Numerical study of achiral phase-change metamaterials for ultrafast tuning of giant circular conversion dichroism

Control of the polarization of light is highly desirable for detection of material’s chirality since biomolecules have vibrational modes in the optical region. Here, we report an ultrafast tuning of pronounced circular conversion dichroism (CCD) in the mid-infrared (M-IR) region, using an achiral phase change metamaterial (PCMM). Our structure consists of an array of Au squares separated from a continuous Au film by a phase change material (Ge2Sb2Te5) dielectric layer, where the Au square patches occupy the sites of a rectangular lattice. The extrinsically giant 2D chirality appears provided that the rectangular array of the Au squares is illuminated at an oblique incidence, and accomplishes a wide tunable wavelength range between 2664 and 3912 nm in the M-IR regime by switching between the amorphous and crystalline states of the Ge2Sb2Te5. A photothermal model is investigated to study the temporal variation of the temperature of the Ge2Sb2Te5 layer, and shows the advantage of fast transiting the phase of Ge2Sb2Te5 of 3.2 ns under an ultralow incident light intensity of 1.9 μW/μm2. Our design is straightforward to fabricate and will be a promising candidate for controlling electromagnetic (EM) wave in the optical region.

photoexcitation [22][23][24][25][26] . The polarization phenomena can also be passively tuned by the tilt of the MM plane relative to the incident beam 27,28 or changing the geometry of the resonance element 29 . Even so, tunable chirality from the MMs still suffers a slow switching speed and narrow tuning range, not to mention the great manufacturing complexity in the optical region. It is still a formidable challenge to ultrafast tune a giant 2D-chiral response with a wide tuning range in the optical region.
Here, we demonstrate that the resonant frequency of giant CCD can be tuned in the M-IR regime using an achiral phase change metamaterial (PCMM). The achiral PCMM is composed of an array of thin Au squares separated from a continuous Au film by an active dielectric interlayer of prototypical phase change material (PCM): Ge 2 Sb 2 Te 5 , where the Au squares occupy the sites of a rectangular lattice. This structure can be called '2D planar metamaterial' since its planar reflectarray of Au squares exhibits subwavelength periodicity and negligible thicknesses as compared to the incident wavelength 30 .
The giant CCD analogous to chiral MMs can be achieved, provided that the structure is illuminated under oblique incidence. This large difference between the left-to-left and right-to-right circularly polarized reflectance conversion efficiencies so called as CCD, attributes to the strong electric and magnetic resonances in the multilayer MM 31 . It is because the chirality is characterized by electric and magnetic dipolar moments and enhancing chirality spectroscopy entails manipulation of both electric and magnetic fields of light 32,33 . With the integration of PCM, a broad range of the spectral tunability of CCD in the proposed structure can be obtained by switching between the amorphous and crystalline states of Ge 2 Sb 2 Te 5 . Importantly, we construct a heat model to show that the temperature of amorphous Ge 2 Sb 2 Te 5 can be raised from room temperature to 433 K (amorphous-to-crystalline phase transition temperature) 34,35 in just 3.2 ns with a low light intensity of 1.9 μ W/μ m 2 , owing to the enhanced light absorbance over a wide range of incident angles through strong plasmonic resonances in the structure 36 . Thereby, our structure can supply sufficient thermal energy to change the amorphous phase to crystalline phase for both LCP and RCP light sources.
We hope the results presented herein will serve as an impetus for the development of PCM specifically for achiral MMs exhibiting tunable 2D-chiroptical effect. Whilst, this tunable PCMM is relatively straightforward to fabricate. Interestingly, PCM does not require any energy to maintain the phase of the material. Therefore once the PCMM has been switched it will retain its chiral response until it is switched again. This clearly makes MM based on PCM interesting from a 'green technology' perspective. Finally, the proposed PCMM is ultrathin that may be integrated within today's nanophotonic systems. It can find diverse functionalities, such as biomolecule sensing, switches, circular polarization transformers, and modulators. Figure 1(a) shows the proposed PCMM consisting of two Au layers spaced by a 40 nm thick Ge 2 Sb 2 Te 5 dielectric interlayer. The top metal layer is a 40 nm thick Au square array, where the pitches along the x and y directions are L x = 400 nm and L y = 800 nm, respectively. The side length of the Au square is d = 200 nm. The bottom Au layer has a thickness of 80 nm, which will prevent the transmission of the incident light hence leading to a nearly zero transmittance 31 . Moreover, the strong electric and magnetic dipolar resonances in the multilayer structure may introduce a big difference in the absorbance (reflectance) for RCP and LCP waves under off-normal incidence. The scheme of the unit cell is shown in Fig. 1(b), while Fig. 1(c) shows the incident wavevector k, the vector normal to the surface n, and the two primitive lattice vectors (a and b) in red. The incident angle θ is measured between the wavevector k and the vector n. ϕ is the rotation angle between the parallel (to the x-y plane) component of k and the x axis. The structure is suspended in a vacuum. A simple Drude model is used for the dielectric The real, ε 1 (ω) and imaginary, ε 2 (ω) parts of the dielectric function for the different states of Ge 2 Sb 2 Te 5 were obtained from the published Fourier transform infrared spectroscopy data in 38 , which for the M-IR spectral range are shown in Fig. 1(d). A pronounced change in the ε 1 (ω ) is obtained during the reversible structural transformation from amorphous to crystalline. The dielectric constant of Ge 2 Sb 2 Te 5 is very dispersive and changes back to its initial value for the reversible structural transformation from amorphous to crystalline. These very different optical properties are realistic and well known but they have predominantly been applied to data storage applications. It should be mentioned that the reversible phase transition in Ge 2 Sb 2 Te 5 is highly repeatable and more than a billion cycles have been experimentally demonstrated in data storage devices 39 . With these unique properties, the Ge-Sb-Te system is of great interest for actively tunable plasmonics and nanophotonics 40,41 .

Results
In order to manifest chiroptical response, here the complex circular reflection matrix r ij of the achiral PCMM is defined in terms of the incident E j in and reflected E i r field vector by , where 'i' and 'j' are the subscripts correspond to RCP (+ ) and LCP (− ) components 42 . The reflectance is defined as = | | R r ij ij 2 and presents the intensities of the corresponding reflected and converted components for RCP and LCP incident waves, and the total reflectance through the PCMM is expressed as The diagonal terms r ++ and r − − of r ij are used to detect 3D chirality which is linked to the circular , where R ++ and R − − stand for direct reflectance of circular polarization. Similarly, the off-diagonal terms r −+ and r +− of r ij represent the values demonstrating 2D chirality related to circular conversion dichroism (CCD): , where R −+ stands for left-to-right polarized conversion efficiencies and R +− for right-to-left polarized conversion efficiencies in reflectance 8,43 . To detect the extrinsic 3D-chiral response, Fig. 2(a) shows the diagonal elements of the reflectance matrix (R − − and R ++ ) in the amorphous state for LCP and RCP oblique incidence with θ = 75°, ϕ = 60°, L x = 400 nm and L y = 800 nm. As can be seen, the R − − and R ++ are equal (CD = 0) showing the absence of an extrinsic 3D chirality. Analogously, to detect the extrinsic 2D-chiral effect, we calculate the off-diagonal elements R −+ and R +− of the reflectance matrix shown in Fig. 2(b). The spectra for R −+ and R +− lie on top of each other away from the optimal wavelength 2664 nm, around which − + R and + − R change sharply in opposite directions. At the optimal wavelength, a large difference between − + R and − + R 0 64 and = .
+ − R 0 02. This CCD arises from the mutual orientation of non-chiral elements and the direction of the light propagation, and its significant value of 0.62 originates from the strong electric and magnetic resonances in the multilayer structure. It should be mentioned that although our structure has a nearly zero transmittance, one may alternatively utilize the reflectance spectra for the possible applications of the 2D chirality. Figure 2(c) shows the CCD spectra of the amorphous structure with different ratios of L y /L x at L x = 400 nm for θ = 75°, ϕ = 60°. The 2D-chiral effect vanishes (CCD = 0) for a square array of the Au patches (L x = L y = 400 nm) as the plane of incidence falls on a line of mirror symmetry of the structure. By increasing the ratio of L y /L x , the CCD can be gradually improved. However, the CCD response is weakened when the ratio of L y /L x is larger than 2 (L y /L x > 2). It is because the coupling of neighboring Au squares along the y direction is reduced as increasing L y . Figure 2(d) demonstrates the CCD spectra for different values of ϕ with θ = 75° at L x = 400 nm and L y = 800 nm, where the CCD can achieve its maximum value of 0.62 at ϕ = 60°. Meanwhile, the 2D-chiroptical effects disappear for ϕ = 0° and 90° as the anisotropic axis of the structure is in the incident plane hence leading to a mirror plane of the experimental geometry. Moreover, opposite rotation angles (± ϕ) result in opposite signs of CCD corresponding to two enantiomeric arrangements. We then study the effect of variation of incident angles on the CCD for fixed ϕ = 60° at L x = 400 nm and L y = 800 nm. As can be seen in Fig. 2(e), the CCD is varied by tilting the array of Au squares from θ = 0° to 75° and obtain the highest value of 0.62 at 2664 nm for θ = 75°. Therefore, the 2D-chiroptical response herein is optimized at θ = 75° and ϕ = 60°. Moreover, it should be noted that the spectra of CCD do not reverse when the signs of θ are opposite due to the property of extrinsic 2D chirality.  amorphous state and crystalline state Ge 2 Sb 2 Te 5 . It can be seen that − − R and + + R overlap (CD = 0) for both of the states, and the reflectance dip shifts towards longer wavelength (from 2664 to 3912 nm) when the phase of Ge 2 Sb 2 Te 5 is switched from amorphous to crystalline, which is a 46% tuning range. In Fig. 3(b), we also find that the off-diagonal elements ( − + R and + − R ) change sharply in opposite directions around 2664 nm for amorphous Ge 2 Sb 2 Te 5 and 3912 nm for crystalline Ge 2 Sb 2 Te 5 , indicating large CCD at the resonant wavelengths for both of the sates. Figure 3(c) shows the evolution of the CCD in the reflectance spectra. With the phase change of Ge 2 Sb 2 Te 5 , the resonance wavelength of the CCD spectra at 2664 nm for the amorphous state shifts to the 3912 nm for crystalline state. Thanks to the large tuning range for the CCD shift of 1248 nm, this proposed PCMM can be very useful in switching on/off the 2D-chiral effect. For example, the CCD appears to be zero around 2664 nm, and thus switching off the chiroptical response when Ge 2 Sb 2 Te 5 is transited from the amorphous to crystalline. We also find that the maximum value of CCD at 3912 nm decreases to 0.44 when Ge 2 Sb 2 Te 5 changes from the amorphous to crystalline in addition to a shift, owing to the weaker magnetic resonance in the crystalline Ge 2 Sb 2 Te 5 .
The giant CCD results from the coupling between the Au-Ge 2 Sb 2 Te 5 -Au multilayers, which gives rise to a strong magnetic response. This strong magnetic resonance is connected to an antisymmetric charge-oscillation eigenmode, providing the combined plasmon mode a twist in the propagation direction of the wave to imitate 2D chirality 44 . In Fig. 4 Fig. 1(c), associated with the resonant wavelength of 2664 nm for the amorphous and 3912 nm for the crystalline Ge 2 Sb 2 Te 5 induced by the off-normal LCP and RCP incident lights at θ = 75°, ϕ = 60°. Figure 4(a,b) show that the H fields in the amorphous phase can be efficiently confined in the Ge 2 Sb 2 Te 5 layer between the Au layers, which is owing to a concomitant coupling between surface plasmons counterpropagating on the two closely spaced interfaces 45 . Meanwhile, the H field distributions in the crystalline phase shown in Fig. 4(c,d) are similar to the amorphous phase shown in Fig. 4(a,b) for both LCP and RCP incidences respectively, which implies that the magnetic resonant dipole can also be excited to create CCD in the crystalline state. However, the difference of the H fields of the crystalline Ge 2 Sb 2 Te 5 between the RCP and LCP incidences is smaller than that of the amorphous Ge 2 Sb 2 Te 5 hence leading to a smaller CCD shown in Fig. 3(c). As can be seen in Fig. 4, the H field pattern appears asymmetric with respect to center under the oblique incidence of θ = 75°, ϕ = 60°. This is because the time of pulse propagating through different regions of the structure is unequal. This also explains how the oblique incidence causes the asymmetric reflectance of the two circular polarization lights shown in Fig. 2(a,b). Since the reversible amorphous -crystalline phase transition of Ge 2 Sb 2 Te 5 can be induced through optical heating, it is important to understand the heat induced switching behavior of the achiral PCMM. To show this, a heat transfer model developed from our previous work 36 is further investigated to obtain the temporal variation of temperature of Ge 2 Sb 2 Te 5 layer for different polarized incident light using the Finite Element Method (FEM) solver within COMSOL. Here, the achiral PCMM model is set up in COMSOL identical to that shown in Fig. 1. A Gaussian pulse is used as the excitation source to evaluate the required time to switch from the amorphous to the crystalline state of the Ge 2 Sb 2 Te 5 . In particular, the Gaussian source has a repetition rate f r = 25 kHz and pulse duration of 2.6 ns. The light fluence shining on the sample from a single pulse is written as where L x = 400 nm, L y = 800 nm and R a the absorbance coefficient of the absorber is 0.1 for LCP and 0.14 for RCP incident light respectively, derived from the overlap integral between the light source power density spectra and the absorbance spectra for θ = 75°, ϕ = 60°, shown in Fig. 2(f). The heat source power is expressed by a Gaussian pulse function where τ = 1.5 ns is the time constant of the light pulse, t 0 = 3 ns is the time delay of the pulse peak. Figure 5 shows Q s (r, t) and the temperature of the amorphous Ge 2 Sb 2 Te 5 interlayer for both LCP and RCP incidences at θ = 75°, ϕ = 60°, where the PCMM is placed at the center of Gaussian beam. As can be seen, the temperature of amorphous Ge 2 Sb 2 Te 5 for the RCP can reach 433 K at 2.8 ns and maximum 505 K at 4.2 ns under an incident light intensity of 1.9 μ W/μ m 2 . Due to heat dissipation to the surroundings, the temperature starts decreasing after 4.2 ns before the next pulse comes. However, Q s (r, t) and the temperature for the LCP are lower than the RCP owing to its smaller absorbance coefficient R a , where the amorphous-to-crystalline phase transition temperature of 433 K is achieved at 3.2 ns under the same light intensity of 1.9 μ W/μ m 2 . Thereby the melting point of 433 K can be obtained to switch the phase of Ge 2 Sb 2 Te 5 for both LCP and RCP incident light at θ = 75°, ϕ = 60°. Tuning of chiroptical response at a large power input may sound challenging, since the high power illumination gives rise to unwanted heating to prevent polarization tuning. To solve this problem, herein an Au-Ge 2 Sb 2 Te 5 -Au trilayers structure is proposed, where the Au bottom layer will interact with the upper Au patches to form electric and magnetic dipoles that efficiently couple the incident light into the dielectric interlayer of Ge 2 Sb 2 Te 5 31 . It has the advantage of transiting the phase of Ge 2 Sb 2 Te 5 under RCP and LCP illumination with an ultralow light intensity of 1.9 μ W/μ m 2 and thus may not prevent the polarization tuning. Meanwhile, we suggest that a future design, with the second external pumping laser, of weaker intensity, should be introduced to heat up the Ge 2 Sb 2 Te 5 layer to change the phase. Or alternatively, one may apply a voltage between the top layer Au patches and bottom Au mirror to electrically switch the state of Ge 2 Sb 2 Te 5 . By means of the external stimulus, the phase transition of Ge 2 Sb 2 Te 5 can be carried out separately hence not interacting with the polarization tuning.

Discussion
In conclusion, we have demonstrated an ultrafast tuning of giant CCD using an achiral PCMM and a large frequency shift of 46% for CCD is observed in the M-IR regime. This CCD is caused by the mutual orientation of the achiral PCMM and the oblique incident wave, where the giant value of the CCD is due to the strong magnetic dipolar resonance in the multilayer structure. The ultrafast tunable effect is due to the short time (3.2 ns) of phase transition from the amorphous to crystalline in the structure under a low pump light intensity (1.9 μ W/μ m 2 ). This work presents a new method to massively tune the resonant frequency of giant CCD in an achiral metamaterial, and can find numerous applications in ultrathin polarization rotators, modulators and circular polarizers.

Methods
For the numerical calculations of the CCD spectra, we used the commercial finite integration package CST MICROWAVE STUDIO ® . To account for the periodic nature of the structure, the model boundary in the x and y directions is set to unit cell boundary conditions, respectively. To achieve the temporal variation of temperature of Ge 2 Sb 2 Te 5 layer, we used the Finite Element Method by means of COMSOL Multiphysics: the model boundary at = ± x L 2 x and = ± y L 2 y is set to condition of perfect magnetic conductor and perfect electric conductor, respectively. A simple Drude model is used for the dielectric constant of Au, is the scattering frequency for Au 37 . The dielectric constants for the different states of Ge 2 Sb 2 Te 5 were obtained from the published Fourier transform infrared spectroscopy data in 38 .