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A metal/phase-change material/metal tri-layer planar chiral metamaterial in the shape of a gammadion is numerically modelled. The chiral metamaterial is integrated with Ge2Sb2Te5 phase-change material (PCM) to accomplish a wide tuning range of the circular dichroism (CD) in the mid-infrared wavelength regime. A photothermal model is used to study the temporal variation of the temperature of the Ge2Sb2Te5 layer and to show the potential for fast switching the phase of Ge2Sb2Te5 under a low incident light intensity of 0.016mW/μm2.
© 2013 Optical Society of America
1. Introduction
Materials exhibiting optical activity are called chiral materials [1,2], where optical activity refers to the ability to tailor the polarization plane of electromagnetic (EM) waves [3]. Due to the unique properties of chiral materials, they have been applied to many research fields, including molecular biology, optoelectronics, analytical chemistry and display applications [3,4]. In particular, chiral materials possess different transmission levels for right handed circularly polarized(RCP) and left handed circularly polarized(LCP) incident light, this is known as Circular Dichroism(CD). Natural chiral materials normally exhibit weak CD, however, much stronger CD can be realized by metamaterials made with subwavelength resonators [3,5–8]. Many metamaterials designs exhibit giant CD, however there is a lack of efficient tunability hence limiting their suitability for practical applications. In order to address this problem, here we numerically demonstrate that a gammadion chiral metamaterial integrated with a phase-change material (PCM) can have a highly tunable CD. The spectral response can be dynamically controlled and is tuned using the thermally induced phase transition between the amorphous and crystalline states of the PCM.
Metamaterials are manmade effective media and have attracted much attention due to their fascinating electromagnetic behaviour that does not occur in nature and their novel applications, such as cloaking [9,10], perfect imaging [11], and miniature antennas [12]. Recently, much attention has been paid to the metamaterials that could be applied to achieve unusual polarization functionality like negative refractive index [13,14] and strong optical activity [15,16]. More recently, Singh et al. have shown that the sign and magnitude of CD can be tuned by the tilt of the metamaterial plane relative to the incident beam [17]. Zhou et al. integrate chiral metamaterials with photoactive inclusions to accomplish a wide tuning range of the optical activity through near-infrared optical excitation [4]. Shi et al. demonstrate the coexistence of two tunable symmetric and asymmetric resonances in a metamaterial composed of asymmetrical split-rings patterned on a dielectric layer [18]. However, the tunability discussed above is still somewhat limited to the sign and magnitude of the CD rather than frequency response. Currently available metamaterials are often non-tunable and narrow band due to large dispersion of the resonant structures [19] thus the realization of tunable optical activity in metamaterials still remains a challenge. One possible route to overcome this limitation is to build tunable materials, such as chalcogenide glasses, into the metamaterials’ constituent layers. Such tunability has, in particular, been used in a PCM-based frequency tuning device [20] and more recently the phase change effect has been demonstrated in the fields of the tunable negative index [21] and tunable perfect absorber [22]. Here, we demonstrate for the first time that the resonant frequency of CD can be tuned using PCMs in the mid-infrared regime. Our structure is developed from the previously studied double layer gammadion chiral metamaterials [23].
With the integration of PCMs, a massive range of the spectral tunability of CD in the presented structure can be obtained by switching between the amorphous and crystalline states of the PCMs. The structure is composed of an array of a tri-layer gammadion shaped magnetic resonators and a prototypical PCM, Ge2Sb2Te5, is selected as the active dielectric layer. Importantly, a heat model is constructed to investigate the temporal variation of the temperature of Ge2Sb2Te5 layer in the structure. The model shows that the temperature of the amorphous Ge2Sb2Te5 layer can be raised from room temperature to > 883K (melting point of Ge2Sb2Te5) [24,25] in just 5 ns with a low incident light intensity of 0.016mW/μm2 thus supplying sufficient thermal energy to change the amorphous phase to crystalline phase for both LCP and RCP light sources [26–28].
We believe this paper shows the first example of using the Ge-Sb-Te system to create tunable optical activity and we hope the results presented herein will serve as an impetus for the development of PCMs specifically for tunable chiral metamaterials. Whilst, this tunable chiral metamaterial is relatively straightforward to fabricate, electronic phase switching technologies can be difficult to integrate into these structures, however, rapid progress is being made in this area for Phase Change based memories [29]. Finally, it should be noted that PCMs do not require any energy to maintain the structural state of the material. Thus once the chiral metamaterial has been switched it will retain its optical activity until it is switched again. This clearly makes PCM based chiral metamaterials interesting from a ‘green technology’ perspective.
2. Structure and design
The unit cell of the tri-layer gammadion chiral metamaterial is shown in Fig. 1.It consists of two Au layers separated by a Ge2Sb2Te5 layer, where a planar resonator is arranged in the shape of a gammadion with the lattice constant equal to 506 nm (L = 506 nm) in both x and y directions. The thickness of the top Au layer is 48 nm (t1 = 48nm), the Ge2Sb2Te5 layer is 24 nm (t2 = 24 nm) and the bottom Au layer is 48 nm (t3 = 48 nm). The Au bottom layer interacts with the upper Au layer to form a magnetic dipole to enhance the CD [23,30]. Each arm of the gammadion cell has two rectangular blocks of dimensions ω × l/2 and s × r connected at right angles shown in Fig. 1(b), where l = 322nm, ω = 92nm, s = 23nm, r = 92nm. The whole structure is fabricated on BK7 silica glass substrate with a 200μm thickness. The simulation is performed by commercial software (Lumerical FDTD Solutions), which is based on the Finite Difference Time Domain (FDTD) method. The dielectric properties of Au as given by Johnson & Christy are used [31].
Fig. 1 (a) Schematic of the gammadion metamaterial and the incident light polarization. The thicknesses of Au film, Ge2Sb2Te5 spacer and Au film are 48nm, 24nm and 48nm respectively. The lattice constant in both x and y-directions is L = 506nm and the dimensions are l = 322nm, w = 92nm, s = 23nm, r = 92nm. The whole structure resides on BK7 silica glass with 200μm thickness. β is a cross section plane along the edge of the arm. (b) Top view of the gammadion metamaterial.
The structure is excited by a source with a wavelength range from 1800 to 5800 nm, propagating along the negative z direction with the E field polarized in the x direction as shown in Fig. 1(a). The light source has a repetition rate, fr = 25 kHz and pulse duration of 2.6 ns. The light fluence on the sample from a single pulse is written as [32]
where P0 = 5mW is the total power of the injection light, r is the distance from the beam center, w1 = 10μm is Gaussian beam waist. Perfectly match layer (PML) absorbing boundaries are applied in the z direction and periodic boundaries are used for a unit cell in the x-y plane.The real, ε1(ω) and imaginary, ε2(ω) parts of the dielectric function of Ge2Sb2Te5 in the amorphous and crystalline structural phases were obtained from well-accepted experimental data in [33], which for the mid-infrared (M-IR) spectral range are shown in Fig. 2.A large change in the real part of the dielectric function is obtained after switching the PCM between its two structural phases. The dielectric constant of Ge2Sb2Te5 is very dispersive and has a non-negligible imaginary part indicating a high loss. The dielectric constant changes back to its initial value for the reversible structural transformation from amorphous to crystalline. It should be mentioned that the reversible phase transition in Ge2Sb2Te5 is highly repeatable and more than a billion cycles have been experimentally demonstrated in data storage devices [27]. Different PCMs can display a similar optical response in other parts of the spectrum. These very different optical properties are realistic and well known but they have predominantly been applied to data storage applications.
Fig. 2 Dielectric constant (a) ε1(ω) vs wavelength, (b) ε2(ω) vs wavelength for both amorphous and crystalline phases of Ge2Sb2Te5 [33].
3. Results and discussions
Circular dichroism is defined as
where the circular polarization absorbance of RCP and LCP incident waves are AR and AL given by and , respectively. TR and TL are the circular polarization transmission for RCP and LCP incident waves,RR and RL are the circular polarization reflection for RCP and LCP incident waves [30]. The second quantity in Eq. (2): is derived from the equal reflections, RR = RL which can be obtained from the reciprocity theorem for structures having four-fold rotational symmetry and a normally incident wave [34,35]. Figure 3(a) shows the spectra of the transmission in the amorphous state for LCP and RCP normal incidence. Two resonant dips at the wavelengths of 2180 nm and 3745 nm appear in the transmission spectrum for each polarization. However, only at λ = 2180 nm the transmission coefficients are significantly different for the different circular polarizations (|TL| = 0.68 and |TR| = 0.78) indicating strong CD. Due to the reciprocity in the structure, the difference of the transmissions relies completely on the absorbance AR and AL, presented in Fig. 3(b). Figure 3(c) shows the phases of TL and TR lying on top of each other far from the resonance. However, in the vicinity of the resonance at λ = 2180 nm, one can observe a clear difference, which will induce the rotation of the polarization plane of linearly polarized light as it passes through the gammadion metamaterial [1]. Figure 3(d) demonstrates CD of the multilayer gammadion metamaterials with the amorphous Ge2Sb2Te5, where the thickness of the Au layers is t1 = t3 = 48 nm and the thickness of the Ge2Sb2Te5 t2 is varied between 12 and 36 nm. The results show that the CD peaks blue shifts as increasing the t2. It is also evident that strength of the CD at the resonant frequency can be enhanced with the thicker Ge2Sb2Te5 dielectric layer.Fig. 3 3D-FDTD simulation of (a) transmission coefficient, (b) absorptance, (c) transmission phase of gammadion metamaterials for both RCP and LCP normal incidence; (d) circular dichorim with t1 = t3 = 48nm if t2 is varied between 12nm and 36 nm in the amorphous state of Ge2Sb2Te5.
The difference between the magnitudes of two transmissions is characterized by the ellipticity, as shown in Fig. 4(a).
Fig. 4 3D-FDTD simulation results of (a) ellipticity τ (b) the polarization rotation angle θ, (c) the real part of chirality κ in amorphous Ge2Sb2Te5.
The difference between the phases is characterized by the polarization rotation angle, as shown in Fig. 4(b).
The chirality, κ is shown in Fig. 4(c) and calculated from the transmissions as
where k0 is the wavevector in the vacuum, d is the thickness of the gammadion metamaterial, and m is an integer satisfied for one unit cell [1,30]. In Fig. 4(c), it can be seen that the real part of κ is associated with the polarization rotation angle.In order to further elucidate the underlying mechanism of CD in the structure, in Fig. 5 we present the total magnetic field intensity distribution, and the displacement current JD at the wavelength of 2180 nm for both amorphous and crystalline Ge2Sb2Te5 along a cross section plane β shown in Fig. 1.
Fig. 5 A map of the normalized total magnetic field intensity distribution H (colour bar) and displacement current JD (arrows) along β plane at 2180nm resonance wavelength:(a)in amorphous Ge2Sb2Te5,(b) in crystalline Ge2Sb2Te5.
In the figure, the arrows represent JD whereas the color represents the magnitude of the total magnetic field intensity. Figure 5(a) clearly shows that the magnetic field is concentrated in the amorphous Ge2Sb2Te5 dielectric layer between Au films. A loop of JD is attained to generate a magnetic moment which can give rise to CD [23]. In Fig. 5(b), we have presented the magnetic field distribution and displacement current along the β plane in crystalline state at the wavelength of 2180nm. We note that the electric displacement current does not form a loop and hence, the magnetic field cannot be efficiently confined in the crystalline Ge2Sb2Te5 layer to support a magnetic resonance. It results in zero values of τ, θ and Re(κ) at 2180nm for the crystalline structure shown in Fig. 8. This suggests that the CD in the multilayer gammadion metamaterial is mainly due to the magnetic resonant dipole. Therefore, to get a tunable CD, the structure design should be optimized so as to effectively tune a magnetic dipole resonance.
Since the reversible amorphous - crystalline phase transition of Ge2Sb2Te5 can be induced through optical heating, it is important to understand the heat induced switching behavior of the metamaterial structure. To show this, a heat transfer model is used to investigate the temporal variation of temperature of Ge2Sb2Te5 layer for different polarized incident light using the Finite Element Method (FEM) solver within COMSOL. The material thermal properties used for the simulation are summarized in Table 1.The thermal conductivity of Ge2Sb2Te5 changes with the temperature are obtained from experiment data in [36].
Table 1. Material thermal properties used in the Heat transfer model
In this simulation, the thermal energy absorbed by one unit cell is defined as [32]
where L the lattice constant of the metamaterials is 506 nm, Ra the absorption coefficient of the absorber is 0.0456 for LCP and 0.0413 for RCP incident light respectively, derived from the overlap integral between the light source power density spectrum and the absorbance spectrum, shown in Fig. 3(b). The heat source power is then described by a Gaussian pulse functionwhere τ = 1.5ns is the time constant of the light pulse, t0 = 3ns is the time delay of the pulse peak. Figure 6 shows Qs(r, t) and the temperature of the amorphous Ge2Sb2Te5 layer for both LCP and RCP incident light, where the structure is located at the center of Gaussian beam. It shows that the temperature of amorphous Ge2Sb2Te5 for LCP incident light can reach 883K at 3.9 ns and maximum 976K at 5 ns under an incident light intensity of 0.016mW/μm2. Due to heat dissipation to the surroundings, the temperature starts dropping after 5ns before the next pulse comes. However, Qs(r, t) and the temperature of amorphous Ge2Sb2Te5 layer for RCP normal incidence are lower than LCP normal incidence owing to its smaller absorption coefficient Ra, where the highest temperature is 913K at 5 ns under the same light intensity of 0.016mW/μm2. Thereby the melting point of 883K can be obtained to switch the phase of Ge2Sb2Te5 for both LCP and RCP incident light.Fig. 6 3D- FEM simulation of heat power irradiating on a gammadion metamaterial located at the beam center, where the solid red line presents the heat power irradiating on the structures for LCP incident light, the solid blue line presents the heat power irradiating on the structures for RCP incident light, the dash red line is the temperature of the amorphous Ge2Sb2Te5 layer during one pulse for LCP incident light, the dash blue is the temperature of amorphous Ge2Sb2Te5 layer during one pulse for RCP incident light.
The temperature distributions of the structure at 5ns along the plane β are shown in Fig. 7(a) for LCP incident light and Fig. 7(b) for RCP incident light. One can observe that the temperature within amorphous Ge2Sb2Te5 layer is uniform and the dominant temperature gradient is along the same direction as the incident light, indicating that BK7 silica substrate is an effective heat sink.
Fig. 7 The temperature distribution of the unit cell of a gammadion metamaterial along a plane β at 5ns, where the color image indicates the temperature distribution and the arrows indicate the heat flux for (a) LCP incident light (b) RCP incident light.
In order to further study the influence of the effective parameters on the tunable gammadion chiral metamaterials.In Fig. 8, we have simulated τ, θ and Re(κ) for different states of Ge2Sb2Te5 at normal incidence and found that the resonances shift towards longer wavelength (from 2180nm to 3460nm) when the phase of Ge2Sb2Te5 switches from amorphous to crystalline which is a 58% tuning range. This result highlights that a widely tunable spectrum of τ, θ and Re(κ) can be obtained by switching between the amorphous and crystalline states of Ge2Sb2Te5. However as the phase of Ge2Sb2Te5 changes to crystalline, the absolute values of τ, θ and Re(κ) decrease correspondingly due to the weaker magnetic resonance in the crystalline Ge2Sb2Te5, shown in Fig. 9(b).
Fig. 8 The comparison of (a) the ellipticity τ, (b) the polarization rotation angle θ, (c) the real part of κ between amorphous Ge2Sb2Te5 and crystalline Ge2Sb2Te5.
Fig. 9 A map of the normalized total magnetic field intensity distribution H (colour bar) and displacement current (JD) (arrows) along β plane (a) at 2180nm resonance wavelength for amorphous Ge2Sb2Te5, (b) at 3460nm resonance wavelength for crystalline Ge2Sb2Te5.
In Fig. 9, we show the total magnetic field H and displacement current JD associated with the resonant wavelength of 2180 nm for the amorphous Ge2Sb2Te5 and 3460 nm for the crystalline Ge2Sb2Te5. It can be seen that H and JD in the crystalline phase shown in Fig. 9(b) are similar to the amorphous phase shown in Fig. 9(a), which implies that the magnetic resonant dipole can also be excited to create CD in the crystalline state. Particularly, the localized magnetic fields of the crystalline Ge2Sb2Te5 are attenuated and smaller than the amorphous Ge2Sb2Te5, implying a weaker magnetic resonant dipole in the crystalline phase.
4. Conclusion
In summary, we have theoretically demonstrated a tunable gammadion chiral metamaterial and a large frequency shift of 58% for CD is observed in the M-IR region. This tunable effect is due to the phase transition from the amorphous to crystalline. A heat transfer model is built to resolve the transient temperature variation in the structure during a photothermal process. Our model predicts that amorphous Ge2Sb2Te5 can reach 883K in only 5 ns through a low light intensity of 0.016mW/μm2 hence being crystallized for both LCP and RCP normal incidence. A map of JD and H at different resonant frequencies for both amorphous and crystalline Ge2Sb2Te5 is used to explain the physical origin of the CD. This work presents a new method to massively tune the resonant frequency of CD in a chiral metamaterial, and can find numerous applications in ultrathin polarization rotators, modulators and circular polarizers.
Acknowledgments
We acknowledge the financial support from National Natural Science Foundation of China (Grant No. 61172059, 51302026), Ph.D Programs Foundation of 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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