1. Introduction

Fano resonance (FR) is an interference effect caused by the coupling of a discrete state with a continuum [1,2]. Recently, FRs have been observed in plasmonic nanostructures and metamaterials (MMs) due to the overlapping of bright (radiating) and dark (non radiating) plasmonic modes [3,4]. The steep dispersion of the FR profile promises applications in chemical and biological sensing [5,6], surface enhanced spectroscopy [7], active plasmonic switching [8], and slow light devices [9]. Since Fedotov et al. first observed FRs in MMs composed of asymmetrically split ring arrays [10], various configurations of asymmetric metamolecules have been adopted to demonstrate FRs based on MMs such as heterodimer structures [11], ring/disk cavities [12], non-concentric multilayered nanoshells [13], nanoparticle clusters [14], nanoslits [15] and intersecting nanorings [16]. However, MMs with broken symmetry are complicated to fabricate and manipulate accurately in experiments, which severely limits their applications [17]. In contrast, only a few groups reported the formation of FRs in symmetric plasmonic structures, such as double layer electric ring resonators in the GHz regime [18] and multilayer half hole resonators in THz regime [19]. However, to the best of our knowledge, limited attempts were made to actively control FRs through the multilayer MMs in the mid-infrared (M-IR) region.

Control of FRs in MMs is highly desirable for practical applications such as tuning the dispersion and group velocity of light [20], multispectral imaging/detection [21] and broadband delay lines [9]. The basic idea for tuning FRs is to adjust the structural parameters of MMs [22,23]. However, it is hard to change the geometry of resonators in MMs once they are fabricated, which limits the scope of their applications. Therefore, a practical way of modulating FRs is desired for real MM applications [24]. For this purpose, MMs combined with optically active materials is a promising approach [25,26]. They rely on integrating the MMs with various active materials such as magnetic materials [27], metal-superconductor [28], chalcogenide glass [29] and grapheme [30]. However, the FRs in these MMs are actively tuned through a magnetic or electrical stimulus and response time a scale of several microseconds to seconds is typical [31]. Moreover, the integration of the required MM structures as well as the electrodes for the tuning of active dielectric layers can be difficult. Quite recently, all-optical tunable FRs in non-linear MMs have attracted growing interest due to their ultrafast modulation speed and small pump light requirements [32,33]. However, such plasmonic structures are based on a single metal layer.

Ge-Sb-Te, a chalcogenide phase-change material (PCM) has recently captured significant attention for actively controlling localized surface plasmon resonances (LSPRs) in dynamic switching plasmonic devices [34,35]. Due to its remarkable change in the dielectric constant between its crystalline and amorphous phases, as well as its stable phases, demonstrated by its commercial application in rewritable digital versatile disc technologies [36], Ge-Sb-Te can be an excellent platform for achieving tunable three-dimensional multilayer MMs in the various applications such as negative refraction [37] and perfect absorbance [38]. More recently, a tunable double Fano resonance (FR) in a metal/PCM/metal multilayer fishnet MM with a broken symmetry has been numerically demonstrated [39]. It shows that the displacement of the resonance elements from their centers can split the single FR into a double FR, exhibiting higher quality factors. However, fabrication of this asymmetric MM in the optical region still remains challenging since it is hard to precisely control the displacement of the elements on the scale of nanometer. Moreover, the two close resonance peaks in the double FR may introduce an interchannel interference.

In this work, we numerically demonstrate that resonant frequency of a single FR in a three-dimensional (3D) multilayer MM can be rapidly tuned using a PCM in the mid-infrared (M-IR) spectral region. Our structure is composed of periodic arrays of elliptical nanoholes etched through a Metal-Dielectric-Metal (MDM) trilayer and a prototypical PCM: Ge₂Sb₂Te₅, is selected as the dielectric layer. A single FR is observed in the structure owing to the overlapping of the bright and dark plasmon modes. The bright mode is generated through electric resonance (namely LSPRs) in the elliptical nanohole array (ENA), and the dark mode due to magnetic resonance (namely inductive-capacitive resonance) in the MDM multilayer [20,40]. Moreover, it is shown that the interference between the electric and magnetic resonances can be significantly enhanced when the elliptical nanoholes occupy the sites of a rectangular lattice, thus providing a FR with a higher value quality factor (Q) compared to the MDM-ENA with a square lattice. A large shift of 855 nm in the FR wavelength can be obtained by switching between the amorphous and crystalline structural states of Ge₂Sb₂Te₅ [41]. A heat model, which has been explicitly demonstrated in [39], is used to investigate the temporal variation of the temperature of Ge₂Sb₂Te₅ layer in the MDM-ENA with a rectangular lattice. It shows that the temperature of the amorphous Ge₂Sb₂Te₅ layer can be raised from room temperature to > 433 K (phase transition point of Ge₂Sb₂Te₅) [42,43] in just 0.38 ns with an ultralow operating pump light intensity of 3.2μW/μm². Such a MDM-ENA exhibiting a single FR can avoid the interchannel interference in the double FR. This is especially important for sensing applications because biological and chemical molecules tend to have vibrational frequencies which obscure the double FR; hence a significantly single FR will be useful for accurate detections of chemical and biological agents. Furthermore, our proposed structure offers an easy-to-implement way of achieving fast all-optical tunable FRs in 3D multilayer phase change metamaterials (PCMMs) in terms of nanofabrications. In order to simplify the model, we do not account for the effect of the dielectric constant change on the optical heating during the phase transition of Ge₂Sb₂Te₅, this will be the subject of future work. Finally, it should be noted that PCMs do not require any energy to maintain the structural state of the material. Thus, once the metamaterial is switched it retains its FRs at a particular frequency until it is switched again. This clearly makes tunable FRs in PCMMs interesting from a 'green technology' perspective.

2. Metamaterials design

The proposed MM structures consist of two gold films (30 nm thick) separated by a dielectric interlayer (160 nm thick Ge₂Sb₂Te₅). Here, we simulate two sets of multilayer MMs starting from the square periodic MDM-ENA in which the elliptical holes are exactly at the sites of the square lattice (see Fig. 1(a)). The unit cell of the structure is shown in Fig. 1(b) where both horizontal lattice constant (L_x) and vertical lattice constant (L_y) are set as 400 nm (L_x = L_y = 400 nm). The longer diameter of the elliptical hole is 320 nm (d₁ = 320nm) and the shorter diameter of the elliptical hole is 150 nm (d₂ = 150nm). In Fig. 1(c), we change L_x from 400nm to 700nm while keeping L_y fixed at 400 nm in order to create a rectangular periodic ENA. Figure 1(d) shows the unit cell of the structure where the elliptical holes (d₁ = 320nm, d₂ = 150nm) are occupying the sites of the rectangular lattice. For both structures, β is a cross-section plane of the structure, and the elliptical holes are periodically arranged in both the x and y directions. The structures are considered to be suspended in a vacuum, which can be achieved by deep etching of a silicon support substrate. Au was selected as the metal due to its stability and low ohmic loss. The Au bottom layer interacts with the upper Au layer, giving rise to a closed loop of displacement current (J_D) and a localized electromagnetic (EM) field within the dielectric interlayer [37]. The simulation was performed by the commercial software COMSOL, which is based on the Finite Element Method (FEM). The dielectric properties of Au, as given by Johnson & Christy, were used [44]. The simulation considers structures that are excited by a source with a wavelength range from 1200 nm to 3200 nm, propagating along the negative z direction with the E-field polarized in the y direction as shown in Fig. 1(a). A light source repetition rate of f_r = 25kHz was used whilst the light fluence illuminating the sample from a single pulse is written as [45]

 

Fig. 1 (a) Schematic of the MDM structure consisting of a 160nm thick Ge₂Sb₂Te₅ dielectric layer between two 30nm thick Au films perforated with a square array of elliptical holes suspended in a vacuum. (b) Illustration of the element of ENA, the horizontal lattice constant (L_x) and vertical lattice constant (L_y) are 400nm (L_x = L_y = 400nm) and hole diameters are d₁ = 320nm, d₂ = 150nm. (c) Schematic of the MDM structure consisting of a 160nm thick Ge₂Sb₂Te₅ dielectric layer between two 30nm thick Au films perforated with a rectangular array of elliptical holes suspended in a vacuum. (d) Illustration of the element of ENA, the lattice constants are L_x = 700nm, L_y = 400nm, hole diameters are d₁ = 320nm, d₂ = 150nm.

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The real, ε₁(ω) and imaginary, ε₂(ω) parts of the dielectric function of Ge₂Sb₂Te₅ at different phases are obtained from the experimental data in Ref [41]. and for the M-IR spectral range the dielectric function is shown in Fig. 2; as can be seen there is a very large change in the dielectric function’s real component. Importantly, Ge₂Sb₂Te₅ has experimentally shown more than a billion cycles of reversible phase transition [46], which is clearly of practical importance when designing modulation devices.

 

Fig. 2 Dielectric constant (a) ε₁(ω) vs wavelength, (b) ε₂(ω) vs wavelength for both amorphous and crystalline phases of Ge₂Sb₂Te_5.

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3. Results and discussions

Figure 3 shows the simulated transmittance and reflectance of the MDM-ENA with both a square lattice (L_x = L_y = 400nm) and rectangular lattice (L_x = 700nm, L_y = 400nm) respectively where the dielectric layer is amorphous Ge₂Sb₂Te₅. As can be seen, the square periodic MDM-ENA exhibits a FR at the wavelength of 2090 nm (902THz) (denoted as P₁ mode) with a transmittance peak of 0.33 and a spectral width of 17 THz, leading to a Q factor of 53. The Q factor is calculated by Q = ω / ∆ω, where ω is resonance frequency and ∆ω is bandwidth at 3 dB below the maximum [47]. When changing L_x from 400 nm to 700 nm, the FR at the wavelength of 2025 nm (931THz) (denoted as P₂ mode) becomes sharper. It has a narrower spectral width of 9 THz with a higher Q factor of 103. This shows how a rectangular lattice can enhance the FR in a multilayer MM. We also show that the transmittance decreases in the rectangular periodic MDM-ENA since the impedance matching between the structure and free space becomes worse with increasing L_x, thus leading to a smaller transmittance in Fig. 3(a) and higher reflectance in Fig. 3(b). Due to the high reflectance of the rectangular periodic MDM-ENA, where the reflectance at P₂ is as large as 0.42, one could alternatively take advantage of the reflectance spectrum for the possible applications of the FRs.

 

Fig. 3 The comparison of (a) the transmittance, (b) the reflectance between square periodic MDM-ENA (L_x = L_y = 400nm) and rectangular periodic MDM-ENA (L_x = 700nm, L_y = 400nm) with amorphous Ge₂Sb₂Te₅ at normal incidence.

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In order to gain a deeper understanding of the physics of this phenomenon, we have plotted distributions of total electric field intensity$E=\sqrt{{\left|E_x\right|}^2+{\left|E_y\right|}^2+{\left|E_z\right|}^2}$, total magnetic field intensity $H=\sqrt{{\left|H_x\right|}^2+{\left|H_y\right|}^2+{\left|H_z\right|}^2}$and displacement current (J_D) along β plane at P₁ mode for amorphous square periodic MDM-ENA(L_x = 400 nm, L_y = 400 nm) in Fig. 4(a) and 4(b), and P₂ mode for amorphous rectangular periodic MDM-ENA(L_x = 700nm, L_y = 400nm) in Fig. 4(c) and 4(d). In the field maps of Fig. 4, the arrows show J_D whereas the colour shows the magnitude of the electric field and magnetic field. Figure 4(a) shows a low concentration of the total E field intensity in the dielectric interlayer and elliptical apertures, indicating a weak electric resonance. However a formation of closed J_D loops can be observed in Fig. 4(b), according to Faraday's law, magnetic dipolar modes are excited. Therefore in Fig. 4(b), the magnetic field can be efficiently confined between the two Au layers to support a magnetic resonance at which light is trapped and strongly absorbed [48]. The interaction of a electric dipole resonance (bright modes) with magnetic dipole resonance (dark modes) in the same spectral region creates a FR response, where the ENA resonator and MDM multilayer serve as the bright modes and dark modes, respectively. Once we move to a rectangular periodic MDM-ENA, in Fig. 4(d), it is seen that the total H field intensity is still confined well in the dielectric interlayer at P₂ mode. Intriguingly, Fig. 4(c) shows that total electric field intensity is more efficiently localized to excite a stronger electric resonance. Thus, for the rectangular periodic MDM-ENA, the overlapping of the magnetic and enhanced electric dipolar moment gives rise to a sharper FR with the increased Q factor of 103 compared to the square periodic MDM-ENA with a Q factor of 53.

 

Fig. 4 3D- FEM simulation of (a) total electric field intensity distribution, (b) total magnetic field intensity distribution and J_D distribution along β plane for the square periodic MDM-ENA (Lx = Ly = 400nm), at normal incident angle where λ = 2090nm; Simulation of (c) total electric field intensity distribution, (d) total magnetic field intensity distribution and JD distribution for rectangular periodic MDM-ENA (Lx = 700nm, Ly = 400nm) at normal incident angle where λ = 2025nm.

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Figure 5(a) shows the evolution of FRs in transmittance and reflectance spectra of the rectangular periodic MDM-ENA at normal incidence, in transiting the state of Ge₂Sb₂Te₅ from amorphous to the metastable cubic crystalline state. With the phase change of Ge₂Sb₂Te₅, the FR at resonance wavelength of 2025 nm (P₂ mode) shifts to 2880 nm (denoted as P₃ mode). The two resonance wavelengths of 2025 nm and 2880 nm are attributed to the magnetic responses of the multilayer structure. Figure 5(b) presents the reflectance of the structure for different states of Ge₂Sb₂Te₅. The Ge₂Sb₂Te₅ variable dielectric function gives rise to a concomitant tunability in the metamaterial absorbance. We also find that the dip of the reflectance increases when Ge₂Sb₂Te₅ changes from amorphous to crystalline in addition to a shift, owing to a reduction in the impedance matching of the structure to vacuum. In addition, it can be seen that the resonance peak broadens which we believe is due to increased damping of the plasmon resonance [29]_.

 

Fig. 5 The comparison of (a) the transmittance, (b) the reflectance between rectangular periodic MDM-ENA with amorphous Ge₂Sb₂Te₅ and crystalline Ge₂Sb₂Te₅.

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In Fig. 6, we show the total electric field E, total magnetic field H and displacement current J_D associated with the resonance wavelengths of 2025nm (P₂ mode) for the amorphous Ge₂Sb₂Te₅ and 2880nm (P₃ mode) for the crystalline Ge₂Sb₂Te₅. It can be seen that E, H and J_D in the crystalline phase, shown in Fig. 6(c) and 6(d), are similar to the amorphous phase shown in Fig. 6(a) and 6(b). This implies that the interference between electric and magnetic resonance dipoles is also maintained to create the FR for the crystalline state. The localized electric and magnetic fields of crystalline Ge₂Sb₂Te₅ are attenuated and smaller than the amorphous Ge₂Sb₂Te₅, implying weaker electric and magnetic resonance moments in the crystalline phase. The interaction between the weaker electric and magnetic resonances broadens the FR in the crystalline phase thus reducing the Q factor to 93. Nonetheless, it is still larger than for the square periodic MDM-ENA with the amorphous state (Q = 53).

 

Fig. 6 3D- FEM simulation of (a) total electric field intensity distribution, (b) total magnetic field intensity distribution and J_D distribution along β plane for the amorphous rectangular periodic MDM-ENA where λ = 2025nm. (c) total electric field intensity distribution, (d) total magnetic field intensity distribution and J_D distribution for the crystalline rectangular periodic MDM-ENA where λ = 2880nm

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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 rectangular periodic MDM-ENA. To show this, a heat transfer model developed from our previous work [39], is used here to investigate the temporal variation of temperature of Ge₂Sb₂Te₅ layer at normal incidence. Figure 7 shows the heat source power Q_s(r, t) and the temperature of the amorphous Ge₂Sb₂Te₅ layer, where the structure is located at the center of light source. The numerical simulation shows that the temperature within the amorphous Ge₂Sb₂Te₅ dielectric layer is a function of the incident radiation flux and can exceed the amorphous to crystalline phase transition temperature of 433K (the phase transition point of Ge₂Sb₂Te₅) after 0.38 ns and has a maximum temperature of 469K after 0.68 ns under a threshold incident flux of 3.2μW/μm². Due to heat dissipation to the surroundings, the temperature starts dropping after 0.68ns before the next pulse arrives.

 

Fig. 7 3D- FEM simulation of heat power irradiating on an amorphous rectangular periodic MDM-ENA located at the beam center, where the solid red line presents the heat power irradiating on the structures under normal incident intensity of 3.2 μW/μm², the dash red line is the temperature of the amorphous Ge₂Sb₂Te₅ layer during one pulse

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The temperature distributions of the structure at 0.38 ns and 0.68 ns along the plane β are shown in Fig. 8(a) and 8(b) respectively. One can observe that the temperature within the amorphous Ge₂Sb₂Te₅ layer is uniform, and the dominant temperature gradient is towards the top and bottom Au films.

 

Fig. 8 The temperature distribution of the unit cell of an amorphous rectangular periodic MDM-ENA along β plane at (a) 0.38ns and (b) 0.68ns, where the color image indicates the temperature distribution and the arrows indicate the heat flux.

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To further test the influence of the hole's shape on the FRs and fast tuning capability, in Fig. 9 we have performed a comparison of the reflectance between the MDM-ENA and round nanohole array(RNA) penetrated through the MDM multilayers, where the lattice is rectangular(L_x = 700nm, L_y = 400nm) and the dielectric layer is amorphous Ge₂Sb₂Te₅. For the circular case shown in Fig. 9(b), the diameter of the aperture is d₃ = 220nm to exhibit the same open area as the elliptical holes(d₁ = 320nm, d₂ = 150nm) shown in Fig. 9(a). As can be seen in Fig. 9(c), the MDM–RNA exhibits a FR at the wavelength of 1925 nm(979THz)(denoted as P₄ mode) with a spectral width of 23THz, resulting in a Q factor of 43 which is smaller than both the rectangular periodic MDM-ENA at P₂ mode(Q = 103). It implies that although the MDM-RNA can still excite a FR once the symmetric round holes are occupying the sites of the rectangular lattice, the FR can be further improved using the asymmetric elliptical holes.

 

Fig. 9 (a) Schematic of the MDM-ENA consisting of a 160nm thick amorphous Ge₂Sb₂Te₅ dielectric layer between two 30nm thick Au films, the lattice constants are L_x = 700nm, L_y = 400nm, hole diameters are d₁ = 320nm, d₂ = 150nm; (b) Schematic of the MDM-RNA consisting of a 160nm thick Ge₂Sb₂Te₅ dielectric layer between two 30nm thick Au films, the lattice constants are L_x = 700nm, L_y = 400nm, hole diameters are d₃ = 220nm;(c)the comparison of the reflectance between the MDM-ENA and MDM-RNA with amorphous Ge₂Sb₂Te₅ at normal incidence.

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In order to understand the mechanism of this phenomenon, we have plotted the distributions of E, H and J_D along the β plane at the resonant wavelengths of 2025nm(P₂ mode) in Fig. 10(a) and 10(b) and 1925nm(P₄ mode)in Fig. 10(c) and 10(d). It shows that the MDM-RNA presents a much lower concentration of both E and H fields in the dielectric spacer and apertures, hence possessing smaller electric resonance and magnetic resonance than the MDM–ENA. The overlap of these smaller electric and magnetic dipolar moments results in a weaker interference of the resonances, thus giving rise to a FR with a lower Q factor.

 

Fig. 10 3D- FEM simulation of (a) total electric field intensity distribution, (b) total magnetic field intensity and J_D distribution for the amorphous rectangular periodic MDM-ENA where λ = 2025nm;(c) total electric field intensity distribution, (d) total magnetic field intensity and J_D distribution along β plane for the amorphous rectangular periodic MDM-RNA where λ = 1925nm.

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Meanwhile, the much lower concentration of the E and H field intensity in the dielectric layer of the MDM-RNA indicates a small absorbance thus lowering the phase transition efficiency. In Fig. 11, the temporal variations of temperature of Ge₂Sb₂Te₅ layer of both the MDM-RNA and MDM-ENA at normal incidence are depicited. It shows that the temperature within the amorphous Ge₂Sb₂Te₅ dielectric layer of the MDM-ENA can obtain the phase transition temperature of 433K at 0.38 ns, whereras the MDM-RNA will not approach this temperature and has a maximum temperature of 382K after 0.62 ns under the incident flux of 3.2 μW/μm².

 

Fig. 11 3D- FEM simulation of heat power irradiating on an amorphous rectangular periodic MDM-ENA and MDM-RNA located at the beam center, where the solid red line presents the heat power irradiating on the rectangular periodic MDM-ENA under normal incident intensity of 3.2 μW/μm², the dash red line is the temperature of the amorphous Ge₂Sb₂Te₅ layer of the MDM-ENA during one pulse; the solid blue line presents the heat power irradiating on the rectangular periodic MDM-RNA under normal incident intensity of 3.2 μW/μm²,the dash blue line is the temperature of the amorphous Ge₂Sb₂Te₅ layer of the MDM-RNA during one pulse.

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4. Conclusions

In conclusion, we present numerical modelling of a fast and low-energy consumption all-optical tunable FR in a metamaterial composed of an elliptical nanohole array embedded through a metal/dielectric/metal multilayer. The Q factor of FR in 3D MDM-ENA can be significantly increased by modifying the cell’s primitive lattice from square to rectangular. Replacing the dielectric spacer with an active phase-change material(Ge₂Sb₂Te₅) allows control of FRs in the structure. In particular, the central wavelength of FRs can be tuned in a range of 855 nm in the M-IR regime. This tunable effect is due to the Ge₂Sb₂Te₅ phase transition from amorphous to crystalline. Our model predicts that the Ge₂Sb₂Te₅ can be heated to its amorphous to cubic phase transition temperature with a laser pulse that is 0.38 ns in duration and a low intensity of just 3.2μW/μm². Our design allows for a new approach of ultralow-power and ultrafast photonic nanodevices and may have potential applications in various fields such as all-optical tunable sensors, all-optical routers, all-optical logic gates and all-optical switching.