Polymer lattices as mechanically tunable 3-dimensional photonic crystals operating in
the infrared
V. F. Chernow, H. Alaeian, J. A. Dionne, and J. R. Greer
Citation: Applied Physics Letters
107
, 101905 (2015); doi: 10.1063/1.4930819
View online: http://dx.doi.org/10.1063/1.4930819
View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/107/10?ver=pdfcov
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Polymer lattices as mechanically tunable 3-dimensional photonic crystals
operating in the infrared
V. F.
Chernow,
1,
a)
H.
Alaeian,
2,3
J. A.
Dionne,
3
and J. R.
Greer
1,4
1
Division of Engineering and Applied Sciences, California Institute of Technology, Pasadena,
California 91125, USA
2
Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA
3
Department of Materials Science and Engineering, Stanford University, Stanford, California 94305, USA
4
The Kavli Nanoscience Institute, California Institute of Technology, Pasadena, California 91125, USA
(Received 17 June 2015; accepted 29 August 2015; published online 11 September 2015)
Broadly tunable photonic crystals in the near- to mid-infrared region could find use in spectroscopy,
non-invasive medical diagnosis, chemical and biological sensing, and military applications, but so far
have not been widely realized. We report the fabrication and characterization of three-dimensional
tunable photonic crystals composed of polymer nanolattices with an octahedron unit-cell geometry.
These photonic crystals exhibit a strong peak in reflection in the mid-infrared that shifts substantially
and reversibly with application of compressive uniaxial strain. A strain of
40% results in a 2.2
l
m
wavelength shift in the pseudo-stop band, from 7.3
l
m for the as-fabricated nanolattice to 5.1
l
m
when strained. We found a linear relationship between the overall compressive strain in the photonic
crystal and the resulting stopband shift, with a
50 nm blueshift in the reflection peak position per
percent increase in strain. These results suggest that architected nanolattices can serve as efficient
three-dimensional mechanically tunable photonic crystals, providing a foundation for new opto-
mechanical components and devices across infrared and possibly visible frequencies.
V
C
2015
AIP Publishing LLC
.[
http://dx.doi.org/10.1063/1.4930819
]
Three-dimensional (3D) photonic crystals (PhCs) have
been the focus of ever-increasing interest in the scientific
community given their potential to impact areas spanning
energy conversion to analyte sensing. These architected mate-
rials have a periodic variation in their refractive index and
selectively reflect light of wavelengths on the order of their
periodicity.
1
Though only a few 3D PhCs possess a complete
photonic bandgap,
2
,
3
defined as a range of frequencies for
which incident light cannot propagate in any direction, all 3D
PhCs have stopbands that forbid light propagation in some
crystallographic directions.
4
Within the spectral range of a
photonic bandgap or stopband, light is selectively reflected,
rendering 3D PhCs applicable in numerous optical devices
such as low-loss mirrors,
5
,
6
lasers,
7
chemical
8
and mechani-
cal
9
,
10
sensors, and displays.
11
–
13
Several of these applica-
tions, including variable filters, laser sources, and strain
sensors,
4
require that the PhC be reconfigurable or reversibly
tunable while maintaining structural integrity, which would
enable them to be optically active over a wide range of fre-
quencies. Most existing fabrication methodologies produce
PhCs that operate over a fixed and limited bandwidth.
14
The
response of these otherwise passive PhCs can be rendered
active by fabricating structures using dynamic materials
which can respond to external stimuli including, for example,
electric fields, solvent swelling, and mechanical deformation.
Stopband position can be tuned by changing either the
refractive index and/or the periodicity of the PhC structure,
with the latter being generally more straightforward.
15
The
number of experimentally available methods for modulating
the lattice periodicity exceeds the number of index-tunable
materials, and, more importantly, altering the lattice constant
often leads to a more substantial stopband shift.
16
,
17
Several
approaches that can reversibly tune the stopband position of
PhCs post-fabrication—for example, methods based on tem-
perature gradients,
18
,
19
electric fields,
20
,
21
and solvent swel-
ling
22
—often suffer from limited tuning ranges, typically
restricted to between 100 and 200 nm shifts. Compositional
or structural changes that arise within 3D PhCs in response
to mechanical deformation allow for wider tuning ranges,
but are sometimes irreversible.
23
,
24
In addition, most of the
existing mechanically tunable 3D PhCs have been limited to
opal and inverse opal type structures.
4
,
16
,
23
,
24
We fabricated 3-dimensional polymer nanolattices with
4
l
m wide octahedron unit cells that act as PhCs and can
be stably and reversibly tuned by mechanical compression
over multiple cycles. The mechanical properties of similarly
architected hollow metallic and ceramic octahedron nanolat-
tices have been reported.
25
–
27
In this work, the polymeric
composition facilitates maximum optical tunability and re-
versibility. We find that a reversible
2.2
l
m stopband blue-
shift can be achieved with a uniaxial compression of
40%
and that the blueshift is linear for applied strains from 0% to
40%.
To fabricate the nanolattices, we used the direct laser
writing (DLW) two-photon lithography (TPL) system,
Photonic Professional (Nanoscribe GmbH, Germany).
Samples were prepared by drop-casting the negative-tone
photoresist “IP-Dip” (Nanoscribe GmbH) on a 500
l
m thick
polished silicon substrate; “IP-Dip” photoresist is composed
primarily (
>
95%) of the monomer pentaerythritol triacry-
late. An infrared laser was then used to crosslink and write a
preprogrammed pattern into the acrylic-based photopolymer
via two-photon absorption. The exposed sample was then
a)
Author to whom correspondence should be addressed. Electronic mail:
vchernow@caltech.edu.
0003-6951/2015/107(10)/101905/5/$30.00
V
C
2015 AIP Publishing LLC
107
, 101905-1
APPLIED PHYSICS LETTERS
107
, 101905 (2015)
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developed for 30 min in propylene glycol monomethyl ether
acetate and isopropanol. This process allows for maximum
control over the final architecture and enables the fabrication
of arbitrarily complex nano- and micro-structures. Figure
1(a)
shows that the nanolattices have individual octahedron
unit cells on the order of
4
l
m and are 6.5 unit cells tall.
Individual beams have elliptical cross-sections, with short
axes of
500 nm and long axes of
1.75
l
m.
Mechanical characterization of the nanolattices was per-
formed using an
in-situ
nanoindentation system, InSEM
(Nanomechanics Inc.), inside an SEM chamber (see Ref.
28
for specifications). This instrument enables precise measure-
ment of applied load vs. displacement data with simultane-
ous real-time visualization of nanolattice deformation.
28
In-situ
uniaxial compression experiments were conducted at
a constant prescribed displacement rate of 50 nm/s.
Nanolattices were aligned orthogonal to the electron-beam
and in line with the nanoindenter arm, such that the periodic-
ity of the lattice was gradually reduced along this compres-
sion axis.
Samples were strained by
>
60% before reaching the
instrument load limit of 35 mN. Figure
1(b)
shows represen-
tative stress-strain data and SEM micrographs captured at
various points during a typical experiment. It appears that
the polymer nanolattices underwent a global compression,
where each layer of unit cells was compressed in a homoge-
nous fashion, gradually decreasing the pitch of the structure.
This is in contrast to a layer-by-layer collapse mechanism
typical of hollow ceramic and metallic octahedron nanolatti-
ces.
25
–
27
It also appears that the Poisson’s ratio of the nano-
lattices is close to zero because no transverse deformation
was observed—the structure neither expanded nor contracted
laterally—in response to axial strain. This behavior is likely
due to the fact that compressive straining will cause beams
to buckle into the pores of the lattice structure, instead of
contributing to lateral expansion or contraction. Analysis of
SEM images and a hysteresis in the stress-strain data
revealed that the structure recovered by
82% nearly imme-
diately following load removal after compression in excess
of 60%. The acrylic-based polymer that comprises the nano-
lattice is viscoelastic and continues to recover with time
through a time-dependent strain response. We observed a re-
covery to
90% of the original height within hours of the
primary compression. Subsequent to the initial cycle of com-
pression and recovery, samples were compressed again to
e
60% and appeared to recover to
100% of their initially
recovered height after this second cycle. Lattices were com-
pressed to
e
60% a 3rd and 4th time and showed similar re-
covery. This result suggests that a few permanent structural
defects were formed during the initial compression, and for
all subsequent deformations, the structure acts elastically
and recovers completely and instantaneously.
The micron-scale unit cell size of the nanolattices sug-
gests that the PhC will exhibit a bandgap in the infrared
range. We used Fourier Transform Infrared (FTIR) micro-
spectroscopy to evaluate the optical properties of the nanolat-
tices, including their reflectance and stopband position.
Spectra were acquired using a Nicolet iS50 FT-IR spectrome-
ter equipped with a Nicolet Continuum Infrared Microscope.
For this particular setup, the angular range of incidence was
16
–35.5
relative to the normal.
To establish a baseline understanding of the relationship
between strain and the position of the stop band, we fabri-
cated several nanolattices which mimicked compressed mor-
phologies for 4 strains—0%, 14.8%, 27.1%, and 38.6%—
corresponding to unit cell angles of approximately 45
,40
,
35
, and 30
, as shown in Figures
2(a)
and
2(b)
. These
“effectively strained” angle-varied nanolattices were fabri-
cated with slightly altered geometries such that the unit cells
evolved from fully isotropic in the unstrained state, to pro-
gressively more anisotropic at higher effective strains
(Figure
2(b)
). Increasing the degree of anisotropy in the unit
cells also serves to uniformly decrease the height and perio-
dicity of the overall lattice, with the effective strains calcu-
lated based on the relative change in the unit cell angle
experienced by octahedron nanolattices during
in-situ
com-
pression experiments. Compacting lattice periodicity along
the z-direction by altering the unit cell angle allowed us to
create a set of effectively strained lattices which represent
idealized versions of the compressed octahedron PhC at 0%,
14.8%, 27.1%, and 38.6% strain.
Figure
2(c)
shows the FTIR reflectance spectra for the
four nanolattices. For the as-fabricated nanolattices, a signifi-
cant peak in normalized reflectance emerges and is centered
at 7.42
l
m, which corresponds to the first order stop band.
The center of this peak shifts to progressively shorter wave-
lengths for nanolattices with decreasing pitch: from 7.42
l
m
for the unstrained nanolattice to 6.40
l
m for the 14.8% effec-
tively strained nanolattice, to 5.38
l
m for 27.1% effective
strain, and to 4.61
l
m for the 38.6% effectively strained sam-
ple. The plot in Figure
2(d)
reveals the relationship between
the central position of each stop band peak, denoted
k
peak
,
FIG. 1. (a) Scanning electron microscopy (SEM) images of a representative
as-fabricated octahedron nanolattice. Inset shows relevant dimensions of the
unit cell. (b) Representative stress-strain data for a uniaxial compression of
an octahedron nanolattice. Inset images are scanning electron micrographs
of the nanolattice, captured simultaneously at various points during the com-
pression experiment.
101905-2 Chernow
etal.
Appl. Phys. Lett.
107
, 101905 (2015)
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and effective strain,
e
eff
, based on the normalized reflectance
measurements of 24 separate unstrained and effectively
strained samples (6 samples for each strain). In addition to
the blueshifting of the photonic bandgap with increasing
effective strain, the stopband data appear to vary linearly
with strain. This is not unexpected because the opto-
mechanical response of these 3D PhCs under uniaxial com-
pression is associated with a change in spacing of closest-
packed planes, and a consequent change in the Bragg reso-
nance condition and peak wavelength. This trend is similar
to the stopband-strain relationships reported for 1D and 2D
mechanically tunable photonic crystals.
1
,
29
The largest stop-
band shift of 2.8
l
m was exhibited by samples that were
effectively strained by
40%. This stopband shift is more
substantial than the 1.25
l
m shift achieved by solvent swel-
ling of lamellar photonic crystal gels outlined by Kang
et al
.,
15
and outperforms other elastomeric 3D photonic crys-
tals like the one reported by Fudouzi and Sawada where a
20% strain leads to a 30 nm stopband shift.
30
The nearly full recoverability of the compressed poly-
meric nanolattices studied in this work required the design of
a special experimental setup which could measure the optical
response of compressed nanolattices in their strained state.
Figure
3(a)
provides a schematic of the custom compression
cell setup, which was constructed by first etching wells of
varying depths into a silicon substrate using deep-reactive
ion etching, followed by the fabrication of pristine unstrained
nanolattices into individual wells. An IR-transparent KBr
slide was then placed on top of the nanolattices and wells,
and then, to ensure uniaxial straining of the lattices, a
washer-shaped lead weight was placed on to the slide. Using
this compression cell, it was possible to strain an as-
fabricated sample to a preordained position and fix it in the
strained state by bounding from above by the IR-transparent
KBr slide, while it sits affixed to the polished Si substrate.
We then collected reflectance with the same FT-IR spec-
trometer as used on the effectively strained samples. Four
experiments on cyclically strained nanolattices were carried
out, with each one corroborating the finding that compress-
ing an octahedron nanolattice leads to a blueshifting in the
PhC stopband, and releasing the load shifts the stopband
back to within 89.8
6
2.8% of the original stopband position
FIG. 2. (a) SEM images of octahedron nanolattices fabricated with varying
angles, corresponding to different degrees of effective strain. (b) Schematic
of the relationship between unit cell angle and effective strain in the fabri-
cated nanolattice. (c) Normalized reflection spectra of a 45
unstrained octa-
hedron nanolattice, and three angle-varied nanolattices, corresponding to
increasing degrees of effective strain,
e
eff
. (d) Effective strain-stopband plot
for the angle-varied lattices. Note that
e
eff
and
k
peak
are directly proportional.
FIG. 3. (a) Schematic of the nanolattice compression cell setup. (b)
Normalized reflectance spectra for an as-fabricated nanolattice outside of
the compression cell (red), and under compression (blue) using the custom
FTIR compression cell setup shown in (a). (c) Normalized reflection spectra
under normal illumination for a simulated 45
unstrained octahedron nano-
lattice, and three simulated angle-varied nanolattices, each with correspond-
ing degrees of increasing effective strain. The main peak for each simulated
nanolattice corresponds to a 1st order Bragg reflection; secondary peaks that
appear at longer wavelengths are caused by the higher order Bragg reflec-
tions. (d) Strain-stopband plots comparing data from the as-fabricated angle-
varied lattices under corresponding effective strain, experimentally strained
nanolattices using a compression cell over multiple cycles, and the simulated
angle-varied lattices at normal incidence, and 25.7
incidence.
101905-3 Chernow
etal.
Appl. Phys. Lett.
107
, 101905 (2015)
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of the pristine nanolattice—
a value commensurate with the
90% recovery observed in nanolattice height following
primary compression. Figure
3(b)
shows the reflection
spectrum of a representative sample. For this particular
sample, the stopband of the initia
l nanolattice was centered
at 7.32
l
m and that of the 15.2% strained nanolattice blue-
shifted to 6.34
l
m. For this series of strained nanolattice
experiments, the applied strain was monitored by calculat-
ing the pathlength of the FTIR compression cell using inter-
ference fringes which appear in the background reflection
spectra.
31
The KBr surface of the cell is positioned nearly
parallel to the Si substrate—between which the nanolattices
are sandwiched—which results in the appearance of sinu-
soidal fringes in the spectra. These fringes are created by
interference between light that has been transmitted through
the sample, and light that has been reflected internally
between the parallel surfaces.
31
The number and the posi-
tion of interference fringes allow us to estimate the path-
length through the compression cell,
31
which is equivalent
to the thickness of the sample and the height of the com-
pressed nanolattices
d
¼
N
k
1
k
2
2
n
ef f
cos
hk
2
k
1
ðÞ
:
Here,
d
is the sample thickness or compression cell path-
length,
N
is the number of interference fringes between the
wavelength range
k
1
and
k
2
,
n
eff
is the effective refractive
index of the material within a well of the compression cell,
and
h
is the average angle of incident light on the sample.
Having measured the height of pristine, unstrained nanolatti-
ces using SEM imaging, and calculated the cell pathlength
for a compressed sample, we obtained a value for applied
compressive strain. Full details on this analysis are provided
in the supplementary material and in Figure S3.
32
Figure
3(d)
shows that
in-situ
straining of the nanolatti-
ces results in a blueshifting of the stopband and that a linear
relationship holds between applied strain and stopband posi-
tion. The slope of this linear dependency is a factor of 1.42
lower than the slope predicted by the idealized, effectively
strained nanolattices, also plotted in Figure
3(d)
for compari-
son. This plot reveals that nanolattices strained by 40.5%
exhibited a stopband shift of 2.19
l
m, compared to a
2.87
l
m shift for the effectively strained angle-varied nano-
lattices compressed by the same amount. This plot also
shows that, at high strains of
e
40%, the percent error
between the measured
k
peak
for
in-situ
strained and angle-
varied lattices is 14.1%, while at low strains, on the order of
e
10%, the percent error is significantly smaller, at 1.7%.
These deviations likely arise from minor shearing in the
in-situ
setup that accompanies the nominal uniaxial compres-
sive straining of the lattice. Shear strain in this system may
take the form of a torquing at the nodes of the unit cells com-
prising the lattice, which leads to a shape change rather than
a volume change and does not affect the periodicity of the
lattice in the vertical direction to the same degree predicted
by the angle-varied lattices modelling effective strain. It has
been previously shown that the stopband position increases
nonlinearly with shear strain,
1
which may also contribute to
our observation of larger deviations from the
k
peak
position
of the angle-varied lattices modelling effective strain, where
only uniaxial strain was taken into account.
Despite the slight differences between the
in-situ
strained and as-fabricated effectively strained lattice spectra,
these experimental results appear to agree well with numeri-
cal calculations. Figure
3(c)
shows full-field Finite
Difference Time Domain (FDTD) simulations of the reflec-
tance from angle-varied nanolattices. The simulated geome-
tries were determined by using SEM images of the
fabricated experimental samples; the polymer refractive
index of n
1.5 was determined by fitting FTIR reflectance
data for TPL polymerized IP-Dip thin films using a scatter-
ing matrix approach combined with a minimization tech-
nique (see supplementary material for a more complete
discussion).
32
IR-VASE ellipsometry would have been the
preferred method for determining the refractive index of IP-
Dip, but, since this resist is designed to be drop cast and
polymerized using two-photon absorption, spin coated and
UV-flood exposed samples did not possess the film uniform-
ity or crosslinking density necessary to obtain accurate index
measurements with this technique.
For the FDTD simulations, nanolattices were assumed
to reside on an infinite slab of Si with a fixed refractive index
of 3.4 over all frequencies. Figure
3(c)
shows the reflectance
spectra for four different simulated angle-varied octahedron
unit cells, 45
,40
,35
, and 30
, illuminated with a normal-
incidence plane wave. The simulations show a clear blueshift
of the reflection peak with decreasing apex angle of the octa-
hedron unit cell, in agreement with experimental results.
These numerical results also display a linear trend between
reflection peak position and effective strain, as do the experi-
ments on the as-fabricated and
in-situ
strained nanolattices
(see Figure
3(d)
). Despite the difference in the actual posi-
tion of
k
peak
for the fabricated and simulated angle-varied
lattices, the slopes of these lines are very similar. While the
simulations appear to over-predict the stopband wavelength,
this discrepancy in
k
peak
position is in large part due to the
angle of incident light used for illuminating simulated and
fabricated samples; simulated samples are illuminated using
plane waves incident at a single angle, and fabricated sam-
ples are under illumination from a Gaussian beam with an
angular range between 16
and 35.5
. Simulating nanolatti-
ces at an average illumination angle of 25.7
does shift the
calculated stopband peak closer to the experimentally meas-
ured peaks. Further discrepancies can be attributed to some
non-idealities in the fabricated samples like the imperfect
uniformity of beams and unit cells, and buckling at the joints
between unit cells.
The reflection peak observed in our experiments and
simulations can be attributed to the 1st order Bragg reflection
in the lattice. Bragg’s law is formulated as 2
d
cos
h
¼
n
k
,
where
d
is the vertical separation between two layers in the
lattice,
h
is the angle of the incident beam with the normal
line, and
n
is the order of the Bragg reflection. A monotonic
decrease in
d
from uniaxial strain will result in a monotonic
decrease in the resonance wavelength
k
peak
. This result is in
agreement with the general blueshift trend observed both in
the numerical and experimental data. Additional reflection
peaks observed at longer wavelengths can be attributed to
higher orders of the Bragg grating and are substantially
101905-4 Chernow
etal.
Appl. Phys. Lett.
107
, 101905 (2015)
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weaker than the main peak of the lattice. More details
regarding the lattice band structure, as well as variation in
the primary resonance peak with the incident angle, can be
found in the supplementary material.
32
This work demonstrates fabrication and characterization
methodologies for 3-dimensional polymer nanolattices,
active in the mid-IR range, whose photonic bandgap can be
reversibly modulated as a function of uniaxial compressive
strain. Opto-mechanical experiments and theory reveal that
applied uniaxial compressive strain and the photonic stop-
band are linearly related, with a maximum attained bandgap
shift of
2.2
l
mat
40% compressive strain. These findings
imply that architected nanolattices may be utilized for
emerging applications including but not limited to optical
strain gauges, accelerometer, and other mechanical sensors,
as well as tunable laser sources and variable filters. And
while 3D lattice fabrication using TPL DLW is currently
constrained by the minimum axial resolution attainable,
restricting the dimensions of the octahedron geometry stud-
ied here to unit cell sizes of no less than 2.5
l
m, advances
like stimulated-emission-depletion (STED) DLW are push-
ing the resolution limits of this technology and may soon
enable the patterning of any arbitrary 3D lattice with pho-
tonic properties extended into the visible range.
V.C. and J.R.G. gratefully acknowledge the financial
support of the Dow-Resnick Grant and of the Defense
Advanced Research Projects Agency under the MCMA
program managed by J. Goldwasser (Contract No.
W91CRB-10-0305). The work of H.A. and J.A.D. was
funded by a Presidential Early Career Award administered
through the Air Force Office of Scientific Research (No.
FA9550-15-1-0006) and funding from a National Science
Foundation CAREER Award (No. DMR-1151231). The
authors thank Seok-Woo Lee for assistance with mechanical
characterization, George Rossman for FT-IR assistance,
Kevin Tran for the creation of preliminary FDTD models,
and Christopher Raum for thought provoking discussions.
The authors also thank the Kavli Nanoscience Institute
(KNI) at Caltech for support and availability of cleanroom
facilities.
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See supplementary material at
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for the
fabrication of the compression cell, cell pathlength calculations, absorption
features in FTIR spectra, polymer refractive index calculations, FDTD pa-
rameters for scattering and band diagrams, and simulation of stopband de-
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101905-5 Chernow
etal.
Appl. Phys. Lett.
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