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Supplementary Information for:
Generation of Wavelength-independent Subwavelength Bessel Beams using Metasurfaces
Wei Ting Chen1, Mohammadreza Khorasaninejad1, Alexander Y. Zhu1, Jaewon Oh1,2, Robert
Devlin1, Aun Zaidi1 and Federico Capasso1,*
1
Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge,
Massachusetts 02138, USA
2
University of Waterloo, Waterloo, ON N2L 3G1, Canada
*Corresponding authors: [email protected]
S1. Maximum attainable numerical aperture (NA) in a conventional axicon made of glass
(SiO2).
0.8
Numerical aperture
0.7

0.6
0.5
0.4
0.3
0.2
0.1
0.0
5
10
15
20
25
30
35
40
45
 (degree)
Fig. S1. Limitation in numerical aperture (NA) of conventional axicons. The NA of a conventional
refractive axicon is limited by total internal reflection. In an axicon made of SiO2 the cutoff occurs at
axicon angle  ~ 42 , which corresponds to a NA of ~ 0.75. The inset in the top-left corner represents a
schematic cross-section of such an axicon with angle .
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S2. Simulated polarization conversion efficiencies for different deflecting angles
Fig. S2. Simulated efficiency for meta-axicons designed at wavelength  = 405 nm with different
numerical apertures (NA). Efficiency drops as the NA (deflecting angle) of the meta-axicon increases.
The efficiency is defined as the optical power deflected to an angle  divided by the incident optical
power. The NA = sin(), where  is indicated at the top-right corner. In meta-axicons, the NA increases as
wavelength increases, which results in a maximum operating wavelength because the light cannot be
deflected more than 90 .
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S3. Schematic experimental set-up
Quarter
waveplate
Fiber Coupled
Collimator
Objective
NA = 0.95
Laser
Tube Lens
Cam era
100X
Polarizer
Meta-axicon
Fig. S3. Sketch of the experimental setup. The laser beam from a fiber coupled laser is collimated by
means of a fiber collimator (Thorlabs RC04APC-P01) with a beam diameter of about 4 mm. The
collimated beam then passes through a Glan-Thompson polarizer (Thorlabs GTH10) and a quarter
waveplate (achromatic (Thorlabs AQWP05M-600) or zero-order (Thorlabs WPQ05M-405) waveplate are
selectively used depending on the bandwidth of the illumination source) to generate circularly polarized
light. This beam illuminates the meta-axicon at normal incidence. Subsequently, the Bessel beam is
collected by an Olympus high numerical aperture (NA) objective (NA = 0.95, 100×) paired with a tube
lens (f = 180 mm) to form an image on a complementary metal-oxide semiconductor (CMOS) camera
(IDS Inc. UI-1490SE). A narrow linewidth laser of 405 nm (Ondax. Inc.) or 532 nm (Laser Quantum Inc.)
or a supercontinuum laser (SuperK and Varia from NKT) are selectively used as the light source.
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S4. Analysis of the beam sizes of Bessel beams generated by meta-axicons
(a)
(b)
Fig. S4. The full-width at half-maximum (FWHM) of J0 and J1 Bessel beam at different planes
along the propagation direction. (a) and (b) show the FWHMs for J0 and J1 Bessel beam, respectively.
The NA and design wavelength are 0.9 and 405 nm, respectively.
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S5. Intensity of electric field of J0 Bessel beam for different numerical apertures
Ex
2
Ey
2
Ex  E y
2
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
2
NA = 0.9
NA = 0.5
NA = 0.25
Fig. S5. Intensity distribution of electric field at wavelength  = 405 nm for different numerical
apertures (NA). The rows show different NAs, while the columns show the intensities of electric field of
x- and y-component and their summation. The scale bar in (a) is 1 m and applies to all plots. Note that
for high NA case, the intensity of Ex at a given point is not equal to that of Ey, except the region near the
center, resulting in space-varying polarization states.
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S6. Space-varying polarization states of Bessel beams
Fig. S6. Polarization properties of NA = 0.9 Bessel beams at wavelength = 405 nm. The first and
second column show polarization orientation and ellipticity angle for the J0 Bessel beam, respectively.
The corresponding plots for the J1 Bessel beam are shown on the right side of the black line. The
theoretical (first row) results agree well with simulations (second row). In case of high NA, Bessel beams
exhibit space-varying polarization states.
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S7. Fourier plane images for a NA = 0.7 meta-axicon designed at wavelength  = 532 nm
(a)
 = 480 nm
(b)
 = 500 nm
(c)
 = 520 nm
(d)
 = 540 nm
(e)
 = 560 nm
(f)
 = 580 nm
(g)
 = 600 nm
(h)
 = 620 nm
(i)
 = 640 nm
(j)
 = 660 nm
(k)
Broadband
Fig. S7. Experimental Fourier plane images. (a) to (j) Fourier plane images at various wavelengths.
The center wavelength is noted on the top of each plot with 5 nm bandwidth. (k) Fourier plane image for
broadband incidence (200 nm bandwidth). Meta-axicons deflect light with a deflection angle proportional
to the wavelength of incidence, resulting in the numerical aperture (NA) being proportional to wavelength
and exhibiting a ring in its Fourier image. The longer the wavelength of incidence, the higher the NA and
the larger the diameter of the ring. The center bright spot is from uncoupled light that does not contribute
to forming Bessel beams.
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S8. Efficiency of a meta-axicon with NA = 0.7 designed at wavelength  = 532 nm.
60
Efficiency (%)
50
40
30
20
10
0
450
500
550
600
650
700
Wavelength (nm)
Fig. S8. Measured efficiency as a function of wavelength for the meta-axicon in case of circularly
polarized incidence. For a given set of geometrical parameters of the nano-fins, the efficiency of the
meta-axicon depends on the numerical aperture, due to sampling. Different numerical apertures also
imply a different tolerance for fabrication issues in the measured efficiency, where e.g. the size of nanofins differ slightly from the intended dimensions due to proximity effects during electron beam
lithography. This can be overcome with sufficient optimization.
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S9. Wavelength-independent FWHM.
(a)
(b)
Wavelength (nm)
Wavelength (nm)
Fig. S9. Measured FWHM of NA = 0.7 Bessel beams. The FWHM of (a) J0 and (b) J1 Bessel beam as a
function of wavelength. Due to engineering the dispersion of the meta-axicons, they are able to
compensate for the wavelength dependence of Bessel beams, showing wavelength independent FWHM.
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S10. Optical spectrum from the supercontinuum laser
Nomalized Power (a.u.)
1.0
0.8
0.6
0.4
0.2
0.0
450
500
550
600
650
700
Wavelength (nm)
Fig. S10. The output spectrum (in arbitrary units) of the supercontinuum laser. The output
spectrum of a supercontinuum laser (NKT photonics) when center wavelength and bandwidth were set to
575 nm and 200 nm. This broadband laser beam was used for results shown in Fig. 4(e), Fig. 4(j) of the
manuscript and Fig. S7(k) of supplementary information.
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S11. Wavelength-independent profile of J0 Bessel beam generated by silicon based metaaxicon
(a)
 = 532 nm
(b)
 = 550 nm
(c)
 = 600 nm
(d)
 = 625 nm
(e)
 = 650 nm
(f)
 = 675 nm
(g)
 = 700 nm
(h)
 = 725 nm
(i)
 = 750 nm
(j)
 = 775 nm
(k)
 = 800 nm
Fig. S11. Experimentally measured J0 Bessel beam profile for different wavelengths. (a) to (k) Bessel
beam profile at different wavelengths (labeled in the plots) generated by a silicon meta-axicon designed
by using the same method described in the main text. This silicon meta-axicon was prepared by
depositing a 500-nm-thick silicon film on glass. E-beam lithography was used to define the size of nanofins with length L = 200 nm and width w = 70 nm followed by dry etching. The NA of this meta-axicon is
0.8 at wavelength  = 785 nm. (a) and (b) are noisy because we increased the gain of camera due to lower
efficiency of the meta-axicon at these wavelengths. The scale bar is 2 m and applies to all plots.
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