Active control of anapole states by structuring the phase-change alloy Ge2Sb2Te5

High-index dielectric nanoparticles supporting a distinct series of Mie resonances have enabled a new class of optical antennas with unprecedented functionalities. The great wealth of multipolar responses has not only brought in new physical insight but also spurred practical applications. However, how to make such a colorful resonance palette actively tunable is still elusive. Here, we demonstrate that the structured phase-change alloy Ge2Sb2Te5 (GST) can support a diverse set of multipolar Mie resonances with active tunability. By harnessing the dramatic optical contrast of GST, we realize broadband (Δλ/λ ~ 15%) mode shifting between an electric dipole resonance and an anapole state. Active control of higher-order anapoles and multimodal tuning are also investigated, which make the structured GST serve as a multispectral optical switch with high extinction contrasts (>6 dB). With all these findings, our study provides a new direction for realizing active nanophotonic devices.

Supplementary Note 2: Multipole expansion for GST spheres with progressive crystallinities and the effects of loss To examine the physical origins of the dynamic scattering bright and dark states in the GST spheres, in Supplementary Fig. 2a we plot the multipole expansion of the scattering response of the GST sphere with varied crystallinities. It is observed that the progressive shifting between the scattering maxima and minima is indeed attributed to the excitation of the ED and the anapole states. Supplementary Fig. 2b provides the total electric field distribution of three representative scattering states (MD, ED, and anapole) as supplements to Fig. 1d-f in the main text. Note that the GST material is lossy in the mid-infrared range, here we also analyze the effects of loss on different Mie states. As shown in Supplementary Fig. 2a, the partial scattering of ED features an evident Fano line shape due to the interference between a resonant eigenmode (internal) and non-resonant background pathway (external) [3]. To extract the Q-factor, the partial scattering contribution of ED at the anapole states was fitted into a Fano line shape given by [4]: with ω 0 is the central resonant frequency; Γ is the full-width at half-maximum (FWHM) of the resonance; q is the asymmetry parameter describing the ratio between the resonant scattering and the non-resonant background. An excellent agreement between the Mie calculation and the Fano fit can be seen in Supplementary Fig. 3a. For all the crystallinities, the asymmetry parameter q is close to 1, indicating the resonant and the non-resonant pathways have similar amplitudes. The Q-factor was then determined by Q = ω 0 /Γ, as plotted in Supplementary Fig. 3b. We can then quantitatively conclude that the ED scattering does not exhibit dramatic broadening linewidths with increasing crystallinities. This is because a larger crystallinity in GST would bring in increases in both real and imaginary parts of the refractive index n = n 0 + ik. For the ED resonance, a larger n 0 would make the structure a more perfect scatterer with a smaller radiative damping and thus lead to a higher Q-factor [5]. Meanwhile, a larger k would result in larger dissipative damping with a smaller Q-factor. Such a trade-off explains why all the ED resonances in Figs. 1, 3 and 4 do not show substantial linewidth broadening and also accounts for the appearance of the maximized Q-factor at C = 50% in Supplementary Fig. 3b. In contrast to the asymmetric Fano line shape of the ED contribution, the MD response manifests a symmetric Lorentzian line shape. This is because the internal resonance arising from the circular displacement currents at the MD state is much stronger than the background pathway, thereby dominating in the interference with q 1 in Eq. (1). Thus, we can directly obtain the FWHM from the spectra and determine the Q-factor of the MD resonances, as shown in Supplementary Fig. 3c. A clear decline in the Q-factor with increasing crystallinities could be seen. We attribute this response to the strong resonant feature at MD states and its large field concentration inside the particle. As such, the increase in k would have a much larger impact on the linewidth than the increase in n 0 , which significantly decreases the Q-factor.

Supplementary Note 3: tunable scattering directionality of GST spheres
The broadband active tuning of the Mie resonances in the structured GST can lead to a variety of interesting phenomena. Here we exemplify this point by considering the same GST nanosphere (R = 450 nm) as in Fig. 1. The scattering spectra of the GST sphere with three different crystallinities C are plotted in Supplementary Fig. 4a, showing the investigated wavelength λ c at 3.97 µm with a dotted line. To depict the far-field scattering patterns, the same coordinate as in Fig. 1 is adopted, in which the incident wave propagates along the x-axis with the polarization of the electric field along the z-axis. When the GST sphere is at the amorphous state, it supports a magnetic dipole resonance at λ c . The far-field scattering in Supplementary Fig. 4b shows a typical radiation pattern of a magnetic dipole oriented along the y-axis. By contrast, after introducing a moderate phase change of 25%, the scattering spectrum shows an intersection between the electric and magnetic dipole contributions. The spectral overlap and equal far-field strengths of the two dipoles indicate the satisfaction of the second Kerker condition [6], as confirmed by the unidirectional scattering in the backward direction. When the phase change continues increasing, the sphere finally reaches its crystalline state with its scattering similar to that of a typical electric dipole oriented along the z axis, i.e., the scattering pattern ( Supplementary Fig. 4d) transforms in orthogonal to that of the amorphous sphere. Therefore, mode shifting between magnetic and electric dipole resonances could also be realized with the GST sphere, which may make a fundamental impact on many intriguing physical phenomena related to Mie resonances.
Supplementary Note 4: scattering efficiencies Q scat of the aGST and the 25%-cGST spheres To verify the "nearly-dispersionless" behavior of the switching effect, in Fig. 2c we plot the scattering contrast of the GST spheres with two different crystallinities, i.e. C = 0% and C = 25% and then analytically investigate the conditions for a rigorous switching (Fig. 2d). Here, as supplements, the scattering efficiencies Q scat of the aGST and the 25%-cGST spheres are provided in Supplementary Fig. 5a, b, respectively.
Supplementary Figure 5. Scattering efficiencies Q scat of amorphous (a) GST spheres and 25%-cGST (b) with varying radii R. (c) The scattering cross sectional contrast of GST spheres at the two phases, which is defined as Q contrast = Q scat-aGST /Q scat-25%-cGST . We mention that the Supplementary Fig. 5c is the same as Fig. 2c and it is provided here just for ease of reference.

Supplementary Note 5: AFM measurement of the disks' geometric profiles
The geometric profiles of the fabricated GST nanodisks were determined by AFM, as shown in Supplementary Fig. 6. We also note that the phase change of the GST material may introduce a volume reduction of ∼ 6% from the amorphous to the crystalline state in thin film [7]. However, it is not clear how such a change would behave and evolve in 3D GST nanostructures, i.e., whether it occurs homogenously along all the directions and linearly in time or not. In our study, we observed a 5% height reduction between amorphous and crystalline GST nanodisks without any noticeable changes in their lateral sizes or surface topology ( Supplementary Fig. 7a). Given the large diameter-to-height ratio of the disks in our study, such a subtle change would not influence the spectral position or the strengths of the resonances (Supplementary Fig. 7b). In this supplementary section, we discuss the impacts of the pitch size (inter-particle distance), the absorption loss of the GST material, and the existence of the substrate on the investigated scattering states and multipolar responses in GST nanodisks. correlates well with those on the scattering spectra. Supplementary Fig. 8a-c, for different pitch sizes g, the optical coupling between adjacent GST disks does not strongly influence the spectral positions of the investigated ED and anapole states. In particular, there is generally no difference between the case of g = 3 µm and g = 5 µm. In the main text, to highlight the resonances of the disks and to mitigate the influence of the CO 2 absorption (around 4.3 µm), we used the spectra with g = 3 µm.

As shown in
In Supplementary Fig. 8d-f, we provide the scattering, the absorption, and the extinction spectra of individual GST disks with different crystallinities. Indeed, as the crystallinity increases, the absorption of the GST material increases. However, given the relatively low loss of the GST material in the wavelength range of interest, the influence of the absorption is mild (e.g. contribute to ∼ 16% extinction at the ED resonance for cGST) and the extinction features (pronounced peaks and dips) correlate well with those on the scattering spectra. In Supplementary Fig. 9a-c, we compare the scattering spectra with and without the substrate. Based on the Mie theory [8], the strengths and the spectral positions of the multipolar responses are directly related to the index contrast between the dielectric material and the environment. Since the GST material possesses extremely high indices (n aGST > 4, n cGST > 6), the existence of the substrate (n CaF 2 ∼ 1.4) thereby only has a very limited impact on the spectral positions of the scattering spectra. The associated multipole expansion in the vacuum ( Supplementary Fig. 9d-f ) thus can be applied to identify the ED and the anapole modes in the experiment. It is also worth noting that our multipole expansion approach (see Methods) allows us to unambiguously identify multipolar contributions up to arbitrarily high order.

Supplementary Note 7: Tunable beam steering of a GST metasurface
In addition to the active control of anapole states and presented optical switch in the main text, here we numerically demonstrate an alternative application of GST metasurfaces composed of disk arrays for tunable and efficient beam steering. Following the general principle for designing gradient metasurfaces [9], here we first set the height of the GST disks to 600 nm and the period of a unit cell to 1800 nm. By varying the diameter of the disks, the Mie resonances supported by the disks would undergo spectral shifts and thereby exhibit varied phase response at the design wavelength λ d = 4 µm. In this way, we can introduce a linear phase gradient along the x-direction, parallel to the incident polarization, as seen in Supplementary Fig. 10. According to the generalized Snell's law [10], the incident light would be anomalously transmitted into a specific angle, as shown in the Supplementary Fig. 11a. 87.6% of the transmission is propagating along the +1 diffraction order at λ d with light in other diffraction orders being strongly suppressed. By contrast, when we introduce a 30% phase change in the GST disks, the refractive index of GST would increase and lead to dramatic redshifts of the supported resonances, thereby limiting the phase variation at λ d . As such, the GST disk arrays would support a nearly constant phase response along the interface, resulting in the metasurface exhibiting the conventional (zero-order) transmission (Supplementary Fig. 11b) with most of the light (95.4%) propagating normally. Hence, in this manner, one can realize a GST metasurface with tunable beam steering by utilizing a simple configuration of GST disks.