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Scientific RepoRts | 6:33627 | DOI: 10.1038/srep33627
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Wavelength-scale light
concentrator made by direct
3D laser writing of polymer
metamaterials
J. Moughames
1,2
, S. Jradi
1
, T. M. Chan
3
, S. Akil
4
, Y. Battie
4
, A. En Naciri
4
, Z. Herro
2
,
S. Guenneau
3
, S. Enoch
3
, L. Joly
5
, J. Cousin
5
& A. Bruyant
1
We report on the realization of functional infrared light concentrators based on a thick layer of air-
polymer metamaterial with controlled pore size gradients. The design features an optimum gradient
index prole leading to light focusing in the Fresnel zone of the structures for two selected operating
wavelength domains near 5.6 and 10.4 µm. The metamaterial which consists in a thick polymer
containing air holes with diameters ranging from λ/20 to λ/8 is made using a 3D lithography technique
based on the two-photon polymerization of a homemade photopolymer. Infrared imaging of the
structures reveals a tight focusing for both structures with a maximum local intensity increase by a
factor of 2.5 for a concentrator volume of 1.5 λ
3
, slightly limited by the residual absorption of the
selected polymer. Such porous and at metamaterial structures oer interesting perspectives to
increase infrared detector performance at the pixel level for imaging or sensing applications.
Gradient index optics plays a major role in micro-optics and micro-photonics to eciently manipulate light using
compact and simple shape optics
1–6
. is attribute has driven a number of applications notably in ber-optic com-
munication, or optical medical devices where they can be used for low-aberration imaging in a space-eective
way
7–9
. In the context of infrared detection and notably mid-infrared imaging, at gradient index (GRIN) lenses
represent an attractive solution to enhance the photometric performances by concentrating light onto ever
smaller active areas. In fact, the ability to focus light directly at the pixel level is highly desirable to reduce the
detector volume and its thermal noise, while having an optimal footprint and resolution. However, challenges
still remain in the integration of light concentrators with dimensions compatible with the small detector size and
pitch.
e interest in down-scaled GRIN lens was recently renewed in the track of metamaterials (MM) studies
10–14
because such engineered structures oer unprecedented control over the achievable refractive index. In this
context, compact designs of Metamaterial GRIN lens derived from transformation optics (TO) methods were
reported
15–16
.
It was notably suggested to design a at metamaterial layer analogous to the Maxwell sheye and Luneburg’s
lens for which the refractive index corresponds to the stereographic projection of a sphere on a plane
17,18
. MM
made of toroidal inclusions were proposed to achieve the hyperbolic secant index prole
10,11
, known to produce
stigmatic images
19
and corresponding to the Mercator projection of a sphere on plane
17,18
. Based on these simu-
lation results
10
, it appears that a few micrometer thick MM layer of small volume (in the order of λ
3
) can produce
the required tight and ecient focusing in the mid-IR with a negligible footprint. Standard GRIN lenses of dif-
ferent materials with continuous index prole can be fabricated via dierent techniques such as Chemical Vapor
1
Laboratoire de Nanotechnologie et d’Instrumentation Optique, ICD, CNRS UMR 6281, Université de Technologie de
Troyes, 12 Rue Marie Curie CS42060, 10004 Troyes Cedex, France.
2
Laboratoire de Physique Appliquée, Université
Libanaise, Faculté des Sciences II, Fanar, Liban.
3
Aix-Marseille Univ., CNRS, Centrale Marseille, Institut Fresnel
UMR 7249, 13013 Marseille, France.
4
Laboratoire de Chimie et Physique, Université de Lorraine, 1 Bd Arago, 57070
Metz Technopôle, France.
5
Groupe de Spectrométrie Moléculaire et Atmosphérique GSMA, UMR CNRS 7331,
Université de Reims, U.F.R. Sciences Exactes et Naturelles, Moulin de la Housse B.P. 1039, F-51687 Reims, France.
Correspondence and requests for materials should be addressed to J.M. (email: johnny.moughames@utt.fr) or
S.J. (email: sa.jradi@utt.fr) or A.B. (email: aurelien.bruyant@utt.fr)
received: 30 March 2016
Accepted: 17 August 2016
Published: 04 October 2016
OPEN
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Scientific RepoRts | 6:33627 | DOI: 10.1038/srep33627
Deposition (CVD)
20
, ion exchange
21–23
, thermal
24
and UV polymerization
25
but all these techniques typically lack
both spatial resolution and sucient refractive index contrast to scale down the lens size.
So far, MM GRIN lenses were realized and tested in the acoustic and microwave domains
26–28
. For shorter
wavelengths, micro-scaled GRIN lenses with a so, continuous, gradient index distribution in a polymer block
were proposed
29
by spatially tuning the cross-linking of the photopolymer under dierent irradiation conditions.
However, the achievable contrast of refractive index measured in the visible is very low (~0.01) and no exper-
imental demonstration of light focusing eect was shown. In the eld of diractive optics, at lenses based on
photonic crystals
30
or blazed binary gratings
31
were also proposed for imaging purpose. For such structures, the
pitch is comparable or larger than the wavelength and their response is chromatic. us, the possible roads to
achieve the fabrication of the proposed MM GRIN lenses in the infrared range (e.g. between 5–11 µ m) with the
required subwavelength discretization step and a sucient index contrast still have to be explored.
In this work, the fabrication of functional IR MM GRIN lenses is carried out using a 3D lithography technique
based on Two Photon Polymerization (TPP) of photopolymers. is technique is distinguished by its exibility,
swiness to fabricate complex 3D microstructures, and its high spatial resolution able to produce minute details
(< 100 nm) over relatively large scale (> 100 µ m). In addition, for reasonably small concentrator thickness (e.g.
< 10 µ m), a number of transparencies windows are present in the infrared range. us the microstructured poly-
mer thick lm was used as the nal material without the need of further transfer processes. is makes TPP very
suitable for direct realization and optimization of functional 3D MM concentrators prior more demanding con-
ventional photolithography and etching processes. e possibility of rapid prototyping of 3D designs and testing
makes it possible to adopt an iterative approach of simulation, fabrication and characterization.
Results
Infrared concentrator design. In order to design the MM GRIN
32,33
lens, shortly referred to as “MM con-
centrator”, our approach consists in creating an eective radial refractive index prole n(r) by introducing an
adequate concentration of subwavelength holes in the polymer block (cf. Fig.1(a)). e ideal hyperbolic secant
distribution previously proposed to focus light
34–36
with MM is expressed as:
α
α
=
=
.
−
nr nhr
r
h
n
n
() sec( ),
with
1
cos
(1)
o
o
ro
1
o
where, n
o
is the refractive index of the bulk polymer at the concentrator center at r = 0, and n
ro
is the minimum
refractive index of the porous polymer at the concentrator edge at r = r
o
. For an incident parallel beam, such
prole is known for long
19
to produce repeated astigmatic focus spots within the graded index material, that are
characterized by a pitch length 4f = 2π/α. e position of the rst spot with respect to the rst interface is equal
to f and can be calculated considering the pixel size (r
o
), and the achievable refractive index ratio. is quarter
pitch distance corresponds to the at lens thickness needed to obtain the best focus exactly at the second inter-
face. However, this thickness can be further decreased (t < f ) to produce a spot in the external air medium, in
the vicinity of the second interface. e aberrations are minimal as long as the focus spot is kept within a sub-
wavelength distance from the interface. While it is interesting to work with the smallest thickness t to speed up
and facilitate the fabrication process, simulations show that a minimum thickness is required for a given pixel
size (e.g. 2r
o
~ two wavelengths) to achieve a correct operation. In the case of wavelength-scale concentrator, the
paraxial formula giving the working distance from the second interface
37
strongly overestimates the spot position
for such wavelength-scale structures and electromagnetic simulation should be carried out to determine more
precisely the short working distance for dierent t. An alternative analytic estimation was derived by neglecting
the impact of the radial propagation in the material on the phase of the rays. By considering only the longitudinal
optical path l(r) = n(r)*t , needed to transform an input plane wave front into an output spherical wave of the form
exp (ik(|r − r
f
|)), focusing in r
f
at a working distance WD from the interface, the following relations are then
obtained:
Figure 1. (a) Example of refractive index proles given by the secant hyperbolic relation (in cyan); the derived
expression (dashed red), and corresponding discretized refractive index (dark blue) along the diagonal prole
shown in the device top view. (b) Top view of the device. e square holes sizes are position dependent.
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Scientific RepoRts | 6:33627 | DOI: 10.1038/srep33627
δ
=
++
+
=
−++
tWD
WD WD
n
n(r)
WD 1WD
t
n,
with ()
1
,
(2)
ro
WD
r
f
o
2
2
2
2
where k = 2 π /λ is the free space wave number. Using the latter relation, WD and r
o
can be freely chosen for
an achievable index contrast δn = n
ro
− n
o
, thus determining the thickness t and the required refractive index
prole n(r). e Fig.1(a) exemplies the refractive index proles similarity given by the two approaches for
typical parameters used in this work. e index proles are almost identical within the small concentrator region
(r < r
o
). While the above formula provides a coarse estimation for the wavelength-scale concentrators’ parame-
ters (t, n(r)), the working distance revealed by electromagnetic simulations tends to be much smaller than the
input value WD when t is smaller or approximately equals to the wavelength. ese aspects are discussed in the
Supplemental Material (Supplemental Fig. S1).
Eective index determination. In order to achieve the nearly equivalent distributions given by eqs1 or 2,
the porosity of the material is engineered with the inclusion of subwavelength air holes inside the material,
as shown in Fig.1(b). e actual size of the square holes is deduced from the required eective permittivity
ε
e
= n
2
(r) using the eective medium described by the Maxwell-Garnett equation
38
εε
εε
εε
εε
−
+
=
−
+
Fr(),
(3)
e
e
o
o
where ε
0
=
n
0
2
and ε = 1 are the permittivities of the resist and background (air), respectively, and F(r) is the lling
fraction equals to the cross-sectional areas of the material (ε
0
) normalized by the surface of the cells visible in
Fig.1(b).
e negative liquid photoresist is a mixture made from Pentaerythritol triacrylate (PETA) which has been
widely used as polymerizable monomer to fabricate micro-optical elements
39–42
, and 2.4% of Irgacure 819
(Irg 819) as photoinitiator
43
.
To determine the possible spectral range of operation, the transmission of the considered polymer was meas-
ured by Fourier transform infrared spectroscopy (FTIR) technique. e infrared refractive indices of the bulk
polymerized resist were also estimated by spectroscopic ellipsometry, in order to determine for each wavelength
44
the maximum refractive index available n
o
(without porosity). e result is shown in Fig.2. For the actual design,
two operating wavelength ranges near 5.6 and 10.4 µm were selected close to the emission lines of our available
laser sources. For these wavelengths, the real refractive index n
o
is found to be close to 1.32 and 1.72, respectively.
MM concentrator optimization. Small concentrator sizes compatible with a possible integration at a pixel
level were selected. Concentrator areas slightly smaller than 3λ
2
(11 µ m ∗ 11 µ m and 18 µ m ∗ 18 µ m, respectively)
were hence designed, with short working distances f close to λ (1 and 2.1 µ m, respectively). For such parameters
and considering the material absorption an optimum metamaterial layer thicknesses were found by simulation
to be about 3 and 6 microns, respectively, resulting in concentrator volumes of about 1.5λ
3
. e width of the sub-
wavelength square holes radially increases from 240 nm to 600 nm for the rst concentrator and from 450 nm to
1.2 µ m for the second one (i.e. from about λ /20 to λ /8).
e 3D photo-polymerization was performed using a femtosecond TPP-based technique from Nanoscribe.
Such Direct Laser Writing (DLW) was used extensively in the past few years to realize nearly arbitrary 3D pat-
terning
45,46
. In order to obtain the required high spatial resolution, we have studied the behavior of our photoresist
by measuring the polymer linewidth obtained for dierent scan speeds. Linewidth down to 75 nm were obtained
and are reported in Supplemental Information (cf. Supplemental Fig. S2). For both structures, a constant writing
Figure 2. Real and imaginary parts of the polymer refractive index obtained from infrared ellipsometric
measurement, by using a wavelength by wavelength inversion method
44
.
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Scientific RepoRts | 6:33627 | DOI: 10.1038/srep33627
speed of v = 75 µ m/s was found to be satisfactory compromise between resolution and speed to process the whole
structure in about 4 hours.
Figure3(a,b) show the SEM images of the experimental realizations having dimensions optimized for two
dierent wavelengths, i.e. 10.4 µ m and 5.6 µ m respectively. e rst structure was made with the above mentioned
scan speed at a laser power of 7 mW. In order to minimize the diraction by the structure edge, the concentrator
was integrated in a thin square block of polymer of 150 µ m size. e second one was written at the same speed but
at a slightly smaller light power of 6 mW to achieve smaller dimensions (the writing linewidth is about 80 nm). In
that case, an impedance matching was done by embedding the structure in a 75 µ m wide grid 0.6 × 0.6 µ m
2
square
holes in order to obtain the same eective refractive index as this of the concentrator edge.
Figure4 shows a 3D electromagnetic simulation of the MM structure designed at 10.4 µ m, illuminated from
the bottom by a plane wave polarized along the x axis direction. e eld intensity is normalized by the eld
intensity obtained without the MM lens. e spot size obtained for the discretized prole is slightly smaller than
λ (7.6 and 5.2 µ m measured along the x and y axis respectively at Full Width Half Maximum). In fact, compared
to simulations performed on a concentrator with a continuous index distributions (shown in the Supplemental
Fig. S3), the working distance is found to be shorter (2.1 µ m vs 7.5 µ m) and the focusing is a bit tighter. is can
be understood by the fact that the refractive index prole tends to be higher in the center of the MM refractive
index distribution due to the rather large discretization step. e discretization also introduces some anisot-
ropy between the transverse and axial planes which is not accounted by the isotropic eective medium theory
employed.
Figure 3. (a) SEM top view of the MM concentrator designed for a wavelength of 10.4 µ m integrated in a
150 µ m thin polymer block. e inset is a SEM side view of MM concentrator; (b) SEM top view of the MM
concentrator designed for 5.6 µ m.
Figure 4. 3D Finite Dierence Time Domains (FDTD) simulation of the MM concentrator spot (energy
density enhancement) at λ = 10.4 µm for the 6 µm high concentrator. (a,b) Axial cross-sections in the (x, z)
and (y, z) plans respectively for an incident plane wave polarization along x. (c) Simulation in the (x, y)
transverse plan at the focus maximum for the same incident plane wave. (d) Simulation in the (x, y) transverse
plan at the focus maximum for a circular polarization, calculated by averaging the energy densities of a
x-polarized and a y-polarized plane wave.
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Scientific RepoRts | 6:33627 | DOI: 10.1038/srep33627
Infrared characterization. e focusing eect of the fabricated structures was imaged with the IR set-up
shown in Fig.5(a) using an IR camera assisted by a visible light microscope. e later was adjusted for each wave-
length to image the same object plane than the IR camera by simultaneously imaging a bright point scatterer. e
measurements were done in transmission on each structure with two available quantum cascade laser sources
(5.67 µ m or 10.37 µ m). A ZnSe aspheric lens with a numerical aperture NA = 0.4 was used as an objective lens
leading to a theoretical Abbe resolution limit of about 9 and 16 µ m, respectively.
e obtained IR images in Fig.5(b,d) and proles in Fig.5(c,e) reveal the presence of a focus spot in the
immediate vicinity of MM lens. One can see from these far-eld images that the rst MM lens designed for the
10.37 µ m exhibits the expected, mostly diraction limited spot as can be judged by comparing the experimental
prole and the point spread function of the objective lens shown in Fig.5(c). In comparison, the smallest MM
lens designed for the 5.67 µ m presents a more modest connement mainly due to the smaller n
o
value (about
Figure 5. (a) Schematic representation of the experimental setup. (b) IR CCD image of the larger concentrator at a
wavelength of λ = 10.4 µ m. e image is normalized by the intensity recorded without polymer structure. (c) Related
intensity prole measure along the segment marked by black arrows in (b). e prole of the point spread function of
the objective lens is shown in dashed red. (d) Normalized IR CCD image of the smaller concentrator at a wavelength
of λ = 5.67 µ m. (e) Related intensity prole measured along the segment marked by the black arrows in (d).