Ultra-thin flat lenses made of Graphene
Sunan Deng, Kyle Jiang, Haider Butt
School Mechanical Engineering
University of Birmingham
Birmingham B15 2TT, UK
Abstract—Flat lenses can be made very thin and have the
advantages of being aberration free when compared to curved
surface lenses. They offer a compact design for a myriad of
electro-optical applications, such as solar cell and fiber
communication systems. This paper reports research into Fresnel
zone plate, which is a flat lens constructed by graphene rings.
Low number multilayer graphene was formed into Fresnel zone
plates which utilize the reflection and transmission properties of
graphene for their operation. The lenses and their performance
in the visible regimes were analyzed computationally.
Experimental measurements were also performed and good
agreements were obtained with the modelling results. The work
demonstrates the feasibility of atom thick graphene-based lenses,
showing perspectives for ultra-compact integration.
Keywords—graphene; flat lens; Fresnel zone plate
I. INTRODUCTION
A flat lens focuses light by changing the phase of light
with surface structure in nano or micro scale, while traditional
curved lens focuses light by propagating light in the lens for a
distance. A flat lens provides the possibility to revolutionize
the design of compact optical systems as it can be made very
thin, even thinner than the wavelength of light. More
importantly, flat lenses do not have imaging distortions, which
is a big problem for traditional lenses. Previously aberration
was corrected by techniques such as aspheric shapes or multilens designs, resulting in heavy weight and extra space. That
problem can be avoided by using flat lenses, leading to
ultrathin lenses, and Fresnel zone plate provides a suitable
solution.
A Fresnel Zone Plate (FZP) consists of a series of radially
symmetric transparent and opaque rings. As it offers the
possibility of designing high numerical aperture (NA) lens
with low weight and small volume, FZP lenses are widely
used in the optical industry and are key elements in systems
like optical interconnects, beam focusing and integrated optics
[1].
We explore the possibility of developing the thinnest lens
by using graphene. Graphene has some excellent optical
properties, especially the tunability under different Fermi
levels. In the visible light regime, optical transmittance for
single layer graphene is determined solely by the fine structure
constant, α=e2/ħc, where c is the speed of light, and 𝑇 ≡
transmittance, the reflectance of mono-layer graphene under
normal light incidence is relatively weak as defined by 𝑅 =
0.25𝜋 2 𝛼 2 𝑇 = 1.3 × 10−4 . However, the reflection will
increase linearly with the number of layers, with 𝑁𝜋𝛼 for N
layer graphene. Unlike single-layer graphene, according to
Skulason et al.[3], few-layer graphene could have very high
reflection contrast, indicating the possibility of making FZP
lens of graphene on glasses.
In this paper, the lensing effect of graphene FZP lens under
light of wavelength 850 nm was studied through FDTD
modelling. We choose 850 nm because it is one of the most
important optical communication windows. Then graphene
FZP lens array were fabricated by CVD and photolithography
processes. Characterization using microscope shows that these
lenses have the ability of focusing light with high contrast.
The lenses were found to be thinner, more efficient, and easier
to fabricate compared to the metasurface based flat lenses.
This research confirms the possibility of making ultra-thin
lens with graphene, which can play a key role in developing
compact optical systems, such as laser focusing for optical
storage and fire-optic system.
II. DESIGN OF THE GRAPHENE FZP LENS
The focal length f of an FZP lens is related to the radii r of
successive zone edges. By means of an approximation for large
focal lengths, the radius of different zones satisfies equation [4]
:
𝑓
𝑟𝑛
𝑟
= 𝑛𝜆𝑛 ( where λ is the wavelength of light, n = 1, 2, 3…),
and the radius of the nth zone (𝑟𝑛 ) in a FZP lens is given by
𝑟𝑛 = √𝑛𝑟1 .
In this work, the lens was designed by setting the focal
length to ~120 µm at an optical wavelength of 850 nm. The
spacing and widths of the Fresnel zones were calculated with
relation to n. Fig. 1 shows a three-dimensional schematic
diagram of the FZP geometry and its operation. The radius of
the central zones was 10 µm and the lens radius was about 49
µm. Light comes from the right side, then is reflected and
diffracted by the FZP lens before being focused in the focal
plane.
2𝜋𝐺 −2
(1 +
) ≈ 1 − 𝜋𝛼 ≈ 0.977, in which G = e2/4ħ is
𝑐
universal conductivity of graphene [2]. Compared with
978-1-4673-8156-7/15/$31.00 ©2015 Crown
focusing effect of the graphene-based FZP lens. The red lines
in Fig. 2(b) and (d) represent power flow extracted at x=0 and
y at the focal plane in Fig. 2 (a) respectively. The focal length
in the simulation is 114.5 nm, which is very close to the
theoretical value.
Fig. 1. A schematic showing the geometry and reflection mode operation of a
graphene Fresnel zone plate. The incident light is from right.
III. SIMULATION
2D simulation was performed owing to the radial symmetry
of the Fresnel zone plates, with light coming from Y direction
and graphene FZP lens with glass substrate on XZ plane. The
computed electric field distribution of light reflected by 5-layer
graphene FZP/glass structure are shown in Fig. 2[5] (a). High
contrast focal point can be observed, which confirms the
Fig. 2(b) compares the electric field distribution along the
vertical lines (x=0) at the focal point of graphene FZP lens
with (red line) and without (black line) glass substrate.
Compared with results without glass substrate, the wave
shapes in the red curves are interference effects produced by
the glass substrate, which could tell from the green line
generated from 5 µm thick glass substrate. When the
interference influence was subtracted from the red curve, very
clear focusing effect was obtained, shown as blue line B-A,
which is very similar to the black line. Thus it can be
concluded that the focal effect is leaded by graphene FZP lens
while the interference is contributed by the glass substrate.
The assumption were further confirmed by Fig.2 (c) and (d),
in which 5-layer and 10-layer graphene FZP lenses on glass
substrate have almost identical interference curves, but shows
obvious difference at the focal point position. 10-layer
graphene FZP lens contributes more to the focal lensing effect
than 5-layer lens is because that the reflection of graphene will
increase with the number of layers.
Fig. 2. [5] Graphene FZP lens on glass substrate. (a) Power flow reflected from 5-layer graphene FZP lens on glass substrate with 850 nm incident light (Fermi
level 0.1 eV) (b) Power flow extracted from x=0, across y-axis. The green line, red line and black line represent power flow when light is shined on glass
substrate, graphene lens /glass substrate, and a graphene lens respectively. The blue line is get from subtracting the green line from the red line. The power flow
distribution of the horizontal and vertical cross sectional via focal point for 5-layer (green lines) and 10-layer (red lines) graphene lenses are demonstrated in (c)
and (d).
Multi-layer graphene were synthesized by chemical
vapour deposition method [6, 7]. Based on the modelling
results, graphene FZP lenses were fabricated by
photolithography processes. The lenses could work both in
reflection and transmission mode of operation, as shown in
Fig. 3, which are characterizations under Alicona microscope.
middle. In this mode, the focal point was produced within the
glass substrate. Then by adjusting the focal position of the
microscopy, the focal point in reflection mode was obtained,
as shown in Fig.3 (c). It is found that the intensity of the focal
point in the reflection mode is lower than that in the
transmission mode, which is corresponding with the optical
properties of graphene.
Fig. 3(a) shows a magnified single graphene FZP lenslet
on glass substrate. The brighter areas are graphene while the
darker areas are glass with graphene etched away, which
shows good reflection optical contrast of few layer graphene
on glass. Fig. 3(b) shows good performance of the lens work
in transmission mode with high contrast focal point in the
The experimental focal length of graphene FZP lens is
175um±10um, with visible incident light. According to the
work principle of FZP lens, it can be derived that the incident
light wavelength ranges from 540.5 nm to 606 nm, which are
in the visible regime. Hence, the experimental data agree well
with the theoretical value.
IV.
FABRICATION AND CHARACRIZAITON
Fig. 3. [8] A single graphene FZP lenslet zoomed under optical microscope. (a) Magnified single graphene lenslet. (b) Graphene lens work as a transmission
lens. (c) Graphene lens work as a reflection lens
To study the surface profile of the multi-layered graphene
lens, measurements were carried out using atomic force
microscope (AFM), as shown in Fig. 4. The bright spots in
Fig. 4(a) arise from the polymer residue post lithography and
lead to artifacts in AFM images i.e. the black lines in Fig. 4(a).
Fig. 4(b) shows the height distribution along the radial blue
line in Fig. 4(a). The Fresnel zone is clearly shown in its
surface profile and the average surface roughness measured
3.47 nm, which corresponds to approximately 10 layers of
graphene.
Fig. 4. [8] (a) An AFM image of a single graphene Fresnal zone plate. (b) Roughness distribution along the blue radial line in (a).
V. CONLUSION
In conclusion, we have developed ultrathin graphene-based
FZP lenses on glass with nanoscale roughness. The lenses
were designed to operate in the optical regime and fabricated
by lithography technique. Their focusing properties were
characterized. The lenses were found to be extremely thin,
efficient, and easy to fabricate compared to the metasurface
based flat lenses. Hence graphene FZP lens are highly
promising as flat and ultrathin lenses. They have the potential
to revolutionize the design of compact optical systems, such as
laser focusing for optical storage and fiber-optic
communications.
ACKNOWLEDGMENT
The authors would thank The Leverhulme Trust for the
research funding. This research is partly funded by the
European Union’s Horizon 2020 research and innovation
program under the Marie Skłodowska-Curie grant agreement
No 644971.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
H. Butt, R. Rajesekharan, Q. Dai, S. Sarfraz, R. V. Kumar, G. A.
Amaratunga, et al., "Cylindrical Fresnel lenses based on carbon
nanotube forests," Applied Physics Letters, vol. 101, p. 243116, 2012.
R. Nair, P. Blake, A. Grigorenko, K. Novoselov, T. Booth, T.
Stauber, et al., "Fine structure constant defines visual transparency of
graphene," Science, vol. 320, pp. 1308-1308, 2008.
H. Skulason, P. Gaskell, and T. Szkopek, "Optical reflection and
transmission properties of exfoliated graphite from a graphene
monolayer to several hundred graphene layers," Nanotechnology, vol.
21, p. 295709, 2010.
Y.-H. Fan, H. Ren, and S.-T. Wu, "Switchable Fresnel lens using
polymer-stabilized liquid crystals," Optics Express, vol. 11, pp. 30803086, 2003/11/17 2003.
S. Deng, A. K. Yetisen, K. Jiang, and H. Butt, "Computational
modelling of a graphene Fresnel lens on different substrates," RSC
Advances, vol. 4, pp. 30050-30058, 2014.
P. R. Kidambi, B. C. Bayer, R. S. Weatherup, R. Ochs, C. Ducati, D.
V. Szabó, et al., "Hafnia nanoparticles–a model system for graphene
growth on a dielectric," physica status solidi (RRL)-Rapid Research
Letters, vol. 5, pp. 341-343, 2011.
K. Xi, P. R. Kidambi, R. Chen, C. Gao, X. Peng, C. Ducati, et al.,
"Binder free three-dimensional sulphur/few-layer graphene foam
cathode with enhanced high-rate capability for rechargeable lithium
sulphur batteries," Nanoscale, vol. 6, pp. 5746-5753, 2014.
C.-F. Chen, C.-H. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit,
et al., "Controlling inelastic light scattering quantum pathways in
graphene," Nature, vol. 471, pp. 617-620, 03/31/print 2011.