Supplementary Information for: Immersion Meta-lenses at Visible Wavelengths for Nanoscale Imaging

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Roderick Dalton
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1 Supplementary Information for: Immersion Meta-lenses at Visible Wavelengths for Nanoscale Imaging Wei Ting Chen 1,, Alexander Y. Zhu 1,, Mohammadreza Khorasaninejad 1, Zhujun Shi 2, Vyshakh Sanjeev 1,3 and Federico Capasso 1,* 1 Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA 2 Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA 3 University of Waterloo, Waterloo, ON N2L 3G1, Canada These authors contributed equally to this work * Corresponding author: capasso@seas.harvard.edu 1

2 S1. Refractive index of immersion oil and cover glass substrate Fig. S1. Refractive index of immersion oil and cover glass used for designing oil immersion metalenses. The immersion oil (Series A, 18091) and cover glass (CG15XH) were purchased from Cargille- Sacher Laboratories Inc. and Thorlabs Inc., respectively. The refractive index mismatch at 532 nm is only 0.001, that is 0.06% of the refractive index of cover glass. 2

3 S2. Scanning electron microscope images Fig. S2. Scanning electron microscope images for the oil immersion meta-lens designed at 532 nm. (a) Top view image at the edge of the meta-lens. Scale bar: 1 m. (b) Oblique view at 45. Scale bar: 1 m. The inset shows a magnified image. Scale bar: 500 nm. 3

4 Focusing Efficiency (%) S3. Focusing efficiency of water immersion meta-lens Wavelength (nm) Fig. S3. Measured focusing efficiency for the NA = 0.9 water immersion meta-lens designed at 532 nm. The efficiency was measured, in case of circularly polarized incidence, by dividing the power of the focal spot by the total power passing through an aperture with the same diameter as the water immersion meta-lens. 4

5 S4. Focal spot mapping for water immersion meta-lenses Fig. S4. Focal spot profiles for meta-lenses with (a) NA = 0.9 and (b) NA = 0.1. These plots were interpolated from measurement data taken by moving the water immersion objective 100 nm and 2 m per step. 5

6 Focusing Efficiency (%) S5. Focusing efficiency of oil immersion meta-lens Wavelength (nm) Fig. S5. Measured focusing efficiency of oil immersion meta-lens designed at 532 nm with NA = 1.1 in under circularly polarized incidence. 6

7 S6. Scanning microscope images for Harvard logo Fig. S6. Scanning electron microscope (SEM) images of Harvard logo prepared by focusing ion beam milling on an 80-nm-thick gold film. (a) A SEM image for the entire logo, (b) a magnified SEM image at the bottom of (a). The minimal line width of the character H is ~ 265 nm. 7

S7. Simulated aberration analysis for a water immersion meta-lens with NA = 1.1. (a) (b) (c) (d) S1 S2 S3 (e) Fig. S7.

1. This water immersion meta-lens was designed such that all rays (depicted in blue), after passing through a 170- mthick cover glass, cross at a single point.

$(c) Spot diagram showing the intersection points of rays on the focal planes of (a) and (b). The black circle shows the diameter of diffraction-limited Airy disk.$

8 S7. Simulated aberration analysis for a water immersion meta-lens with NA = 1.1. (a) (b) (c) (d) S1 S2 S3 (e) Fig. S7. Ray-tracing simulation at 532 nm analyzing the effect of variations in cover glass thickness. (a) Ray-tracing diagram for a water immersion meta-lens with NA = 1.1. This water immersion meta-lens was designed such that all rays (depicted in blue), after passing through a 170- mthick cover glass, cross at a single point. The labels refer to S1: Immersion meta-lens. S2: The interface between cover glass and water. S3: Focal plane. (b) Ray-tracing diagram for the case when the cover glass thickness is changed by 5 m, i.e. to 175 m. The 5 m thickness error results in a focal plane shift (see inset) due to spherical aberration. (c) Spot diagram showing the intersection points of rays on the focal planes of (a) and (b). The black circle shows the diameter of diffraction-limited Airy disk. Since most of intersected points in case (b) still fall into the diffraction-limited Airy disk, the 5 m thickness error results in weak spherical aberration. (d) Optical path difference (OPD) with respect to the chief ray as a function of the radial coordinate of meta-lens. (e) A comparison of the intensity of focal spots for the case of (a) and (b). This plot was calculated using Huygens transform function in OpticsStudio. The weak spherical aberration lowers the Strehl ratio to

9 Water meta-lens (NA = 0.1 at 532 nm) Water meta-lens (NA = 0.9 at 532 nm) Oil meta-lens (NA = 1.1 at 532 nm) Oil meta-lens (NA = 1.1 at 405 nm) Oil meta-lens (NA = 1.1 at 532 nm) R ( m) a 1 a 2 a 3 a 4 a 5 a 6 a 7 a Table S1. Polynomial coefficients of immersion meta-lens phase profiles. The last row with the largest diameter was used for confocal scanning imaging. 9

A broadband achromatic metalens for focusing and imaging in the visible

SUPPLEMENTARY INFORMATION Articles https://doi.org/10.1038/s41565-017-0034-6 In the format provided by the authors and unedited. A broadband achromatic metalens for focusing and imaging in the visible