Nature - USA (2020-06-25)

(Antfer) #1
Nature | Vol 582 | 25 June 2020 | 509

With Fourier surfaces, a simple solution is immediately available.
Three spatial frequencies can be included on a single surface to diffract
three colours at a common angle. Figure 4a, b shows such a profile,
designed, implemented and templated in Ag. The three sinusoidal
components simultaneously couple red, green and blue photons at nor-
mal incidence (Fig. 4c), as seen by the three reflectivity dips in Fig. 4d,
which arise due to photon–SPP coupling.
Additional applications of optical Fourier surfaces can benefit from
deeper structures and a diverse material library. We patterned polymers
of various refractive index (Methods) up to about 300 nm deep. When
these deeper surfaces are templated into Ag, the resulting Fourier sur-
faces can provide efficient diffraction gratings (Extended Data Fig. 8).
For a p-polarized beam at normal incidence, we measured 97 ± 5% in
the +1 and −1 diffraction orders for a single-component sinusoidal
grating. With two sinusoidal components, a ‘blazed’ Fourier surface
is obtained that diffracts nearly all intensity into just the +1 diffraction
order. The polymer profiles can also be transferred into substrates
via etching, for example silicon (Si; Fig. 4e) or silicon nitride (SiNx;
Extended Data Fig. 9). With this we could amplify the profile depth^8. Like
the patterned polymer, the etched substrate can provide a multi-use


template^9. Extended Data Fig. 9 shows a titania (TiO 2 ) Fourier surface
templated from an etched Si substrate.
Thus, ‘wavy’ diffractive surfaces can be provided for a broad spec-
tral range (X-ray to infrared). Templating, extendable to rollable sub-
strates^37 , enables high-throughput production of many materials
including active and multilayer solids^38 ,^39. Optical wavefronts can be
manipulated (including direction, phase and polarization^40 ,^41 ) with
diffractive surfaces that can be accurately placed within or on top of
elements in integrated photonic devices, allowing miniaturized optical
systems^20 ,^36. Thus, researchers in photonics can exploit the previously
unavailable capabilities of optical Fourier surfaces to address applica-
tions as well as to explore emerging phenomena.

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g 1
g 2
g 3
g 4
g 5
g 6

30°

3 μm e

g 1
g 2

g 3

60°

0

98 nm

b

f

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100

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0

–0.8
kx/k 0

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kx/k 0

ky

/k

0

c

y

x
y

x
103 nm

0

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3 μm

a

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d

y

x

Fig. 3 | Periodic and quasiperiodic Fourier surfaces. a, d, SEMs (45° tilt) of
periodic and quasiperiodic optical Fourier surfaces templated in Ag with 6- and
12-fold rotational symmetry, defined when three and six sinusoids are
superimposed, respectively. b, e, Measured topographies (obtained during
patterning) for the polymer films (PMMA/MA; see Methods) used to template
the structures in a and d, respectively. All sinusoids have Λ = 600 nm and their
corresponding vectors gi are oriented in-plane, as shown, spaced by 60° and
30°, respectively. c, f, Measured k-space ref lectivity images for photons
(570 nm wavelength) incident on the patterns in a and d, respectively. Six and 12
orange arcs appear, caused by decreased ref lectivity when photons launch
SPPs with wavevector kSPP, that is, when k‖ ± gi = kSPP (dashed white lines). kx and
ky are normalized by the magnitude of the photon wavevector, k 0. For all
structural design parameters, see Extended Data Table 1.


ac

b d

Reectivity (%)

Wavelength (nm)

MeasuredTarget function

gi

Ai^50450500550600650

60

70

80

90

100

4 μm

3 μm

e

x

y

x

y

70 nm

Fig. 4 | Applications of Fourier surfaces. a, Comparison of the measured
(atomic force microscopy) and targeted surface topography (accounting for a
slight distance miscalibration in the thermal scanning probe) for a Ag Fourier
surface that couples red, green and blue photons at normal incidence to SPPs.
Scan length is 22.0 μm. The profile contains three sinusoids with design
periods Λ 1  = 620 nm, Λ 2  = 520 nm and Λ 3  = 4 45 nm. b, SEM (30° tilt) of the Ag
Fourier surface in a. The inset shows the sinusoidal amplitudes Ai and spatial
frequencies gi. All design parameters are given in Extended Data Table 1.
c, Cartoon of the coupling of red, green and blue light simultaneously at normal
incidence. d, Measured ref lectivity as a function of photon wavelength for light
at normal incidence (within ±0.25°). The three prominent ref lectivity dips
(coloured as a visual guide) correspond to the coupling of red, green and blue
light at normal incidence. e, SEM (45° tilt) of a 12-fold rotationally symmetric
quasicrystal, defined with twelve sinusoids, etched into Si. For design
parameters, see Extended Data Table 1.
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