Topological insulator metamaterials with tunable negative refractive index in the optical region
© Cao and Wang; licensee Springer. 2013
Received: 27 October 2013
Accepted: 3 December 2013
Published: 13 December 2013
A blueshift tunable metamaterial (MM) exhibiting a double-negative refractive index based on a topological insulator (bismuth selenide, Bi2Se3) has been demonstrated in the near-infrared (NIR) spectral region. The potential of Bi2Se3 as a dielectric interlayer of the multilayer MM is explored. The optical response of elliptical nanohole arrays penetrating through Au/Bi2Se3/Au films is numerically investigated using the finite difference time domain (FDTD) method. The blueshift tuning range of the MM is as high as 370 nm (from 2,140 to 1,770 nm) after switching the Bi2Se3 between its trigonal and orthorhombic states.
Metamaterials (MMs) are artificially engineered composites that attract considerable interests due to their exceptional electromagnetic properties, which are not typically found in nature, such as negative refractive index and cloaking[1–4]. These MMs with various subwavelength resonant elements have offered magnetic and/or electric resonant responses to incident electromagnetic radiation, scalable from the microwave frequencies up to the terahertz and optical ones[5–7]. Particularly, nanohole resonators embedded in metal-dielectric-metal (MDM) multilayers are frequently used as building blocks of negative-refractive-index MMs[8–11], owing to the coupling between surface plasmons counterpropagating on the two closely spaced interfaces which results in a closed loop of the electric currents. This gives rise to magnetic dipolar resonances between the two coupled metal layers, while the continuous metallic strip parts provide the electric resonance moments[12, 13]. All these features make the nanohole array perforating through MDM films become a strong candidate for developing three-dimensional negative-index MMs[14, 15].
One of the obstacles in this progress is the resonance responses of MMs to the impinge light which are usually fixed once the dimension of the structure is determined, thus making the MMs possess a limited bandwidth. However, for many applications (switching, modulation, filtering, etc.), it would be highly desirable to tune the MM resonances over a wide bandwidth. To this end, tunable photonic MMs, the spectral range of which can be controlled by changing the dielectric environment of the resonator with liquid crystals (LCs)[16–18]; phase transition materials[19, 20]; and optical pumping[21, 22] have been discussed recently. However, the challenge is to develop tunable MDM-MMs in the near-infrared (NIR) regime. It is due to the fact that frequency tunability of the MDM-MM mainly requires for the interlayer dielectric material to possess a tunable effective dielectric constant in the NIR region, hence limiting the choice of the active materials. Here, we take a different approach to actively tune the resonant frequency of the MDM-MMs in the NIR regions by using bismuth selenide (Bi2Se3) as the dielectric layer.
Recently, a rising Dirac material - topological insulators (TIs) - had been intensively researched in condensed matter physics[23, 24]. In analogy to the optoelectronic applications of graphene, a thin layer of TIs has been theoretically predicted to be a promising material for broadband and high-performance optoelectronic devices such as photodetectors, terahertz lasers, waveguides, and transparent electrodes. Among these TIs, Bi2Se3 is a particularly interesting compound due to its relatively large bulk band gap and a simple surface state consisting of a single Dirac cone-like structure[26, 27]. Study of the dielectric function reveals that the optical dielectric constant of Bi2Se3 can be very different for the trigonal and orthorhombic phases in the NIR regime. Bi2Se3 exhibits a number of means through which their dielectric properties can be altered[28–33]. Herein, structural phase transition between trigonal and orthorhombic states, which is achieved by a high pressure and temperature, is proposed and studied as a means to change the intrinsic effective dielectric properties of the MDM-MMs.
Here, we numerically demonstrate a blueshift tunable nanometer-scale MM consisting of an elliptical nanohole array (ENA) embedded in the MDM multilayers where the dielectric core layer is a Bi2Se3 composite. Under a high pressure of 2 to 4.3 Pa at 500°C, Bi2Se3 occurring in trigonal phase undergoes a transition to orthorhombic phase and features a large change in the values of the effective dielectric constant. Accordingly, a massive blueshift of the resonant response (from 2,140 to 1,770 nm) of a Bi2Se3-based MDM-ENA is achieved in the NIR region. Our proposed blueshift tunable negative-index MM provides greater flexibility in the practical application and has a potential of enabling efficient switches and modulators in the NIR region.
After the complex coefficients of transmission and reflection are obtained by the 3D EM Explorer Studio, in which T a is the amplitude and φ a is the phase of the transmission coefficient, and R a is the amplitude and φ ra is the phase of the reflection coefficient, the effective optical parameters can be extracted using the Fresnel formula.
where neff is the effective refractive index, η is the impedance, h is the thickness of the structure, k = ω/c, c is the speed of light, m is an arbitrary integer, and n1 = n3 = 1 since the structure is suspended in a vacuum. The signs of neff and η and the value of m are resolved by the passivity of the metamaterial that requires the signs of the real part of impedance η and imaginary part of effective index neff to be positive, i.e., Real(η) > 0, Imag(neff) > 0 which is consistent with the study described in[39, 40]. We then apply this extraction approach to determine the change in the optical response of the structure when the phase of Bi2Se3 is switched between its trigonal and orthorhombic states.
Results and discussion
Specifically, H for the orthorhombic phase shown in Figure 7b is weaker than the trigonal phase shown in Figure 7a. It depicts that the MM based on orthorhombic phase has a smaller magnetic dipolar moment than the trigonal phase and thus smaller FOM.
Recalling the coupling condition from light to SPP modes, it can be seen that the (1,1) internal resonance of the Au-Bi2Se3-Au trilayer is excited at 2,350 nm associated with the trigonal Bi2Se3 in Figure 8a. This internal SPP resonance blueshifts to 2,010 nm when the trigonal state changes to the orthorhombic state as shown in Figure 8b. We also observe that the two internal (1,1) modes which appear at 2,350 and 2,010 nm in the simple MDM structure do not perfectly match the two absorbance peaks at the resonance wavelengths of 2,140 and 1,770 nm in the multilayer metamaterials for both the trigonal and orthorhombic phases, respectively. This difference is because the dispersion relation of the SPP modes used as matching condition does not include the resonant squares, which cause a resonance shift.
In conclusion, this work numerically demonstrates the tunable optical properties of an ENA perforated through Au/Bi2Se3/Au trilayers. We present that the MDM-ENA can be improved to exhibit a substantial frequency tunability of the intrinsic resonance in the NIR spectral region by selecting Bi2Se3 as the active dielectric material. Particularly, the resonant transmission, reflection, and the effective constitutive parameters of the Bi2Se3-coupled multilayer MM can be massively blueshifted by transiting the phase of the Bi2Se3 film from the trigonal to orthorhombic. This may offer an innovative and practical paradigm for the development of tunable photonic devices. We expect that our results will facilitate further experimental studies of the tunable MMs and make this technique suitable for tuning of plasmon resonance in the optical regime.
We acknowledge the financial support from National Natural Science Foundation of China (grant nos. 61172059, 51302026), PhD Programs Foundation of the Ministry of Education of China (grant no. 20110041120015), Postdoctoral Gathering Project of Liaoning Province (grant no. 2011921008), and The Fundamental Research for the Central University (grant no. DUT12JB01).
- Pendry JB: Negative refraction makes a perfect lens. Phys Rev Lett 2000, 61: 3966–3969.View Article
- Qiu CW, Gao L: Resonant light scattering by small coated nonmagnetic spheres: magnetic resonances, negative refraction and prediction. J Opt Soc Am B 2008, 25: 1728–1737.View Article
- Shalaev VM: Optical negative-index metamaterials. Nat Photonics 2007, 1: 41–48. 10.1038/nphoton.2006.49View Article
- Soukoulis CM, Wegener M: Past achievements and future challenges in the development of three-dimensional photonic metamaterials. Nat Photonics 2011, 5: 523–530.
- Zheludev N: The road ahead for metamaterials. Science 2010, 328: 5582–5583.View Article
- Zhou S, Huang X, Li Q, Xie YM: A study of shape optimization on the metallic nanoparticles for thin-film solar cells. Nanoscale Res Lett 2013, 8: 447. 10.1186/1556-276X-8-447View Article
- Liaw JW, Chen HC, Kuo MK: Plasmonic Fano resonance and dip of Au-SiO2-Au nanomatryoshka. Nanoscale Res Lett 2013, 8: 468. 10.1186/1556-276X-8-468View Article
- Zhang S, Fan W, Panoiu NC, Malloy KJ, Osgood RM, Brueck SRJ: Experimental demonstration of near-infrared negative-index metamaterials. Phys Rev Lett 2005, 95: 137404.View Article
- Li T, Li JQ, Wang FM, Wang QJ, Liu H, Zhu SN, Zhu YY: Exploring magnetic plasmon polaritons in optical transmission through hole arrays perforated in trilayer structures. Appl Phys Lett 2007, 90: 251112. 10.1063/1.2750394View Article
- Valentine J, Zhang S, Zentgraf T, Ulin-Avila E, Genov DA, Bartal G, Zhang X: Three-dimensional optical metamaterial with a negative refractive index. Nature 2008, 455: 376–379. 10.1038/nature07247View Article
- Minovich A, Neshev DN, Powell DA, Shadrivov IV, Lapine M, Hattori HT, Tan HH, Jagadish C, Kivshar YS: Tilted response of fishnet metamaterials at near-infrared optical wavelengths. Phys Rev B 2010, 81: 115109.View Article
- Zhang S, Fan W, Panoiu NC, Malloy KJ, Osgood RM, Brueck SRJ: Demonstration of metal-dielectric negative-index metamaterials with improved performance at optical frequencies. J Opt Soc Am B 2006, 23: 434–438. 10.1364/JOSAB.23.000434View Article
- Cao T, Cryan MJ: Study of incident angle dependence for dual-band double negative-index material using elliptical nanohole arrays. J Opt Soc Am A 2012, 29: 209–215.View Article
- Pendry JB, Holden A, Robbins D, Stewart W: Magnetism from conductors and enhanced nonlinear phenomena. IEEE Trans Microw Theory Tech 1999, 47(11):2075–2084. 10.1109/22.798002View Article
- Smith DR, Padilla WJ, Vier DC, Nemat-Nasser SC, Schultz S: Composite medium with simultaneously negative permeability and permittivity. Phys Rev Lett 2000, 84: 4184–4187. 10.1103/PhysRevLett.84.4184View Article
- Zhao Q, Kang L, Du B, Li B, Zhou J, Tang H, Liang X, Zhang B: Electrically tunable negative permeability metamaterials based on nematic liquid crystals. Appl Phys Lett 2007, 90: 011112. 10.1063/1.2430485View Article
- Wang X, Kwon DH, Werner DH, Khoo IC, Kildishev AV, Shalaev VM: Tunable optical negative-index metamaterials employing anisotropic liquid crystals. Appl Phys Lett 2007, 91: 143122. 10.1063/1.2795345View Article
- Minovich A, Neshev DN, Powell DA, Shadrivov IV, Kivshar YS: Tunable fishnet metamaterials infiltrated by liquid crystals. Appl Phys Lett 2010, 96: 193103. 10.1063/1.3427429View Article
- Dicken MJ, Aydin K, Pryce IM, Sweatlock LA, Boyd EM, Walavalkar S, Ma J, Atwater HA: Frequency tunable near-infrared metamaterials based on VO2 phase transition. Opt Express 2009, 17: 18330–18339. 10.1364/OE.17.018330View Article
- Driscoll T, Kim HT, Chae BG, Kim BJ, Lee YW, Jokerst NM, Smith DR, Ventra MD, Basov DN: Memory metamaterials. Science 2009, 325: 1518–1521. 10.1126/science.1176580View Article
- Chen HT, O'Hara JF, Azad AK, Taylor AJ, Averitt RD, Shrekenhamer DB, Padilla WJ: Experimental demonstration of frequency-agile terahertz metamaterials. Nat Photon 2008, 2: 295–298. 10.1038/nphoton.2008.52View Article
- Hu XY, Zhang YB, Fu YL, Yang H, Gong QH: Low-power and ultrafast all-optical tunable nanometer-scale photonic metamaterials. Adv Mater 2011, 23: 4295–4300. 10.1002/adma.201101350View Article
- Hasan MZ, Kane CL: Topological insulators. Rev Mod Phys 2010, 82: 3045. 10.1103/RevModPhys.82.3045View Article
- Qi XY, Zhang SC: Topological insulators and superconductors. Rev Mod Phys 2011, 83: 1057. 10.1103/RevModPhys.83.1057View Article
- Zhang X, Wang J, Zhang SC: Topological insulators for high-performance terahertz to infrared applications. Phys Rev B 2011, 82: 245107.View Article
- Hsieh D, Xia Y, Qian D, Wray L, Dil JH, Meier F, Osterwalder J, Patthey L, Checkelsky JG, Ong NP, Fedorov AV, Lin H, Bansil A, Grauer D, Hor YS, Cava RJ, Hasan MZ: A tunable topological insulator in the spin helical Dirac transport regime. Nature 2009, 460: 1101. 10.1038/nature08234View Article
- Pan ZH, Vescovo E, Fedorov AV, Gardner D, Lee YS, Chu S, Gu GD, Valla T: Electronic structure of the topological insulator Bi2Se3 using angle-resolved photoemission spectroscopy: evidence for a nearly full surface spin polarization. Phys Rev Lett 2011, 106: 257004.View Article
- Sharma Y, Srivastava P: First-principles study of electronic and optical properties of Bi2Se3 in its trigonal and orthorhombic phases. AIP Conf Proc 2009, 1249: 183–187.
- Shao LH, Ruther M, Linden S, Essig S, Busch K, Weissmüller J, Wegener M: Electrochemical modulation of photonic metamaterials. Adv Mater 2010, 22: 5173–5177. 10.1002/adma.201002734View Article
- Peng H, Dang W, Cao J, Chen Y, Wu D, Zheng W, Li H, Shen ZX, Liu Z: Topological insulator nanostructures for near-infrared transparent flexible electrodes. Nat Chem 2012, 4: 281–286. 10.1038/nchem.1277View Article
- Dordevic SV, Wolf MS, Stojilovic N, Lei H, Petrovic C: Signatures of charge inhomogeneities in the infrared spectra of topological insulators Bi2Se3, Bi2Te3 and Sb2Te3. J Phys Condens Matter 2013, 25: 075501. 10.1088/0953-8984/25/7/075501View Article
- Hafiz MM, El-Shazly O, Kinawy N: Reversible phase change in BixSe100-x chalcogenide thin films for using as optical recording medium. Appl Surf Sci 2001, 171: 231–241. 10.1016/S0169-4332(00)00709-1View Article
- Zhao J, Liu H, Ehm L, Dong D, Chen Z, Gu G: High-pressure phase transitions, amorphization, and crystallization behaviors in Bi2Se3. J Phys Condens Matter 2013, 25: 125602. 10.1088/0953-8984/25/12/125602View Article
- EM Explorer http://www.emexplorer.net/
- Johnson PB, Christy RW: Optical constants of the noble metals. Phys Rev B 1972, 6: 4370–4379. 10.1103/PhysRevB.6.4370View Article
- Berenger JP: Three-dimensional perfectly matched layer for the absorption of electromagnetic waves. J Comput Phys 1996, 127: 363–379. 10.1006/jcph.1996.0181View Article
- Born M, Wolf E, Bhatia AB: Principles of Optics. Cambridge: Cambridge University Press; 1997:61–70.
- Nicolson AM, Ross GF: Measurement of the intrinsic properties of materials by time-domain techniques. IEEE Trans Instrum Meas 1970, 19: 377–382.View Article
- Smith DR, Schultz S, Markos P, Soukoulis CM: Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients. Phys Rev B 2002, 65: 195104.View Article
- Chen XD, Grzegorczyk TM, Wu B, Pacheco JJ, Kong JA: Robust method to retrieve the constitutive effective parameters of metamaterials. Phys Rev E 2004, 70: 016608.View Article
- Zhang S, Fan W, Malloy KJ, Brueck SRJ: Near-infrared double negative metamaterials. Opt Express 2005, 13: 4922–4930. 10.1364/OPEX.13.004922View Article
- Ortuño R, García-Meca C, Rodríguez-Fortuño FJ, Martí J, Martínez A: Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays. Phys Rev B 2009, 79: 075425.View Article
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.