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).
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