A broadband achromatic metalens for focusing and imaging in the visible

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1 SUPPLEMENTARY INFORMATION Articles In the format provided by the authors and unedited. A broadband achromatic metalens for focusing and imaging in the visible Wei Ting Chen 1, Alexander Y. Zhu 1, Vyshakh Sanjeev 1,2, Mohammadreza Khorasaninejad 1, Zhujun Shi 3, Eric Lee 1,2 and Federico Capasso 1 * 1 Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA. 2 University of Waterloo, Waterloo, ON, Canada. 3 Department of Physics, Harvard University, Cambridge, MA, USA. * capasso@seas.harvard.edu Nature Nanotechnology Macmillan Publishers Limited, part of Springer Nature. All rights reserved.

2 Supplementary Information for: A broadband achromatic metalens for focusing and imaging in the visible Wei Ting Chen 1, Alexander Y. Zhu 1, Vyshakh Sanjeev 1,3, Mohammadreza Khorasaninejad 1, Zhujun Shi 2, Eric Lee 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 * Corresponding author: capasso@seas.harvard.edu 13 1

$14 15 16 17 18 19 20 21 22 23 24 25 26 S1. Strong dispersion from periodicity Figure S1(a) shows a schematic of a conventional glass prism, with a constant refractive index (dispersionless).$ $S1(b) shows an example, assuming that a given green wavelength λ g is diffracted to an angle θ following the Bragg equation: Λ sin( θ) = mλ (1) where Λ is the periodicity and m is an integer. From Eq.$

3 S1. Strong dispersion from periodicity Figure S1(a) shows a schematic of a conventional glass prism, with a constant refractive index (dispersionless). A broadband chromatic beam is deflected by this prism to the same angle. Figure S1(b) is its diffractive counterpart comprising of periodic miniature prisms. Once these miniature prisms are arranged together in a periodic manner, they start showing strong dispersion. The inset of Fig. S1(b) shows an example, assuming that a given green wavelength λ g is diffracted to an angle θ following the Bragg equation: Λ sin( θ) = mλ (1) where Λ is the periodicity and m is an integer. From Eq. 1, another wavelength, λ g + δλ, is forbidden from propagating to the same angle θ ; it would have to go to a larger angle because of the increase in wavelength. This results in a strong negative dispersion property compared to refractory optics. Alternatively, this can be intuitively understood from the fact that a constant g 27 wavenumber from periodicity ( 1 ) is applied to different wavelengths of incident light, causing Λ 28 each wavelength to be deflected to a different angle Figure S1: Schematic illustrating the origin of the chromatic effect in periodic meta-surfaces and diffractive optics. Colors are representative of their respective wavelengths (red, green and blue). (a) A conventional glass prism. (b) Diffractive counterpart of (a). The inset in (b) shows a magnified view, assuming that the green wavelength is deflected to an angle θ. The optical path difference between the two green beams is equal to an integer multiplied by Λ sin( θ ). 2

35 36 S2. Scanning microscope images 37 38 39 40 41 42 Figure S2: Scanning microscope images of an achromatic metalens.

4 35 36 S2. Scanning microscope images Figure S2: Scanning microscope images of an achromatic metalens. (a) and (b) Top view images. Scale bar: 1 μm. The inset of (a) shows an oblique view with larger magnification. Scale bar: 500 nm. 3

5 43 44 S3. Available choices of element at wavelength λ = 530 nm Figure S3: Polarization conversion (PC) efficiency versus group delay for different elements after filtering those with PC efficiencies lower than 5%. Each dot represents an element with its x and y coordinates determined by the group delay and PC efficiency respectively. The group delays are obtained by linearly fitting the phase plots at λ = 530 nm within a 120 nm bandwidth. The elements with R-squared values lower than 0.98 are dropped. Most of the high polarization conversion efficiency nano-fins have group delays between 2 to 5 femto-seconds. This is a result of the waveguiding effect being dominant. The observed group delay values can be obtained by substituting the appropriate n eff between 1 and 2.4 (the refractive index of air and TiO 2 ) into the first term of Eq. 5 in the main text. 56 4

6 57 58 S4. Focal spot characterization (a) 1 (b) 0.95 Strehl ratio Wavelength (nm) Figure S4: (a) Strehl ratio and (b) full-width at half-maximum (FWHM) for the achromatic metalens with a numerical aperture of 0.2. Their corresponding focal spot profiles are shown in Fig. 3(f) of the main text. The dashed black line shows the theoretical FWHM of the Airy disk. 64 5

7 65 66 S5. Focal spot under incoherent illumination Figure S5: Focal spot profile for the achromatic metalens (NA = 0.2) under broadband incoherent illumination. (a) Focal spot profile taken by a color CCD camera (UI-1540SE, IDS Inc.). Scale bar: 5 μm. (b) Normalized intensity of light source measured by a spectrometer (USB4000, Ocean optics) for a Tungsten source coupled to a light guide (OSL1, Thorlabs Inc.). The focal spot size is slightly beyond the diffraction limit because the light guide has ~ 5 mm in diameter and the metalens is not corrected for the whole spectrum. A pair of crossed circular polarizer was used to remove background. 76 6

8 77 78 S6. Focal spot profiles and images from a resolution target Figure S6: A comparison for the measured focal spot profiles and images of the USAF resolution target using the achromatic and diffractive metalenses (NA = 0.02, diameter = 220 μm) for different wavelengths. (a) and (c) Focal spot profiles of achromatic and diffractive metalenses. Scale bar: 20 μm. These focal spot profiles were taken without re-focusing to visualize chromatic focal length shift. The bottom rows show intensity along the horizontal cut through the center of each focal spot. The illumination wavelength (with a bandwidth of about 5 nm) is denoted on the top. (b) and (d) Imaging using the metalenses. Schematic set-up is shown in Fig. S11. These images were taken at the focal plane for wavelength λ = 470 nm. Scale bar: 100 μm

9 93 94 S7. Focal spot characterization under oblique incidence. (a) 15 = 470 nm 17 = 530 nm 20 = 670 nm Angle of incidence (deg) Angle of incidence (deg) Angle of incidence (deg) (b) 1 = 470 nm 1 = 530 nm 1 = 670 nm Angle of incidence (deg) Angle of incidence (deg) Angle of incidence (deg) Figure S7: Analysis for the achromatic metalens (NA = 0.02, diameter = 220 μm) under different angles and wavelengths of incidence. (a) and (b) Experimentally measured full-width at half-maximum (FWHM) and Strehl ratio for different angles of incidence and wavelengths. The theoretical values of FWHM are marked as dashed lines. The Strehl ratio indicates how close a focal spot is compared to the theoretical Airy disk profile. A Strehl ratio larger than 0.8 is commonly acknowledged as a requirement of diffraction-limited focusing

10 104 S8. Efficiencies as a function of wavelength Figure S8: Efficiencies of metalenses. (a) Measured (blue line) versus theoretical efficiencies (red and yellow lines) for the achromatic metalens (NA = 0.02, diameter = 220 μm). The efficiency is defined by the power of focal spot divided by that of light passing through an aperture with the same diameter. The power of the focal spot was measured by placing a power meter on the image plane of a custom-built microscope. An aperture with a size about the diameter of Airy disk was used to filter out the background light. Theoretical values were obtained by the averaged polarization conversion efficiency of each element on the achromatic metalens. Although the coupling between each element and the diffraction effect are neglected, this gives an upper limit of efficiency. (b) Measured efficiencies of metalenses with the same NA of 0.02 but different diameters. The diameters are labeled in the legend. The efficiency becomes higher for smaller diameters because the required group delay is smaller than our current realized values. This avoids choosing those efficiency elements (see Fig. S3 for a plot of group delay versus efficiency)

11 S9. Correcting aberrations using dispersion-engineered metalens. Using our approach, it is possible to correct not only monochromatic but also chromatic aberrations of a refractive lens. As an example, we chose a commercially available and low-cost plano-convex lens from Thorlabs Inc. Figure S9(a) shows a raytracing diagram at wavelength λ = 530 nm. A metalens is attached to the planar side of the lens (depicted by the blue line). The diameter of the entrance aperture is 5.4 millimeters, and the refractive/metalens doublet has a numerical aperture of about 0.1. The frequency-dependent metalens was designed by the principle described in Fig. 1 in the main text, i.e. it needs to provide various group delays and group delay dispersions such that all wavepackets from different lens coordinates arrive at the focus together and with the same pulse shape. The green and black curves in Fig. S9(b) show focal spot intensity profiles with and without the metalens, respectively. The metalens corrects the spherical aberration of the refractive lens by introducing a W-shaped phase profile similar to the well-known Schmidt plate (see the green curve in Fig. S9(c)). Moreover, the phase profile of the metalens changes as a function of wavelength to correct chromatic aberration simultaneously. The required range of group delay and group delay dispersion for this frequency dependent phase profile is shown in Fig. S9(d). These required values are only a few times larger than those provided by our current library shown in Fig. S10(a) and can be readily achieved with modifications of the nanostructure design. The focal length shift is about 700 μm for the uncorrected lens, i.e. without the metalens (the orange curve of Fig. S9(e)). Intriguingly, if one only corrects for group delay (see the red curve of Fig. S9(e)), the focal length changes by an amount similar to that of an achromatic doublet. Taking the group delay dispersion into account results in a performance close to a triplet lens, as shown in the blue curve of Fig. S9(e). The 10

12 metalens-corrected spherical lens is now achromatic and diffraction-limited from 450 nm to 700 nm, as seen in Fig. S9(f) with < λ root-mean-square wavefront error Figure S9: Simulation results for aberration correction using a metalens. The refractive lens is a generic spherical lens available from Thorlabs Inc. The metalens corrector was designed with a frequency dependent phase profile, using the method described in the text. (a) A raytracing simulation of the refractive/metalens doublet at λ = 530 nm. The simulation was done using a commercial software OpticsStudio (Zemax Inc.). The layout of the refractive lens was obtained from Thorlabs website. (b) Focal spot intensities with and without the metalens. The 11

13 spherical lens suffers spherical aberrations resulting in low Strehl ratio (black curve) away from the diffraction limit. (c) Phase profile across the center of the frequency-dependent metalens. The chosen wavelengths are shown in the legend; units are in nanometers. (d) The required group delay and group delay dispersion from the center to the edge of the metalens. (e) A comparison between relative focal length shifts for the refractive lens (orange), the metalens with engineered group delay only (red) and the metalens with simultaneously engineered group delay and group delay dispersion. (f) Root-mean-square wavefront error of the refractive/metalens doublet. The metalens provides group delay and group delay dispersion, showing the frequency-dependent phase profile in (c). The black dashed line shows a wavefront error of λ, corresponding to Strehl ratio of

14 166 S10. Group delay and group delay dispersion plot of elements (a) Group delay dispersion (fs 2 ) Original data Original data + offsets Required Group delay (fs) (b) (c) Group delay (fs) Group delay dispersion (fs 2 ) Realized Required Coordinate (μm) Realized Required Coordinate (μm) Figure S10: (a) Group delay (GD) and group delay dispersion (GDD) of elements (colored circles) versus that of the required GD and GDD (black circles) for realizing a metalens with n = 2. The coordinate of each purple circle represents the group delay and group delay dispersion of an element. The group delay and GDD were obtained by fitting the phase as a function of angular frequency using a quadratic polynomial for a bandwidth of 120 nm centered at 530 nm. Only the elements with R 2 values larger than 0.99 are shown. Since only the relative group delay and GDD of the metalens need to be fulfilled, one can introduce two different offsets to the group delay and GDD, which is equivalent to translating the data for the best fit. We determine the appropriate offsets using the particle swarm method, and the data after adding the offsets are shown in green symbols. (b) and (c) Realized GDs and GDDs (green symbols) versus that of the required (black lines)

15 S11. Experimental setup used for imaging with metalenses. For imaging, a pair of crossed circular polarizer was used to reduce background signals. The images were projected on a semi-transparent screen to show the full field of view, without being limited by the size of a camera sensor. The tube lens was removed to show the whole view given in Fig. 4(c) and 4(d) in the main text. We adjust the distance between the resolution target and the achromatic metalens such that the image is best focused on the screen at wavelength λ = 470 nm. This distance is maintained when changing laser center wavelength from 470 nm to 670 nm in steps of 20 nm. For each wavelength, the laser bandwidth is 40 nm and a camera (Fujifilm X- T10) was utilized to take photos. The achromatic metalens was replaced by a diffractive metalens for comparing the imaging quality. LP λ/4 Resolution Target λ/4 LP Screen Laser 10x 193 Fiber Coupled Collimator Condenser Metalens Tube Lens Camera Figure S11: Schematic diagram of the experimental setup used for imaging by the achromatic metalens with a numerical aperture of The laser beam is collimated by a fiber collimator (Thorlabs, RC08APC-P01). The collimated beam then passes through a Glan- Thompson polarizer (Thorlabs, GTH10) and a quarter waveplate (Thorlabs, AQWP05M-600) to generate circularly polarized light. The Mitutoyo objective (10 magnification, NA=0.28) was used as a condenser for providing more intensive illumination on the target. The target was placed at the focal plane of meta-lens under wavelength λ = 470 nm illumination. To reduce background, we use another pair of quarter waveplate and wire or Glan-Thompson polarizer aligned in crossed polarization with respect to that of the incident light. A tube lens with focal 14

16 length f = 180 mm (Thorlabs, TTL180-A) was selectively used to form image on a semi- transparent screen. 15

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

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