao, J. Rho, X. Yin, and X. Zhang, “Experimental realization of three-dimensional indefinite cavities at the nanoscale with anomalous scaling laws,” Nat. Photonics6(7), 450–454 (2012). [CrossRef]
  7. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science306(5696), 666–669 (2004). [CrossRef] [PubMed]
  8. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature438(7065), 197–200 (2005). [CrossRef] [PubMed]
  9. A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics6(11), 749–758 (2012). [CrossRef]
  10. F. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B87(7), 075416 (2013). [CrossRef]
  11. M. A. K. Othman, C. Guclu, and F. Capolino, “Graphene-based tunable hyperbolic metamaterials and enhanced near-field absorption,” Opt. Express21(6), 7614–7632 (2013). [CrossRef] [PubMed]
  12. G. V. Naik, J. Liu, A. V. Kildishev, V. M. Shalaev, and A. Boltasseva, “Demonstration of Al:ZnO as a plasmonic component for near-infrared metamaterials,” Proc. Natl. Acad. Sci. U.S.A.109(23), 8834–8838 (2012). [CrossRef] [PubMed]
  13. G. V. Naik and A. Boltasseva, “A comparative study of semiconductor-based plasmonic metamaterials,” Metamaterials (Amst.)5(1), 1–7 (2011). [CrossRef]
  14. C. Rizza, A. Ciattoni, E. Spinozzi, and L. Columbo, “Terahertz active spatial filtering through optically tunable hyperbolic metamaterials,” Opt. Lett.37(16), 3345–3347 (2012). [CrossRef] [PubMed]
  15. M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K. Y. Kang, Y. H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature470(7334), 369–373 (2011). [CrossRef] [PubMed]
  16. J. Shin, J. T. Shen, and S. H. Fan, “Three-Dimensional Metamaterials with an Ultrahigh Effective Refractive Index over a Broad Bandwidth,” Phys. Rev. Lett.102(9), 093903 (2009). [CrossRef] [PubMed]
  17. R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature417(6885), 156–159 (2002). [CrossRef] [PubMed]
  18. R. Colombelli, F. Capasso, C. Gmachl, A. L. Hutchinson, D. L. Sivco, A. Tredicucci, M. C. Wanke, A. M. Sergent, and A. Y. Cho, “Far-infrared surface-plasmon quantum-cascade lasers at 21.5 μm and 24 μm wavelengths,” Appl. Phys. Lett.78(18), 2620 (2001). [CrossRef]
  19. M. Beck, D. Hofstetter, T. Aellen, J. Faist, U. Oesterle, M. Ilegems, E. Gini, and H. Melchior, “Continuous Wave Operation of a Mid-Infrared Semiconductor Laser at Room Temperature,” Science295(5553), 301–305 (2002). [CrossRef] [PubMed]
  20. R. Soref, “Mid-infrared photonics in silicon and germanium,” Nat. Photonics4(8), 495–497 (2010). [CrossRef]
  21. C. Xu, Y. Jin, L. Yang, J. Yang, and X. Jiang, “Characteristics of electro-refractive modulating based on Graphene-Oxide-Silicon waveguide,” Opt. Express20(20), 22398–22405 (2012). [CrossRef] [PubMed]
  22. G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys.103(6), 064302 (2008). [CrossRef]
  23. A. Vakil and N. Engheta, “Transformation Optics Using Graphene,” Science332(6035), 1291–1294 (2011). [CrossRef] [PubMed]
  24. T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B78(8), 085432 (2008). [CrossRef]
  25. S. H. Lee, M. Choi, T. T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater.11(11), 936–941 (2012). [CrossRef] [PubMed]
  26. C. A. Foss, G. L. Hornyak, J. A. Stockert, and C. R. Martin, “Template-synthesized nanoscopic gold Particles: optical spectra and the effects of particle size and shape,” J. Phys. Chem.98(11), 2963–2971 (1994). [CrossRef]
  27. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007), Chap. 1.
  28. J. Yao, X. Yang, X. Yin, G. Bartal, and X. Zhang, “Three-dimensional nanometer-scale optical cavities of indefinite medium,” Proc. Natl. Acad. Sci. U.S.A.108(28), 11327–11331 (2011). [CrossRef] [PubMed]
  29. Y. Zou, P. Tassin, T. Koschny, and C. M. Soukoulis, “Interaction between graphene and metamaterials: split rings vs. wire pairs,” Opt. Express20(11), 12198–12204 (2012). [CrossRef] [PubMed]
  30. A. Satta, E. Simoen, T. Clarysse, T. Janssens, A. Benedetti, B. De Jaeger, M. Meuris, and W. Vandervorst, “Diffusion, activation, and recrystallization of boron implanted in preamorphized and crystalline germanium,” Appl. Phys. Lett.87(17), 172109 (2005). [CrossRef]
  31. M. Björk, J. Knoch, H. Schmid, H. Riel, and W. Riess, “Silicon nanowire tunneling field-effect transistors,” Appl. Phys. Lett.92(19), 193504 (2008). [CrossRef]

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