1. Introduction

A toroidal dipole is produced by poloidal currents with a corresponding closed head-to-tail magnetic loop. It is an elementary electromagnetic source, and is usually overlooked in natural media because it arises against a background of much stronger electric and magnetic dipoles [1,2]. A few years ago, the dynamic toroidal dipole response was experimentally demonstrated using metamaterials in the microwave region [1]. It has subsequently been applied in different frequency regions by employing various nanostructures, including dielectric and metallic metamaterials [3–21]. The interference between the toroidal and electric dipoles can suppress the far-field radiation and create a nonradiative anapole mode [22–32], which was also first verified experimentally in the microwave range using metallic split-ring metamaterials [22]. Miroshnichenko et al. extended this concept to the visible region using dielectric nanoparticles in 2015 [23]. Owing to their pronounced confinement of energy, nanostructures supporting anapoles have shown great potential in applications such as harmonic generation [33], Raman scattering enhancement [34], nanolasers [35], and sensors [36].

Active metadevices play an increasingly important role in nanophotonics, as they open an entirely new area of applications. An efficient method of achieving tunable metadevices is to introduce phase changing materials such as ${{\rm Ge}_{2}{\rm Sb}_{2}{\rm Te}_{5}}$ (GST), ${\rm{VO}_2}$, or GeTe [37–39], which can offer flexible control of the optical properties when they transition between different crystalline states. Among them, GST has attracted widespread attention in recent years owing to its quick response, good stability, and significant refractive index contrast [37,40]. What makes GST a better candidate for active devices is that it has zero-static-power and requires no power to maintain its product, which enables a lot of applications such as thermal camouflage [41,42]. While other phase changing materials, such as ${\rm{VO}_{2}}$, need a constant power to maintain their states [43]. Considerable effort has been made recently to investigate active metasurfaces associated with GST [44–60]. For example, in 2016, Chu et al. theoretically studied the switchable electric dipole resonance of GST rods [45]; then Karvounis et al. experimentally realized a switching contrast ratio of up to 7 dB in a laser-induced GST metasurface [46]. Li et al. [47–50] and Cao et al. [52] also realized thermal emission switching in a series of metasurfaces based on GST in the past few years. Tian et al. recently realized broadband mode shifting between an electric dipole resonance and an anapole state, and obtained an optical switch with high extinction contrasts in structured GST [59]. However, these works focused only on the switching characteristic of resonant nanostructures. A more interesting phenomenon is that phase changing materials may significantly affect the multipole interference, thus affording flexible radiation manipulation. Very recently, Lepeshov et al. demonstrated the transitions between superscattering and nonradiative cloaking states arising from multipole interference in phase changing materials in different states [61]. However, further research on this topic is still necessary given the important role of actively tunable multipole interference in on-demand radiation manipulation.

In this work, we theoretically study the manipulation of optical radiation in a hybrid Si-GST metasurface. First, a Si metasurface consisting of a double-nanodisk array that supports a strong toroidal dipole resonance at 1550 nm is designed and discussed in depth. Then we add a GST thin film under the Si nanodisks to manipulate the amplitude of the toroidal dipole and thus produce observable destructive interference between the toroidal dipole and electric dipole, which results in significant optical radiation suppression and the creation of a weak anapole mode. Moreover, by controlling the crystallization ratio of GST, an active manipulation of optical manipulation can be obtained. Similar behavior is also produced using GST of different thicknesses. Multipole decomposition in Cartesian coordinates is employed to calculate each moment and its contribution to the far-field radiation. In addition, the near-field distributions and radiation pattern at the resonant wavelength are also illustrated to extend the discussion.

2. Toroidal dipole response in Si metasurface

As discussed above, the toroidal dipole response is usually neglected. Here, to enhance its contribution, double Si nanodisks are arranged on a ${\rm{SiO}_{2}}$ substrate to obtain two anti-phase electric fields, as shown in Fig. 1(a). Simulations using the finite-difference-time-domain (FDTD) method and COMSOL Multiphysics are employed to calculate the optical properties of this metasurface (for details, see Appendix A). The thickness and radius of the nanodisks are both fixed at 210 nm, and the gap between them is 50 nm. The lattice constant of the unit cell is 1 $\mu$m. Figure 1(b) shows the simulated transmission spectrum; the sharp resonance peak at a wavelength of approximately 1550 nm is governed by the symmetry-protected bound state in the continuum (BIC) as explained in Appendix B. The resonant position is most sensitive to the radius of Si nanodisks, because the scattering of light by Si nanodisks is governed by the Mie resonance, which oscillates along the transverse direction of disks. The strength of this resonance varies with the changing gap size, given that it is governed by the symmetry-protected BIC. Figure 1(c) shows the electric field distribution on the nanostructure at the resonant wavelength, which demonstrates that considerable energy is trapped inside the subwavelength nanodisks. Two distinct circular displacement currents with opposite orientations are observed in the $x$-$y$ plane, and thus excite opposite magnetic dipoles along the $z$ axis, as illustrated in Fig. 1(d). In combination with the incident light, a circular magnetic loop in the $x$-$z$ plane produces strong toroidal dipole excitation along the $y$ axis. Finally, the collective oscillations of this nanodisk array form the strongest toroidal response. To further analyze this resonance, electromagnetic multipole expansion in Cartesian coordinates is performed (for details, see Appendix A), and the calculated scattered power of different multipoles is shown in Fig. 1(e). It is clear that at the resonant wavelength, the contributions of the magnetic dipole and electric quadrupole are strongly suppressed. The toroidal dipole dominates and is accompanied by a notable contribution from the magnetic quadrupole, because both of them are induced by a pair of counter-oriented magnetic dipoles [3,29]. Note that the toroidal dipole response along the $y$ axis is predominant, as illustrated in Fig. 6(a), which is consistent with the near-field analysis above. The three-dimensional far-field radiation pattern at the resonant wavelength is illustrated in Fig. 1(f) and shows strong scattering toward the $x$ axis. In addition, the scattered power of the electric dipole is also strong, especially for the $y$-directed component, as shown in Fig. 6(b), which is a significant factor for realizing radiation manipulation by controlling the coupling of the toroidal and electric dipoles.

 

Fig. 1. (a) Geometry of the unit cell of the designed metasurface. (b) Simulated transmission spectrum. (c), (d) Calculated electric and magnetic field distributions at the resonant wavelength, respectively. The arrows represent the field direction, and the color scales correspond to the field intensity. (e) Total scattered power (Total) and the contributions of the electric dipole (P), magnetic dipole (M), toroidal dipole (T), magnetic quadrupole [${\rm Q}^{(m)}$] and electric quadrupole [${\rm Q}^{(e)}$]. The log scale is used on the $y$ axis to clearly distinguish the contributions of each moment. (f) Far-field radiation pattern at the resonant wavelength.

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3. Optical radiation manipulation using GST with different crystallization ratios

Next, we investigate the effect of GST with different crystallization ratios on the optical radiation of the metasurface. As shown in Fig. 2(a), a GST film is added to the ${\rm{SiO}_{2}}$ substrate, with Si nanostructures lying on it. This device can be fabricated by growing amorphous GST and Si films on the ${\rm{SiO}_{2}}$ substrate using magnetron sputtering [49,50], followed by patterning nanodisks on the top Si layer. The amorphous GST can be gradually transformed into crystalline GST when annealed around 160$^{\circ }$ [49,62]. When partial crystallization is taken into account, continuous multi-level radiation modulation can be realized. By varying the energy applied to the GST and the stimulus duration, the effective dielectric constant of this material is changed owing to nucleation in $a$-GST, which results in multi-level electro-optical properties. The effective dielectric constants of GST with various crystallization ratios are modeled using the Lorentz-Lorenz relation according to the effective-medium theory [44,45]:

 

Fig. 2. (a) Geometry of the unit cell of the designed metasurface with GST film. (b) Transmission spectra of GST with different crystallization ratios.

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Fig. 3. Total scattered power and contributions of different multipoles at each crystallization ratio.

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Figure 2(b) shows the calculated transmission spectra for different $m$ values. These resonances are still strong, and their specific electric and magnetic fields are also the same as those without GST, demonstrating that the strong toroidal dipole excitation is maintained, as confirmed for $a$-GST (Fig. 8). With increasing crystallization ratio $m$, the resonance peak is red-shifted owing to the increase in the refractive index of the GST film, as illustrated in Fig. 7(a), where the spectral shift is 110 nm when $a$-GST transitions to the $c$-GST state. In addition, a lower extinction ratio and broader resonance can also be observed owing to the higher absorption loss of GST with larger crystallization ratios, as shown in Fig. 7(b). To clearly identify the contributions to the far-field radiation, we calculate the scattered power of each multipole and the corresponding total scattered power for different $m$ in Fig. 3. As $m$ increases, the toroidal dipole radiation is gradually suppressed. However, for the other multipoles, especially the electric dipole, this suppression effect is relatively weak. Thus, an interference channel for the electric and toroidal dipoles is opened, in contrast to the metasurface without GST, resulting in tunable radiation manipulation. For $m$=0, a dip appears in the total scattered power spectrum when the scattered powers of the electric and toroidal dipoles are equivalent ($I_P=I_T$). The corresponding phase difference at this wavelength is $\Delta \varphi =\varphi (P_y)-\varphi (ikT_y)=2.55$ rad. So the production of this dip is mainly due to the destructive interference of the electric and toroidal dipoles owing to their similar far-field scattering patterns. This phenomenon can also be observed for GST with other crystallization ratios. Note that when the electric and toroidal dipole moments satisfy $\vec P=-ik\vec T$, their radiation fields exhibit complete destructive interference, creating an anapole state [23,32]. When the crystallization ratio of GST ($m$) is 60$\%$ (Fig. 10), a pronounced resonant dip appears in the total scattered spectrum at a wavelength of approximately 1579.4 nm. This feature is attributed to the incomplete destructive interference between the electric and toroidal dipoles when $I_P=I_T$, and the corresponding phase difference at this position is $\Delta \varphi =2$ rad, which ultimately creates a weak anapole mode [29]. Note that, $\Delta \varphi$ reaches a maximum of 2.4 rad at 1581.8 nm instead of at the scattering minimum, because the larger scattered power difference between the electric and toroidal dipoles ($\Delta I_{P,T}$) at this wavelength weakens the destructive interference effect. In addition, a peak appears at 1576.6 nm owing to a relatively large $\Delta I_{P,T}$ and a reduced phase difference. This peak vanishes for $m$=80$\%$ and $c$-GST, because the smaller $\Delta I_{P,T}$ at these states induces stronger destructive interference and reduces the radiation. For $m$=1, the scattering of the toroidal dipole is suppressed dramatically, while the radiation of the electric dipole almost remains the same. Therefore, the toroidal dipole scatters less power into the free space than the electric dipole and there is even no point of $I_P=I_T$.

 

Fig. 4. Total scattered power and contributions from different multipoles (solid lines) for GST of different thicknesses. The corresponding transmission spectra (dark blue dashed lines) are also shown.

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4. Optical radiation manipulation using GST of different thicknesses

In the study above, we found that active optical radiation manipulation of resonant metasurfaces can be realized using GST with different crystallization ratios by introducing significant refractive index contrasts and absorption. Here, we supplement the demonstration of the tunable mechanism by investigating the radiation properties of the metasurfaces when the thickness of the GST film is changed. Figure 4 shows the multipole interference for different GST thicknesses ($h$=20, 30, 40 and 50 nm), with $m$=0 and a nanodisk height of 210 nm. The dark blue dashed line represents the transmission. As the thickness of the GST film increases, the resonance is also red-shifted because the effective refractive index of the nanostructures increases. A broader bandwidth and reduced extinction ratio are ascribed to a larger loss in the GST thin film. According to the scattered power spectra of the multipoles, the toroidal response is gradually suppressed, and the destructive inference between the toroidal and electric dipoles becomes remarkable; ultimately, a weak anapole mode is produced. This mode will disappear entirely when the thickness of GST is too high owing to the larger material loss. These results, which supplement the explanation of the phenomena produced using GST at different crystallization ratios, also confirm that the variation of the refractive index and absorption play significant roles in the active radiation manipulation. Note that the thickness of the GST film is fixed once the metasurface is fabricated. Hence, controlling the crystallization ratio of the GST is a more flexible method of manipulating the optical radiation.

5. Conclusion

In conclusion, we investigate the optical radiation manipulation of a resonant Si metasurface by introducing a phase changing material (a GST film). A double-nanodisk array is designed to support strong toroidal dipole excitation at a wavelength of 1550 nm. When the GST film is added, the toroidal response is suppressed owing to material loss, whereas the electric response remains almost the same. Thus, a distinct destructive interference effect between the toroidal and electric dipoles suppresses the total scattered power, exciting a weak anapole mode. The strength and position of this mode can be flexibly controlled by changing the crystallization ratio of the GST film. In addition, the effect of the GST thickness on the optical radiation is also investigated to demonstrate the tunable mechanism. Our work is the first to suggest that introducing a phase changing material can produce a weak anapole mode from a metasurface supporting strong toroidal responses. Our findings reveal the physics behind active optical radiation manipulation and may provide a potential route to tunable metadevices with broader applications.

Appendix

A. Electromagnetic simulations and multipole decomposition

The FDTD method is used to calculate the transmission spectra, planar field distributions, and current density distribution in the nanostructures. The steric field distributions and three-dimensional far-field radiation pattern in Fig. 1 are obtained using COMSOL Multiphysics. In the simulation, periodic boundary conditions are set in the $x$ and $y$ directions, and perfectly matched layers are set in the $z$ direction. The incident light propagates in the $z$ direction, and the electric field is parallel to the $y$ direction. The complex dielectric constants of Si and ${\rm{SiO}_{2}}$ are taken from Palik [63].

Cartesian electromagnetic multipole decomposition is used to analyze each moment and its contribution to the far-field radiation. The multipole moments can be defined as [3,29] electric dipole moment:

(2)$$\vec P = \frac{1}{i\omega}\int {\vec j{d^3}r} ,$$

magnetic dipole moment:

(3)$$\vec M = \frac{1}{2c}\int {(\vec r \times \vec j){d^3}r} ,$$

toroidal dipole moment:

(4)$$\vec T = \frac{1}{10c}\int {[(\vec r \cdot \vec j)\vec r - 2{r^2}\vec j]{d^3}r} ,$$

electric quadrupole moment:

(5)$$Q_{\alpha \beta }^{(e)} = \frac{1}{2i\omega }\int {[{r_\alpha }{j_\beta } + {r_\beta }{j_\alpha } - \frac{2}{3}(\vec r \cdot \vec j){\delta _{\alpha ,\beta }}]{d^3}r} ,$$

magnetic quadrupole moment:

(6)$$Q_{\alpha \beta }^{(m)} = \frac{1}{3c}\int {[{{(\vec r \times \vec j)}_\alpha }{r_\beta } + ({{(\vec r \times \vec j)}_\beta }{r_\alpha })]{d^3}r} ,$$

where $c$ and $\omega$ are the speed and angular frequency of light, respectively, and $\alpha , \beta =x, y, z$. $\vec {j}=-i\omega \epsilon _{0} (n^2-1) \vec {E}$ is the current density distribution in a unit cell. The far-field scattered power of these multipole moments can be calculated using the following formulas: ${I_P} = \frac {2{\omega ^4}}{3{c^3}}{\left | \vec P \right |^2}$, ${I_M} = \frac {2{\omega ^4}}{3{c^3}}{\left | \vec M \right |^2}$, ${I_T} = \frac {2{\omega ^6}}{3{c^5}}{\left | \vec T \right |^2}$, ${I_{Q^{(e)}} = \frac {\omega ^6}{5{c^5}}\sum {\left | {Q _{\alpha \beta }^{(e)}} \right |}^2}$, and ${I_{Q^{(m)}} = \frac {\omega ^6}{40{c^5}}\sum {\left | {Q _{\alpha \beta }^{(m)}} \right |}^2}$. The total scattered power of the multipole moments can be given as [29]

(7)$${I_{total}} = I_P+I_M+\frac{4{\omega ^5}}{3{c^4}}(\vec P \cdot \vec T)+I_T+I_{Q^{(e)}}+I_{Q^{(m)}}+O(\frac{1}{c^5}) ,$$

where $\frac {4{\omega ^5}}{3{c^4}}(\vec P \cdot \vec T)$ is the interference term of the electric and toroidal dipoles, and $O(\frac {1}{c^5})$ has a small value.

B. Demonstration of symmetry-protected BIC

Symmetry-protected BICs exist at the $\Gamma$ point of the reciprocal space based on the symmetry incompatibility between the bound state and the continuum [64–69], whose Q-factors satisfy the following formula [64,65,68]:

(8)$${Q\propto\alpha^{{-}2}},$$

where $\alpha$ is the asymmetry parameter defined as $\alpha =D_0/D_i$. The lattice constant of the unit cell is 1 $\mu$m. $D_0$ is 500 nm long, equivalent to half of the lattice constant and located at the center of the unit cell; $D_i$ represents the distance between centers of these two nanodisks. When $D_i$ deviates from $D_0$, the symmetry of the structure is perturbed, leading to the transformation of a nonradiative BIC mode into a leaky resonance. Figure 5 shows the calculated Q-factors of the resonance at different asymmetry parameters $\alpha$, where purple balls and magenta pentagrams represent results when $D_i<D_0$ and $D_i>D_0$, respectively. The gray line shows an inverse quadratic dependence of $\alpha$ as described in Eq. (8), matching well with the variation of calculated Q-factors. Therefore, the sharp resonance excited by this metasurface is governed by the symmetry-protected BIC.

 

Fig. 5. Log-log plot of radiative Q-factors as a function of the asymmetry parameter $\alpha$.

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C. Scattered power of toroidal and electric dipole components

 

Fig. 6. Scattered power of toroidal and electric dipole components along the $x$, $y$, and $z$ directions. The $y$-directed toroidal and electric dipoles clearly make the largest contributions.

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D. Refractive index and extinction coefficient of GST with different crystallization ratios

 

Fig. 7. Refractive index $n$ and extinction coefficient $k$ of GST with different crystallization ratios.

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E. Electric and magnetic field distributions for $a$-GST

 

Fig. 8. (a) Electric field distributions in the $x$-$y$ plane at the resonant wavelength for $a$-GST. (b) Corresponding magnetic field distribution in the $x$-$z$ plane. Black dashed lines denote the boundaries of the nanostructure region. White arrows represent the field direction, and the color scale corresponds to the field intensity. The choice of cutting-planes is represented by the green dashed line.

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F. Transmission spectra of metasurfaces with GST at different positions

The transmission spectra of metasurfaces with GST at different positions are shown in Fig. 9. Figure 9(a) shows the result when the GST film lies under silicon nanodisks, corresponding to the situation investigated in this work. In Fig. 9(b), GST is deposited on Si nanodisks and ${\rm{SiO}_{2}}$ substrate. And in Fig. 9(c), GST is only deposited on Si nanodisks. It can be observed that the same mode is excited at all these three situations, with only slight differences in the resonant position and strength because of the different effective refractive index and loss of nanodisks introduced by GST.

 

Fig. 9. The transmission spectra of metasurfaces with GST at different positions.

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G. Multipole decomposition and phase difference spectra

 

Fig. 10. Total scattered power and contributions of electric and toroidal dipoles (solid lines), and phase differences (dashed lines) of the electric and toroidal dipole moments along the $y$ direction. (a) $m$=60$\%$; (b) $m$=80$\%$.

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Funding

National Natural Science Foundation of China (11764008, 11947065, 51567017); Natural Science Research Project of Guizhou Minzu University ([2018]23, GZMU[2019]YB20, GZMU[2019]YB22, GZMU[2019]YB30); Interdisciplinary Innovation Fund of Nanchang University (2019-9166-27060003).

Disclosures

The authors declare no conflicts of interest.

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