www.sciencemag.org/content/352/6290/1190/suppl/DC1

Supplementary Materials for

Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging

Mohammadreza Khorasaninejad, Wei Ting Chen, Robert C. Devlin, Jaewon Oh, Alexander Y. Zhu, Federico Capasso *

*Corresponding author. Email: capasso@seas.harvard.edu

Published 3 June 2016, Science 352, 1190 (2016) DOI: 10.1126/science.aaf6644

This PDF file includes:

Materials and Methods Figs. S1 to S10 References

Other Supplementary Material for this manuscript includes the following: (available at www.sciencemag.org/cgi/content/full/352/6290/1190/DC1)

Movie S1

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Materials and Methods

Experimental setup used for focal spot characterization and efficiency measurement The focal spots of the metalenses were characterized using a custom-built

microscope consisting of a fiber-coupled laser source, linear polarizer, quarter-waveplate, and Olympus objective (100×, NA = 0.9) paired with a tube lens (f = 180 mm) to form an image on a CMOS camera (Edmund EO-5012). The sources used were lasers (Ondax Inc.) with linewidths less than 100 MHz. For efficiency measurements, we used a supercontinuum laser (SuperK) as the source. The efficiency is defined as the ratio of the optical power of the focused beam to the optical power of the incident beam, as captured by a photodetector (Thorlabs S120C) located at the same position as the CMOS camera. The incident optical power was measured as the light passing through an aperture (aluminum on glass) with the same size as the metalens.

Measurement of intensity distribution at x-z plane shown in Fig. 3B

First, the Olympus objective is focused on the plane 20 μm (z = 70 μm) in front of the focal plane, x-y, to capture the first image. The objective lens and tube lens are then successively moved toward the focal plane. An image is captured at each 500 nm increment. This process is repeated up to z = 110 μm, 20 μm beyond the focal plane. Finally, the intensity distributions of all captured images, along the z axis, are stitched together to visualize light propagation in the vicinity of the focal point. A movie showing beam propagation along the focal axis is provided in Movies S1.

Strehl ratio calculation

The Strehl ratios are calculated by comparing the measured intensity distributions in the focal spots to the calculated profiles with a full-width at half-maximum FWHM = λ/(2NA) for NA =0.8 according to the diffraction limit (i.e. Airy disks). The intensities of the measured profiles are then normalized to the calculated ones to achieve the same energy within a given area. The Strehl ratio is the ratio of maximum peak value of the measured intensity curve to that of the calculated one (38). Strehl ratios of 0.76, 0.78 and 0.77 are achieved for metalenses designed for wavelengths of 405 nm, 532 nm and 660 nm, respectively, at their design wavelengths. Experimental setup used for imaging with metalens

For imaging, we paired our metalens with a tube lens (f = 100 mm), Fig. S6. A collimated beam was passed through a diffuser to reduce laser speckles before being focused by a Mitutoyo objective (10×) to illuminate the target object. We adjusted the distance between the object and metalens based on the illumination wavelength.

Modulation transfer function (MTF) measurement

The MTF measurement was performed using a standard slant-edge test (Thorlabs R2L2S2P) and is shown in Fig. S10. The MTF value of 0.1 is a good guide to the limit of the resolving power of the metalens (39). Figure S10 shows that this occurs at the spatial frequency of 1000 line pairs per millimeter (lp/mm). This cut-off value corresponds to a resolution limit of 500 nm (106/(2× cut-off spatial frequency)).

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a

2 m

A

B

2 m

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200 nm

Fig. S1.

Scanning electron microscope micrographs of fabricated metalenses with diameter D = 240 μm and focal length f = 90 μm. (A) Tilted view of the metalens edge. (B) Top view of the center of the metalens. (C) High magnification image of the metalens at the edge.

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Laser

Metalens

Fiber Coupled Collimator

LP

100x

Tube Lens

Camera

zyx

/4

Camera

Fig. S2

Measurement setup for metalens characterization. Schematic of the experimental setup used for measuring the size of the focal spot. The laser beam is collimated by a fiber collimator (Thorlabs RC04APC-P01) with a beam size diameter of 4 mm. The collimated beam then passes through a Glan-Thompson polarizer (Thorlabs GTH10) and a quarter-waveplate (Thorlabs AQWP05M-600) to generate circularly polarized light. An Olympus objective (100× magnification, NA=0.9) was used to image the light focused by a metalens. A tube lens with focal length f = 180 mm was used to form an image on a CMOS camera (Edmund EO-5012).

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A

B

C

Fig. S3

Strehl ratio calculation. Diffraction-limited (theory) and measured focal spot intensity distributions for three metalenses designed at wavelengths of (A) 405, (B) 532 and (C) 660 nm. Focal spots are measured at corresponding design wavelengths.

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C

720 nm

D

590 nm

B

1 m1 m

A

Fig. S4

Focal spot of a metalens at wavelengths away from the design wavelength of 532 nm. (A to D) Measured focal spot intensity profile and its corresponding vertical cut at 660 (A and C) and 405 nm (B and D) for a metalens designed for 532 nm.

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A B

Fig. S5

Focal length and magnification of the metalens at different wavelengths. (A) Measured focal length of the metalens as a function of wavelength. (B) Magnification corresponding to these focal lengths are also calculated and shown after taking into consideration the tube lens with focal length of 100 mm. The metalens here has diameter D = 2 mm and focal length f = 0.725 mm with the design wavelength of 532 nm.

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Laser

Diffuser

Fiber Coupled Collimator

LP

10x

zyx

/4 Tube Lens

CameraCamera

Object LP/4

Fig. S6

Measurement setup used for imaging. Schematic diagram of the experimental setup used for imaging by the metalens. The laser beam is collimated by a fiber collimator (Thorlabs RC04APC-P01) with a beam size diameter of 4 mm. The collimated beam then passes through a Glan-Thompson polarizer (Thorlabs GTH10) and a quarter-waveplate (Thorlabs AQWP05M-600) to generate right circularly polarized light. This beam is passed through a diffuser to reduce speckles and then focused by a Mitutoyo objective (10× magnification, NA=0.28) onto the target object. The metalens is placed a focal length away from the object and paired with a tube lens (f =100 mm) to form an image on a CCD camera (Point Grey, GX-FW-28S5C-C). To reduce background signals, we use a polarizer paired with a quarter-waveplate in cross polarization.

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A B

C D

E F

Fig. S7

Images formed by a metalens designed at λd = 532 nm with diameter D = 2 mm, and focal length f = 0.725 mm captured by a Cannon DSLR camera. Image of the 1951 USAF resolution test chart formed by the metalens taken with a Cannon DSLR camera at

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wavelengths of (A) 480, (B) 550, (C) 580, (D) 590, (E) 620 and (F) 640 nm. Scale bar: 40 μm.

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A B

C D

E F

Fig. S8

Images formed by a metalens designed at λd = 532 nm with diameter D = 2 mm, and focal length f = 0.725 mm captured by a Cannon DSLR camera. Image of a Siemens star formed by the metalens at wavelengths of (A) 480, (B) 500, (C) 540, (D) 580, (E)

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600 and (F) 620 nm. Scale bar: 50 μm. The blurring near the center results from projecting the images onto a translucent screen.

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A

B

C

Fig. S9

Images formed by a metalens designed at λd = 532 nm with diameter D = 2 mm, and focal length f = 0.725 mm captured by a CCD camera. Image of a Siemens star formed

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by the metalens at wavelengths of (A) 480, (B) 540, and (C) 620 nm. Scale bar: 10 μm. The features near the center of the star target can be well resolved.

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0 500 1000 1500 2000

Spatial frequency (lp/mm)

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0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

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MT

F

Fig. S10

Measured modulation transfer function (MTF) as a function of spatial frequency in line pairs per millimeter (lp/mm). The slant-edge target was imaged using the metalens designed at λd = 532 nm with diameter D = 2 mm and focal length f = 0.725 mm. The line is to guide the eye.

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Movie S1 Intensity distribution in the focal (x-y) plane for a metalens designed at λd = 532 nm with diameter D = 240 μm and focal length f = 90 μm. The intensity distribution is captured 20 μm before and after the focus at 500 nm intervals. The resulting images are stitched together to produce the movie.

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