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1 Optically reconfigurable metasurfaces and photonic devices based on phase change materials S1: Schematic diagram of the experimental setup. A Ti-Sapphire femtosecond laser (Coherent Chameleon Vision S) generates 80 MHz trains of 85 fs pulses at 730 nm wavelength. An electro-optical modulator pulse picker (Conoptics Corp.) is used to reduce the repetition rate and generate trains of pulses of 1 MHz. The output pulse is then expanded with a telescope system and incident onto the spatial light modulator (SLM, Holoeye PLUTO), which is used to imprint computer-generated phase patterns to control the beam scanning on the sample surface. The modulated wavefronts from the SLM are transferred by a 4f telescope system (f 1 =300 mm and f 2 =280mm) to the back aperture of the objective lens (Nikon UL Plan Fluor 50, NA= 0.8) and the lens focuses the light onto the GST thin film. Optical measurements of the change in reflectance of GST film are conducted by using 633nm LED illumination, a 50 objective lens (Nikon Epiplan NA 0.7), tube lens and a CCD camera. For normal illumination of sample, a long focal length lens (f=200 mm) is inserted into the optical path to project the SLM wavefront on the sample surface. For imaging of Fresnel zone-plate, the collection objective lens is moved away from the sample surface by 50 µm to obtain the transmission hotspot image. Fig. S1 (Color online) Schematic diagram of the experimental setup. S2: The simulation of Fresnel zone-plate and super-oscillatory lens focal spot In Fig. S2.1, the angular spectrum method is used to simulate the focusing performance of Fresnel zone-plate and super-oscillatory lens. The diffracted field from each zone of the Fresnel zone-plate constructively interferes at the focus producing a diffraction-limited spot. In the super-oscillatory lens design, the irregular rings produce either constructive or destructive interference forming a hotspot with sub-diffraction-limited size, but at the expense of creating apparent sidebands. NATURE PHOTONICS 1 1

2 Fig. S2.1 (Color online) The simulation of Fresnel zone-plate and super-oscillatory lens focal spots at λ=730 nm. a,b The pixelated Fresnel zone-plate ( pixels), and its theoretical calculation of focal spot. c, The pixelated super-oscillation lens pattern ( pixels). d, Simulation result of the optical hotspot as focused by the super-oscillatory lens with 43.8 µm focal length in transmission mode. In the experimentally recorded diffraction patterns of Fresnel zone-plates and super-oscillatory lenses, we observed the hotspots on an apparent background. It is partially caused by the pixilation of the mask and the limited transmission ratio between amorphous and crystalline GST films (the crystalline GST is not completely opaque). The latter effect brings in additional amplitude modulation and will change the energy concentration ratio in the hotspot. In order to address this issue, for the case of super-oscillatory lenses we theoretically calculated the dependence of the energy concentration ratio in the hotspot on the transmission ratio of the GST film in the amorphous and crystalline states at the focal plane (z=43.8µm) of the super-oscillatory lens (discussed in Fig. 2d-f in the main text). The results are shown in Fig. S2.2. It is seen that as the increasing of t c /t a, where t c and t a are transmission efficiency of crystallized GST and amorphous GST, respectively, the energy concentrated in the hotspot is reduced monotonically, revealing more and more energy are dissipated into the sidebands of the diffraction fields. A similar tendency is observed for the Fresnel zone-plates. In case of the super-oscillatory lens the transmission efficiency at t c /t a =0.07 (λ=730nm) corresponds to an energy concentration ratio in the hotspot of around 1.06%. However, if t c /t a goes up to 0.5, the energy ratio in the hotspot is decreased significantly down to 0.14%, and therefore more intense sidebands can be observed. 2 2 NATURE PHOTONICS

3 SUPPLEMENTARY INFORMATION Fig. S2.2 (Color online) The theoretical energy concentration ratio in the super-oscillatory hotspot with varying of the transmission ratio of the crystallization and amorphous GST films (t c /t a ) at focal length of z=43.8 µm. Insets show three examples of the intensity profiles at t c /t a =0.07 (theoretical calculation based on the experimental ellipsometry data at λ=730 nm, see Section 3), 0.3 and 0.5 respectively. S3: Theoretical calculation of reflection (R), transmission (T) and absorption (A) of GST thin film (70 nm ZnS-SiO 2 /70 nm GST/70nm ZnS-SiO 2 ) Calculations have been performed using COMSOL commercial software. The reflective indexes of amorphous and crystallized GST are measured on thin film sample with ellipsometry system (Horiba UVISEL 2). The calculations of the dielectric function (in the wavelength range 400 nm to 800 nm) reveal that the reflectance is 267% larger in crystalline phase than the amorphous phase at 633 nm illumination, and the transmission is 93% lower at 730 nm. Fig S3 (Color online) The theoretical calculation of R, T and A of three layer amorphous and crystalline GST stack in visible region. S4: The simulation of wavelength multiplexing Fresnel zone-plate foci The angular spectrum method is used to model the propagation of the waves through our wavelength multiplexing devices. The simulation results show the designed lenses focusing two different optical wavelengths in spatially separated or co-located foci at the focus plane 3 NATURE PHOTONICS 3

4 of 50 µm. The sub-foci behind or before the focal plane are due to Fresnel zone-plate diffraction and interference of light. Fig. S4 (Color online) The theoretical calculation of wavelength multiplexing devices focusing at xz plane. a,b, A lens focusing two different optical wavelengths (λ=730nm, 900nm) in spatially separated foci on the focal plane of 50 µm. c,d, A lens focusing two different optical wavelengths (λ=730nm, 900nm) in the same focus plane of 50 µm. S5: Theoretical calculation of reflection and transmission of GST dielectric metamaterial (Fig. 5 a) Calculations have been performed using the COMSOL commercial software based on the dielectric permittivity data in reference [Nano Lett. 2013, 13, 3470]. Periodic and perfectly matched layer (PML) boundary conditions are used in the transverse direction and vertical direction, respectively. The simulated reflection and transmission of the dielectric metamaterial are shown in Fig. S5 with resonance at 2460 nm for horizontal (X) polarization (red and purple solid lines), and no resonance of the orthogonal (Y) polarization (black/purple dashed line), respectively. In the experiment, it is possible we do not achieve complete phase transition from amorphous to crystalline, which would lead to a smaller refractive index relative to a fully crystallized GST. Therefore we calculate the performance metamaterial of our meta-material with partially crystalized spots, which demonstrates a blue-shifted resonance and reduced modulation depth. 4 4 NATURE PHOTONICS

5 SUPPLEMENTARY INFORMATION Fig S5 (Color online) Theoretical calculation of reflection and transmission of GST dielectric metamaterial. The black/purple dashed line is the reflection/transmission of metamaterial of vertical (Y) polarization. The red/purple solid line is the reflection/transmission of fully crystallized metamaterial cell with peak at 2460 nm of horizontal (X) polarization. The blue, pink, green, dark blue and light blue lines are calculation results of partial crystallized metamaterial cells (30%, 40%, 50%, 60% and 70%), respectively. 5 NATURE PHOTONICS 5