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Characterization of a Mechanically Tunable Gyroid Photonic Crystal Inspired by the Butterfly Parides Sesostris

  • AMOLF & Eindhoven University of Technology

Abstract and Figures

A mechanically tunable macroscale replica of the gyroid photonic crystal found in the Parides sesostris butterfly's wing scales is systematically characterized. By monitoring both photonic frequency changes and the distribution of stress fields within the compressed structure, electromagnetic transmission features are found and can be frequency-tuned and the structure only contains localized high stress fields when highly compressed.
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© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1
geometries. Using the naturally occurring photonic gyroid
found in the wing scales of Parides sesostris butterfl ies
[ 28 ] as an
experimental model system ( Figure 1 ), we employed high-reso-
lution additive manufacturing to replicate its 3D architectural
details in a reversibly deformable macro-scale analogue. We
specifi cally used a fi lling fraction of 40% that closely matches
the fi lling fraction of the butterfl y gyroid.
[ 28 ] The tunability of
the deformable PC’s electromagnetic properties can be inves-
tigated by imposing controlled anisotropic deformations of the
crystal structure through compressive loading. By fabricating
exible dielectric PCs with centimeter-scale unit cells, it is pos-
sible to produce materials with tunable photonic responses
in the microwave regime (0.3–300 GHz). By exploiting the
scale-invariance of Maxwell’s equations and of the elastic
material response, the structure–function relationships of
photonic materials can be directly investigated. By working
at the macroscale, we are taking full advantage of the design
freedom of additive manufacturing, comprehensive optical
characterization using microwave technology, and the in situ
3D structural characterization capabilities of microscale X-ray
computed tomography. This method could readily be applied
to assess any other structural motif in a similar manner. Once
the fundamental structure–function relationships underlying
the dynamics of reversibly deformable photonic materials are
understood at the macroscale, this insight can be applied for
the realization of structural motifs at smaller length scales to
create tunable photonic devices for the Terahertz, Telecom,
Near-IR, visible, UV, and X-ray frequency ranges.
Inspection of P. sesostris (Figure 1 ) reveals that the brightly
colored metallic appearance of the green wing patches origi-
nates from scales that are not individually resolvable by the
human eye (Figure 1 C–E). These scales have a complex mor-
phology, including surface ridges (Figure 1 D–G),
[ 33–35 ] spec-
trally selective pigment-based absorbers, as proposed by Wilts
et al.,
[ 35 ] and an underlying gyroid PC (Figure 1 G),
[ 28,33–38 ] rst
proposed by Michielsen and Stavenga
[ 28 ] arranged in intrascale
domains (Figure 1 F), [ 28,33–38 ] which are all expected to contribute
to the scales’ optical appearance.
[ 28,30,35–38 ] A graphical repre-
sentation of the gyroid is presented in Figure 1 H, with its unit
cell highlighted in green. Using the key dimensional parame-
ters obtained from previous transmission electron microscopy
(TEM) studies,
[ 28 ] a fl exible macroscale model of the gyroid was
fabricated using high-resolution 3D printing ( Figure 2 A,B).
The resulting structure was investigated to see if its photonic
response could be deliberately tuned and controlled by system-
atically varying the applied compressive load.
In order to characterize the gyroid’s deformation modes,
X-ray computed microtomographic (micro-CT) reconstructions
were obtained from the fl exible 3D-printed models at various
Characterization of a Mechanically Tunable Gyroid Photonic
Crystal Inspired by the Butterfl y Parides Sesostris
Caroline Pouya , * Johannes T. B. Overvelde , Mathias Kolle , Joanna Aizenberg ,
Katia Bertoldi , James C. Weaver , and Pete Vukusic *
Dr. C. Pouya, Prof. P. Vukusic
School of Physics and Astronomy
University of Exeter
Exeter EX4 4QL , UK
J. T. B. Overvelde, Prof. K. Bertoldi
School of Engineering and Applied Sciences
Harvard University
Cambridge , MA 02138 , USA
Dr. M. Kolle, Prof. J. Aizenberg, Dr. J. C. Weaver
Wyss Institute for Biologically Inspired Engineering
Harvard University
Cambridge , MA 02138 , USA
Dr. M. Kolle
Department of Mechanical Engineering
MIT, Cambridge , MA 02139 , USA
DOI: 10.1002/adom.201500436
Photonic crystals [ 1–5 ] (PCs) can be used to selectively refl ect spe-
cifi c frequencies of electromagnetic radiation. Since most PCs
are static in material composition and geometry, their refl ec-
tion or transmission behavior can only be changed through
angular reorientation. In contrast, fl exible PCs can exhibit tun-
able photonic responses,
[ 3,5–7 ] where refl ected or transmitted
frequencies can be controlled through structural deformation.
Tunable responses can also be achieved via the application
of voltage,
[ 8,9 ] by adsorption of vapors,
[ 10,11 ] via temperature
[ 12,13 ] or by the application of strain.
[ 14–16 ] Recently,
increased efforts have been aimed at fabricating 1D,
[ 16 ] 2D, [ 17,18 ]
and 3D
[ 19 ] tunable PCs. Since the requirements imposed on PC
geometry and material compositions vary between applications,
the development of robust fabrication strategies for the custom-
izable and large-scale production of 3D PCs is a research area
of great interest. Accordingly, material scientists have embraced
the study of structurally colored biological photonic systems
to gain inspiration for synthesis routes that can facilitate the
fabrication of novel optical materials with exploitable proper-
[ 16–20 ] Such biological photonic structures found in terres-
trial and aquatic environments typically comprise polymeric
materials including keratin, cellulose, and chitin. They exhibit a
wide range of geometries including colloidal particles,
[ 21,22 ] con-
[ 23 ] or discrete units of multilayers,
[ 24,25 ] concentric cylin-
[ 16,26 ] and bicontinuous gyroids.
[ 27–30 ] Despite the promise
of new biologically inspired design routes for photonic material
production, there is currently a dearth of cost-effective high-
throughput methods by which synthetic analogues of these bio-
photonic materials can be fabricated.
In an effort to address these limitations, we have utilized
an effi cient experimental approach to investigate electromag-
netic responses
[ 31,32 ] and structural properties of tunable gyroid
Adv. Optical Mater. 2015,
DOI: 10.1002/adom.201500436 © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
stages of compression ( Figure 3 ). The reconstructions of the
deformed gyroid models were then compared to the results
obtained from the fi nite element analysis (FEA) compression
simulations ( Figure 4 A). The nonlinear fi nite element simula-
tions were performed on virtual gyroid models constructed from
approximately 10 000 tetrahedral elements per unit cell, which
were compressed uniaxially by applying a vertical displacement
to the top face, while leaving all lateral faces free to expand. The
results obtained from these studies revealed that the mechan-
ical response of the gyroid was only moderately affected by the
number of unit cells. Models comprising 3×3×3, 5×5×5, and
7×7×7 unit cells exhibited a similar extent of lateral expan-
sion. In particular, for a gyroid containing 7×7×7 unit cells, the
maximum lateral expansion was measured to be 2.15%, 4.38%,
6.78%, and 9.25% for applied strain values of 5.6%, 11.1%,
16.7%, and 22.2%, respectively. These values correlated well
with the 10×10×10 structure tested experimentally, in which
the maximum lateral expansion was observed to be 9.7% at a
compression of 22.2%. The results of these simulations are pre-
sented in Figure 4 , clearly showing the large geometric changes
induced by the applied compression. The contour colors cor-
respond to the Von Mises stress ij ij kk
denoting a component of the Cauchy stress), where the most
highly stressed regions are denoted in red. Signifi cantly, these
stress fi eld intensity data (Figure 4 A) revealed that, at moderate
compressions, the stress is very uniformly distributed over the
unit cell, only beginning to show the tendency to localize at
much higher compressions. This form of resistance to shear
stress in the gyroid, highlighted previously by different studies
on primitive and diamond structures,
[ 39 ] is a property that
would improve the system’s toughness.
Adv. Optical Mater. 2015,
DOI: 10.1002/adom.201500436
Figure 1. Mechanistic origins of structural color in the neotropical butterfl y, Parides sesostris. Located on A) the wings of P. sesostris are B) striking
metallic green patches and C–F) high-resolution structural characterizations of their constituent scales reveals a complex composite architecture con-
sisting of E) surface ridges and F) an underlying photonically active multi-domain gyroid.
[ 33,34 ] D) shows an electron beam Moiré pattern, generated by
matching the e-beam scanning periodicity with the structural periodicity of the wing scales. G)
[ 33,34 ] shows a the 3D structure present within P. sesostris
wing scales, which can be graphically represented by H) the photonic gyroid structure with an individual unit cell highlighted in green. For reference,
each scale measures 150 µm in length. Scale bars: A) 1 cm, B) 5 mm, C) 200 µm, D) 50 µm, E) 10 µm, F) 4 µm, G) 2.5 µm.
© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Excluding the boundary effects where the physical gyroid
model contacted the compression plates, the X-ray computed
micro-tomography and FEA data sets agreed surprisingly well
within the bulk core of the gyroid, thereby providing a robust
model for performing realistic microwave electromagnetic
transmission simulations. Figure 4 B,C show the theoretical and
experimental transmitted fi eld magnitude data, respectively,
obtained using transverse magnetic incident polarization, with
respect to the plane of incident radiation, from the compliant
gyroid. The structure was compressed in the [100] direction by
0%, 5.6%, 11.1%, 16.7%, and 22.2% of the original size of the
gyroid model. The observed frequency shifts that occurred upon
compression of the sample were similar for both transverse
magnetic and the equivalent transverse electric polarizations.
Based on these observations and since the linear polarization
dependence of the gyroid has been discussed previously,
[ 29,32 ]
the transverse electric results are not presented here. The
sample was positioned at an azimuthal angle of
= 0° and was
rotated over a polar angle range of 45°
45° for each com-
pressed state (Figure 2 C). The dark bands in Figure 4 B,C are
representative of low electromagnetic transmission through the
gyroid PC structure for each of the indicated states of compres-
sion. The frequency axes are presented in normalized reduced
frequency units of c/a where c is the speed of light in free space
and a is the uncompressed lattice constant of 9 mm. In the
native, uncompressed state, two of the transmission minima
(labeled “P” and “Q” on the central graph of Figure 4 B) are in
very close proximity and appear to overlap or merge, particu-
larly at normal incidence. As compression of the sample begins
to extend beyond 11.1%, these previously overlapping features
separate into two discrete and distinctly resolvable bands (“P”
and “Q”). From theoretical electric fi eld plots (Figure S1, Sup-
porting Information) and geometric analyses, these two fea-
tures originate from standing wave-type resonances along the
[101] and [001 ] directions (labeled “P” and “Q,” respectively,
on the central graph of Figure 4 B). The resonant feature labeled
“P” on the central graph of Figure 4 B also results from signifi -
cant absorption. When the structure is uncompressed, the fre-
quency position of these features also lies close to the crossing
point of a third feature (labeled “R” on Figure 4 B), which origi-
nates from a standing wave-type resonance along the
[001 ]
direction. When compressed by 22.2%, in the [100] direction as
described, the gyroid model's central region expands by 9.7%
along the
[001 ] direction. From trigonometric analysis, and by
using these expansion values, we can identify similar expan-
sions across the [010],
[001 ], and [011] directions with corre-
sponding decreases in frequency of the resonant features (“Q”
and “R” on Figure 4 B) associated with these directions. Simi-
larly, the structural confi gurations in the [100] and
[101] direc-
tions are reduced to 77.8% and 95.1% of their original sizes:
Adv. Optical Mater. 2015,
DOI: 10.1002/adom.201500436
Figure 2. Fabrication and characterization of the gyroid photonic crystal. High-resolution additive manufacturing was used to generate a A,B) com-
pressible gyroid from a rubber-like polymer (permittivity of
= 2.85 + 0.15i). C) illustrates a schematic diagram of the microwave transmission experi-
mental set-up, showing the relative positions of the broadband horns, the gyroid photonic crystal sample, and the compression device. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Figure 4 B,C show a corresponding increase in frequency of the
associated resonant features along these directions (labeled “P”
on Figure 4 B). At 22.2% compression, the experimentally deter-
mined frequency shifts of each transmission minimum, in
reduced units, were measured to be 0.072 (c/a), 0.039 (c/a), and
0.177 (c/a) (Figure 4 C) for the features labeled “R,” “Q,” and
“P,” respectively, in Figure 4 B. These values were measured
at the polar angle of 45° (Figure 4 C). As a result of the gyro-
id's bicontinuous nature (consisting of a solid/polymer phase
and a void/air phase), the application of a compressive load
results in a net volume reduction of the structure (Figure 3 ).
This increase in material fi lling fraction directly corresponds
to a slight narrowing of the transmission minima, which is
observed both theoretically (Figure 4 B) and experimentally
(Figure 4 C). A very slight red-shift in frequency is also expected
from a change in fi lling fraction away from the optimum condi-
tion for large stop-band width as occurs in the uncompressed
gyroid structure.
[ 28,32 ] For the simulated gyroid modeling, when
the maximum compression of 22.2% was applied to the struc-
ture, the frequency shifts of each of the corresponding features
labeled “R,” “Q,” and “P,” respectively, in the theoretical data
plots (Figure 4 B) were measured to be approximately 0.057,
0.033, and 0.165, in reduced frequency units ( c/a ). These values
were also measured at the polar angle of 45° (Figure 4 C). These
frequency changes were marginally smaller than those obtained
from the experimental measurements, with a slight variability
in fi lling fraction and the lack of graded expansions, being the
most likely contributing factors.
[ 40 ]
In conclusion, through both theoretical and experimental
approaches, in this study, we have performed a quantitative
assessment of a fl exible gyroid PC structure and compression-
dependent optical response. We found that, when compressed,
previously overlapping transmission minima spectrally sepa-
rate. While this observed overlap in dispersion features and
consequent shifting behavior will only occur for specifi c geom-
etries, similar results are predicted for other PC structures that
exhibit a similar bcc Bravais lattice symmetry. Through the
structural investigation, we also found that the gyroid does not
tend to localize stresses but uniformly distributes them at mod-
erate compressions. This structural property is of particular
importance from a mechanical engineering perspective as it
would greatly enhance the toughness of the system. A robust
sample that can withstand variable degrees of structural defor-
mation is a necessity when designing and mechanically tuning
a robust photonic system.
As shown in these studies, the capacity of 3D printing to
rapidly create prototypes of almost any morphology in a broad
range of material compositions makes it an ideal tool to build
and systematically experimentally investigate macroscale
photonic materials that can be assessed electromagnetically in
Adv. Optical Mater. 2015,
DOI: 10.1002/adom.201500436
Figure 3. Micro-CT reconstructions of the compressible gyroid. X-ray computed microtomographic reconstructions of the 3D-printed gyroid in its
uncompressed state and when compressed by 22.2% of its original size, clearly showing the reduction of volume fraction upon loading and the cor-
responding lateral expansion of the structure.
© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
the microwave regime and structurally characterized through
micro-CT. Consequently, the photonic response of periodic
geometric solids, such as the single gyroid, can be dynami-
cally tuned for a specifi c application of interest, while providing
critical design cues for the fabrication of their micro- and
nanoscale structural analogues.
Experimental Section
Research Species : Dry specimens of P. sesostris were acquired from
commercial sources (Worldwide Butterfl ies (
For optical characterization, the wings were imaged with a Keyence
digital microscope (VHX-2000). The same samples were then mounted
to conductive carbon tape, sputter-coated with gold, and examined with a
Tescan VegaIII scanning electron microscope (SEM). For the generation
of electron beam Moiré patterns, the SEM scan line periodicity was
matched to the ridge periodicity in the wing scales, thus permitting the
illustration of nanoscale structural periodicity in a macroscale sample.
Using information from previously published TEM studies,
[ 28,34 ] the
critical parameters of the gyroid structure, principally its fi lling fraction
of 40%, were identifi ed.
Gyroid Modeling and Fabrication : Gyroid model rendering for
3D-printing compatible STereoLithography (.stl) fi les was achieved with
a custom-made MATLAB code.
[ 41 ] Briefl y, level set functions were used
as versatile approximations to calculate inter-material dividing surfaces
of the gyroid.
[ 28,42–46 ] In particular, to describe the surface of the gyroid
structure investigated in this study, we used Equation ( 1) with t = 0.3
and L = 9 mm.
[ 41 ]
LxLyLyLzLzLxtsin 2cos 2sin 2cos 2sin 2cos 2
ππ ππ ππ
()() ()() ()()
++= (1)
Vertices and facets of these surfaces were then rendered using
MATLAB’s isosurface function. Facet normals and vertex coordinates
were written to an STL fi le directly from MATLAB using a custom
script. The resulting 3D model had a material fi lling fraction of 40%
and a lattice constant a = 9 mm (Figures 2 , 3 ), designed so that the
model’s structure was directly analogous to the P. sesostris wing-scale
Adv. Optical Mater. 2015,
DOI: 10.1002/adom.201500436
Figure 4. A) Finite element compression simulations of the gyroid and B) its corresponding theoretical and C) experimental photonic responses. FEA
simulations of A) the fl exible gyroid reveal a relatively uniform strain fi eld through the entire experimental loading regime. The results shown here are
extracted from a 6×6×6 unit cells simulation, and show the internal deformation, which is not affected by boundaries. B) Theoretical and C) experimental
transmitted fi eld magnitude data showing the resonant electromagnetic features associated with the gyroid photonic crystal structure with an initial
material volume fraction of 40% and lattice constant of 9 mm using transverse magnetic linearly polarized incident radiation.
[ 40 ] The structure was com-
pressed by 0%, 5.6%, 11.1% 16.7%, and 22.2%, from left to right in (B) and (C), across the [100] direction. A reduced frequency regime was employed,
normalized by the initial lattice constant value of a = 9 mm and c , the speed of light in free space. The sample was rotated over a polar angle range of
45° at an azimuthal angle of
= 0° for each compressed state.
[ 40 ] The labels “P,” “Q,” and “R” (shown only in the central graph of Figure 4 B)
refer to individual dispersion features that originate from resonances in the [101], [001], and [011] directions, respectively, through the gyroid. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Adv. Optical Mater. 2015,
DOI: 10.1002/adom.201500436
gyroid system
[ 28 ] but suitable for electromagnetic characterization using
microwave radiation. The models were then fabricated using a Stratasys
Connex500 3D printer from a rubber-like UV cross-linkable material
(TangoBlack+). The model was fabricated using a 32 µm z-step height,
which resulted in a high quality smooth surface fi nish without any
visible layers (a common problem for thermoplastic fi lament-based 3D
printing methods). The fabrication process lasted several hours. Based
on established techniques,
[ 47,48 ] the material permittivity was measured
to be
= 2.85 + 0.15i in the frequency regime used for our experiments.
The key geometrical parameter that was replicated from the P. sesostris
gyroid was the material fi lling fraction, which was 40%.
[ 28 ] The remaining
volume was air, which was easily displaced throughout the system upon
compression due to the bicontinuous nature of the gyroid. Gyroids were
fabricated with 5×5×5 and 10×10×10 unit cells dimensions in order to
explore the high- and low-resolution response of this material under
different loading regimes. For the microwave studies, a 10×10×10 unit
cell structure was fabricated such that the incident face was parallel to
the (001) set of periodic planes of its photonic structure.
Microcomputed Tomography Studies : For micro-CT studies, the gyroid
model was scaled up by a factor of two and the 3D model was reprinted
in a 5×5×5 geometry in order to obtain better X-ray transmission
and a more detailed 3D reconstruction during the various stages of
deformation. In order to visualize the gyroid under compression at the
specifi c strain levels of interest, the specimen was immobilized using
a fi xture made of acrylic plates, nylon bolts/nuts and 2.5 cm thick rigid
closed-cell foam plates placed between the specimen and the fi xture (see
Figure S2, Supporting Information). The foam plates were used as low-
electron-density spacers that would be nearly invisible in the acquired
X-ray transmission images and thus not interfere with volume rendering
of the higher-electron-density gyroid. The gyroid/fi xture assembly was
then placed into a XRA-002 X-Tek micro-CT system for image data
collection. The 3D reconstructions were performed using CT-Pro (Nikon
Metrology) and the surface renderings were generated using VGStudio
Gyroid Modeling for Finite Element Analysis Compression Studies :
Static nonlinear FEA of the gyroid structure was performed using the
commercial fi nite element software Abaqus/Standard. The material was
modeled using a nearly incompressible neo-Hookean model, whose
energy is given by
where µ and K are the initial shear and bulk moduli, respectively.
Moreover, J = det F and FFFFIJ TT
= where F is the deformation
gradient. Note that in all our simulations, we assumed that K =
10 000, so that the material response is nearly incompressible. The
mesh was built using linear hybrid solid elements (Abaqus element type
C3D4H). Models comprising 3×3×3, 5×5×5, and 7×7×7 unit cells were
compressed uniaxially by applying a vertical displacement to the top
face, while leaving all lateral faces free to expand. During the analysis,
the maximum lateral expansion was monitored as a function of the
applied compression. The results obtained from the FEA compression
simulations agreed well with the compression results obtained from the
experimental micro-CT studies and were thus used as a basis for the
corresponding microwave simulations.
Experimental and Simulated Electromagnetic Studies : For the
experimental electromagnetic characterization, the compliant 10×10×10
gyroid was placed inside a custom-designed compression device
(Figure 2 C), which was centered between aligned source and detector
microwave broadband horns (Flann model DP241-AB; dual-polarized
horn; option 10–50 GHz). These were connected to an Anritsu Vector
Star 70 kHz to 70 GHz vector network analyzer (VNA) (Figure 2 C). The
source horn emitted a Gaussian microwave beam with a full-width half
maximum of approximately 5 cm measured at a distance of 22 cm away
from the source, which corresponded to the relative sample position
in the experimental set-up.
[ 40 ] The compression device applied a force
to the gyroid in a direction orthogonal to that of the incident beam as
shown in Figure 2 C. The gyroid was rotated over a polar angle range of
45° at each compressed state and the transmitted magnitude
was recorded. Due to the number of unit cells across the sample and
the signal attenuation by the constituent material, absorption occurred,
particularly at the edges of resonant electromagnetic features and at
higher frequencies. As a result, transmitted microwave magnitude was
used in all graphical plots to clearly illustrate the presence and frequency
change of the electromagnetic features. The sample was compressed
by 0%, 5.6%, 11.1%, 16.7%, and 22.2% of the initial array size and the
resulting transmitted magnitude data was recorded.
In order to perform analogous numerical modeling of the
transmission, the fi nite element method software HFSS was used
(Ansoft HFSS, Version 13.0.0, ANSYS, Inc.). When building the model,
the sample was assumed to expand uniformly in directions orthogonal
to that of compression, an assumption that was validated by the FEA
deformation analysis and experiments. The expansion value was taken
as the measured maximum expansion across the mid-plane of the
structure since the Gaussian beam used in the experiments centers
most of its power in this region. The electromagnetic simulation was
performed on a gyroid array comprising 5 unit cells in the comparable
z -direction, and infi nite in the x- and y- directions for computing
effi ciency. The same real and imaginary values of permittivity were used
to defi ne material properties in the simulations. Using fewer unit cells
along this z -direction results in a reduction of signal attenuation by the
constituent materials, compared to the fabricated sample. An incident
plane wave was used for excitation in the model and the transmitted
electromagnetic fi eld magnitude was measured over a range of angle
and compression values. The initial lattice constant, fi lling fraction, and
refractive indices used in the modeling were identical to those of the
sample used in the electromagnetic experiments.
Supporting Information
Supporting Information is available from the Wiley Online Library or
from the author.
The authors thank Nick Cole for construction of the custom-made
compression device used in the microwave spectroscopy experiments
and Dr. Maik Scherer for providing a customized MATLAB code for
the rendering of virtual gyroid models. C.P. acknowledges fi nancial
support from The University of Exeter EPSRC DTA. M.K. acknowledges
nancial support from the Alexander von Humboldt Foundation in the
form of a Feodor-Lynen Postdoctoral Research Fellowship. P.V. and J.A.
acknowledge fi nancial support from AFOSR Multidisciplinary University
Research Initiative under FA9550-10-1-0020 and FA9550-09-1-0669-
DOD35CAP. This work was performed in part at Harvard University’s
Center for Nanoscale Systems (CNS), a member of the National
Nanotechnology Infrastructure Network (NNIN), which is supported by
the National Science Foundation under NSF award no. ECS-0335765.
Received: August 5, 2015
Published online:
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forAdvancedOpticalMaterials,DOI:10.1002/adom. 201500436
Characterization of a Mechanically Tunable Gyroid Photonic
Crystal Inspired by the Butterfl y Parides Sesostris
Caroline Pouya,* Johannes T. B. Overvelde, Mathias Kolle,
Joanna Aizenberg, Katia Bertoldi, James C. Weaver, and Pete
Copyright WILEY-VCH Verlag GmbH & Co. KGaA, 69469 Weinheim, Germany, 2015.
Supporting Information
Characterization of a Mechanically Tunable Gyroid Photonic Crystal Inspired by the
Butterfly Parides sesostris
Caroline Pouya*, Johannes T. B. Overvelde, Mathias Kolle, Joanna Aizenberg, Katia
Bertoldi, James C. Weaver, and Pete Vukusic*
Figure S1.
The arrangement of time-averaged electric fields over either the material or air labyrinths of
the gyroid at the associated band edges of the transmission features P, Q, and R in figure 4b.
Field plots were obtained from either the air or material band-edge of each observed ‘stop-
band’ using the finite element method modeling software HFSS (Ansoft HFSS, Version
13.0.0, ANSYS, Inc.). The images show 5 unit cells in the depth of the structure (z) and a
section one unit cell in size in all other dimensions. The orientation of the gyroid sections
shown here are such that one side of the structure is in view in each case. For instance, the
electric field arrangement labelled ‘Q’ appears to be a repeated high and low electric field
distribution directed along the [101] direction (i.e. in the x-z plane). The compressive force
applied to the structure was in the x-direction and expansions occurred in the y- and z-
directions and the materials used possessed the same real and imaginary permittivity as the
printed experimental sample.
Figure S2.
Schematic illustration of the experimental set up for microCT scanning of the flexible 3D-
printed gyroid, showing the X-ray transparent closed cell foam plates and the surrounding
support structure composed of acrylic plates held in place by nylon bolts and nuts.
... The simplicity of the design, mathematical control of geometric features, ability to generate low-volume fraction structures, naturally inspired porous structures, and highly interconnected porous architectures are some advantages of these structures. On the other hand, TPMS-based structures in cases such as multi-scale manufacturing, characterization of mechanical properties and topology optimization, have innovative applications in multi-purpose devices and in various fields, e.g., energy absorption [15,16] , heat transfer (for instance due to the high volume of special surfaces, TPMS can be used as a heat sink [17][18][19]), acoustic and optical applications (TPMS acoustic band gaps [20], and photonic crystal based as TPMS [21]), and biological application (bone scaffolds designed with excellent properties [22][23][24]). So far, most research has been devoted to the structural perspective of TPMS (i.e., microstructures), including geometric patterns and assembly strategies (e.g., hybrid and functionally graded TPMS structures [25][26][27]). ...
... Pre force 100 (21) As shown in Figure 5, the RVEs of TPMS structures are subjected to tensile loading under 10% ...
Full-text available
Triply periodic minimal surfaces (TPMS) are a type of metamaterial that get their unusual properties from the topology of microstructure elements, but they provide non-controllable properties. Utilizing shape memory polymer as a base material, it is possible to control the properties of these structures and create significant and reversible changes in the stiffness, geometry, and performance of metamaterials which could be applicable in many application fields. In this work, the thermal, mechanical, and shape memory behavior of 8 SMP-based TPMS structures has been studied in a wide range of the solid phase volume fractions (i.e., 35–65%). In the thermomechanical analysis, we consider the shape recovery%, the force recovery%, and the shape fixity% as the shape memory properties. For this purpose, the structures were simulated using thermo-visco-hyperelastic constitutive equations. Also, the temperature rate and elastic modulus are considered as the representative thermal and mechanical properties, respectively. Results of this study indicate that the best shape memory and mechanical behaviors belong to the Primitive structure at all different Volume fractions. And the best overall performance for different 8 TPMS structures including the best thermal, mechanical, and thermomechanical behavior accrues at VF = 40% and is sorted as FKS > FRD > Diamond > Diamond-type 2 > Gyroid > IWP > Primitive > Neovious.
... Moreover, the natural world itself provides instructive examples that inform electromagnetics research through the many elaborate structures that have evolved in living organisms for the control of light. 1 Natural structures that determine optical properties, including reflectivity, iridescence, and polarization control, have provided inspiration and design information for analogous biomimetic devices 2 as well as the translation of their geometries from optical to microwave length scales. 3 One goal for engineered metamaterials and meta-atoms is the manipulation of the scattering of electromagnetic waves by particles with dimensions smaller than or close to the wavelength. It has been shown that the strength and directionality of scattering may be controlled by structuring a particle in order to adjust the frequencies and magnitudes of the Mie resonances that it supports. ...
Enhanced backscattering of microwave radiation is demonstrated experimentally in a biomimetic radially anisotropic spherical metamaterial component. The core-shell device replicates the optical function of nanospheres observed in the tapetum reflector of the compound eye of the shrimp Litopenaeus vannamei (Boone, 1931) and translates the effect from the optical domain to microwave frequencies. Analytical Mie theory calculations and numerical-method simulations are used to describe the origin of the observed scattering from a single dielectric sphere in terms of its multipolar Mie resonances. The fabrication of components using additive manufacture and their experimental characterization are described. The results show that the introduction of radial anisotropy in the shell more than doubles the monostatic radar cross section compared to the equivalent isotropic case. This work represents a practical demonstration of a synthetic bio-inspired structure, harnessing performance-enhancing adaptations that have evolved in nature. The results augment the range of techniques available for the control of electromagnetic scattering with relevance to applications in the manipulation of radar return signals.
... A novel study[17, 28- 30] has revealed that previous works failed to use the mechanical properties of the solid material in numerical simulations; instead, these simulations employed experimental tests on a lattice structure and inverse engineering to determine the mechanical properties of the numerical model. In certain cases, previous studies have also failed to reveal the values used and/or their precedence[31][32][33][34][35][36]. Ruiz de Galarreta et al.[37] tested a single strut element under traction to determine the final mechanical properties of a strut lattice structure. ...
Numerical simulations are essential for predicting the mechanical properties of different structures like gyroids that center this study. Three different methods are explored: shell elements, solid elements, and homogenization. Results reveal that homogenization is only suitable for obtaining the properties in the elastic zone, whereas solid models can determine also the behaviors in the plateau zone and the densification point. In the case of shell elements model, it can predict the elastic behavior model and the levels of stress in the plateau zone but with a lower accuracy than the solid element, but it cannot predict the densification point.
Due to the outstanding mechanical properties of gyroid structures, the design of cellular structures based on gyroid lattices and topology optimization is currently a prominent research area in the field of additive manufacturing structural design. Stiffness topology optimization is commonly used in these designs, which improves the stability during specific loadings and the continuity of structures. However, there seems to be little discussion on manufacturing deformable cellular structures based on topology optimization for deformation. This topic has significant value in functionally graded material and programmable soft robotics design. In this work, a hyperelastic material is utilized to construct deformable gyroid lattices. The homogenization method is used to establish a database of variable-stiffness gyroid lattices with varying relative densities. The feasibility of guiding structural deformation through stiffness distribution is proved, and a pixel design method for deformable structures is proposed. In this work, the average normalized stiffness coefficient (ANSC) distribution is calculated by pixelating stiffness distribution. The soft gyroid lattices are used to fill up the design domain according to the ANSC distribution. Finally, two deformable structures, a cloaking metamaterial, and a compliant plier are analyzed to demonstrate the practicality of the proposed method.
Full-text available
Optical metamaterials manipulate light through various confinement and scattering processes, offering unique advantages like high performance, small form factor and easy integration with semiconductor devices. However, designing metasurfaces with suitable optical responses for complex metamaterial systems remains challenging due to the exponentially growing computation cost and the ill‐posed nature of inverse problems. To expedite the computation for the inverse design of metasurfaces, a physics‐informed deep learning (DL) framework is used. A tandem DL architecture with physics‐based learning is used to select designs that are scientifically consistent, have low error in design prediction, and accurate reconstruction of optical responses. The authors focus on the inverse design of a representative plasmonic device and consider the prediction of design for the optical response of a single wavelength incident or a spectrum of wavelength in the visible light range. The physics‐based constraint is derived from solving the electromagnetic wave equations for a simplified homogenized model. The model converges with an accuracy up to 97% for inverse design prediction with the optical response for the visible light spectrum as input, and up to 96% for optical response of single wavelength of light as input, with optical response reconstruction accuracy of 99%.
Triply periodic minimal surface lattices have mechanical properties that derive from the unit cell geometry and the base material. Through computation software like nTopology and Abaqus, these geometries are used to tune nonlinear stress–strain curves not readily achievable with solid materials alone and to change the compliance by two orders of magnitude compared to the constituent material. In this study, four elastomeric TPMS gyroids undergo large deformation compression and tension testing to investigate the impact of the structure's geometry on the mechanical properties. Among all the samples, the modulus at strain ε varies by over one order of magnitude (7.7–293.4 kPa from FEA under compression). These lattices are promising candidates for designing multifunctional systems that can perform multiple tasks simultaneously by leveraging the geometry's large surface area to volume ratio. For example, the architectural functionality of the lattice to bear loads and store mechanical energy along with the larger surface area for energy storage is combined. A compliant double‐gyroid capacitor that can simultaneously achieve three functions is demonstrated: load bearing, energy storage, and sensing.
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Traditional honeycomb-like structural electromagnetic (EM) wave-absorbing materials have been widely used in various equipment as multifunctional materials. However, current EM wave-absorbing materials are limited by narrow absorption bandwidths and incident angles because of anisotropic structural morphology. The work presented here proposes a novel EM wave-absorbing metastructure with an isotropic morphology inspired by the gyroid microstructures seen in Parides sesostris butterfly wings. A matching redesign methodology between the material and subwavelength scale properties of the gyroid microstructure is proposed, inspired by the interaction mechanism between microstructure and material properties on the EM wave-absorption performance of the prepared metastructure. Bioinspired metastructure is fabricated by additive manufacturing (AM) and subsequent coating through dipping processes, filled with dielectric lossy materials. Based on simulations and experiments, the metastructure designed in this work exhibits an ultra-wide absorption bandwidth covering the frequency range of 2-40 GHz with a fractional bandwidth of 180% at normal incidence. Moreover, the metastructure has a stable frequency response when the incident angle is 60° under the transverse electric (TE) and transverse magnetic (TM) polarization. Finally, the synergistic mechanism between microstructure and material is elucidated, which provides a new paradigm for the design of novel ultra-broadband EM absorbing materials. This article is protected by copyright. All rights reserved.
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Brilliant iridescent colouring in male butterflies enables long-range conspecific communication and it has long been accepted that microstructures, rather than pigments, are responsible for this coloration. Few studies, however, explicitly relate the intra-scale microstructures to overall butterfly visibility both in terms of reflected and transmitted intensities and viewing angles. Using a focused-laser technique, we investigated the absolute reflectivity and transmissivity associated with the single-scale microstructures of two species of Morpho butterfly and the mechanisms behind their remarkable: wide-angle visibility Measurements indicate that certain Morpho microstructures reflect up to 75% of the incident blue light over an angle range of greater than 100 degrees in one plane and 15 degrees in the other. We show that incorporation of a second layer of more transparent scales, above a layer of highly iridescent scales, leads to very strong diffraction, and we suggest this effect acts to increase further the angle range over which incident light is reflected. Measurements using index-matching techniques yield the complex refractive index of the cuticle material comprising the single-scale microstructure to be n = (1.56 +/- 0.01) + (0.06 +/- 0.01)i. This figure is required for theoretical modelling of such microstructure systems.
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The Emerald-patched Cattleheart butterfly Parides sesostris is known to possess a gyroid-type photonic crystal within its wing scales. However, the photonic crystal is observed to be separated into many small domains with different crystal orientations. It has been assumed that this domain structure causes the beautiful tessellated pattern of the scale that can be observed under a crossed polarizer and analyzer. To confirm this assumption, we carefully observed the polarization-dependent reflection from the wing scale, examined the surface morphology of photonic crystal domains using electron microscopy, and theoretically calculated the reflectance of a gyroid-type photonic crystal. By comparing the results of these investigations, we show that the tessellated pattern originates from different angle between the incident polarization and the crystal orientations of different crystal domains.
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The single Gyroid, a triply-periodic ordered chiral network of cubic symmetry, appears as a nanostructure in the green-colored wing scales of various butterflies. In lossless and perfectly ordered single Gyroid materials, the structural chirality leads to circularly polarized reflections from crystals oriented in the [100] direction. Here we report a circular polarisation study of the macroscopic reflections of the wing scales of Callophrys rubi and Teinopalpus imperialis that reveals no circular dichroism, that is, we find no significant difference in the reflectance values for left- and right-circularly polarized light. The reasons for the absence of circularly polarized reflections is likely to be a compound effect of various factors, including crystallite orientation, presence of both left- and right-handed single Gyroid enantiomers, and structural disorder. Each of these factors weakens, but does not fully extinguish, the circular polarisation signal. We further find a substantial amount of blue-absorbing pigment in those wing scales of C. rubi that are structured according to the single Gyroid. Numerical simulations demonstrate that absorption, while evidently reducing overall reflectance, does generally not reduce the circular dichroism strength. The experimental findings of this paper, however, clearly demonstrate that circular dichroism is absent from the reflections of the butterfly wing scale. Henceforth, the chiro-optical response of the idealised structure does not fulfil a biological photonic function.
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It is known that the wing scales of the emerald-patched cattleheart butterfly, Parides sesostris, contain gyroid-type photonic crystals, which produce a green structural colour. However, the photonic crystal is not a single crystal that spreads over the entire scale, but it is separated into many small domains with different crystal orientations. As a photonic crystal generally has band gaps at different frequencies depending on the direction of light propagation, it seems mysterious that the scale is observed to be uniformly green under an optical microscope despite the multi-domain structure. In this study, we have carefully investigated the structure of the wing scale and discovered that the crystal orientations of different domains are not perfectly random, but there is a preferred crystal orientation that is aligned along the surface normal of the scale. This finding suggests that there is an additional factor during the developmental process of the microstructure that regulates the crystal orientation.
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The cover scales on the wing of the Emerald-patched Cattleheart butterfly, Parides sesostris, contain gyroid-type biological photonic crystals that brightly reflect green light. A pigment, which absorbs maximally at approximately 395 nm, is immersed predominantly throughout the elaborate upper lamina. This pigment acts as a long-pass filter shaping the reflectance spectrum of the underlying photonic crystals. The additional effect of the filtering is that the spatial distribution of the scale reflectance is approximately angle-independent, leading to a stable wing pattern contrast. The spectral tuning of the original reflectance is verified by photonic band structure modelling.
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We have used three-dimensional stereolithography to synthetically replicate the gyroid photonic crystal (PC) structure that occurs naturally in the butterfly Parides sesostris. We have experimentally characterized the transmission response of this structure in the microwave regime at two azimuthal angles (ϕ) over a comprehensive range of polar angles (θ). We have modelled its electromagnetic response using the finite-element method (FEM) and found excellent agreement with experimental data. Both theory and experiment show a single relatively broad transmission minimum at normal incidence (θ = 0°) that comprises several narrow band resonances which separate into clearly identifiable stop-bands at higher polar angles. We have identified the specific effective geometric planes within the crystal, and their associated periodicities that give rise to each of these stop-bands. Through extensive theoretical FEM modelling of the gyroid PC structure, using varying filling fractions of material and air, we have shown that a gyroid PC with material volume fraction of 40 per cent is appropriate for optimizing the reflected bandwidth at normal incidence (for a refractive index contrast of 1.56). This is the same gyroid PC material volume fraction used by the butterfly P. sesostris itself to produce its green structurally coloured appearance. This infers further optimization of this biological PC beyond that of its lattice constant alone.
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Significance Morpho butterflies are a brilliant spectacle of nature’s capability for photonic engineering. Their conspicuous appearance arises from the interference and diffraction of light within tree-like nanostructures on their scales. Scientific lessons learned from these butterflies have already inspired designs of new displays, fabrics, and cosmetics. This study reports a vertical surface polarity gradient in these tree-like structures. This biological pattern design may be applied to numerous technological applications ranging from security tags to self-cleaning surfaces, gas separators, protective clothing, and sensors. Here it has allowed us to unveil a general mechanism of selective vapor response in photonic Morpho nanostructures and to demonstrate attractive opportunities for chemically graded sensing units for high-performance sensing.
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We report a tunable nanophotonic device concept based on flexible photonic crystal, which is comprised of a periodic array of high-index dielectric material and a low-index flexible polymer. Tunability is achieved by applying mechanical force with nano-/microelectromechanical system actuators. The mechanical stress induces changes in the periodicity of the photonic crystal and consequently modifies the photonic band structure. To demonstrate the concept, we theoretically investigated the effect of mechanical stress on the anomalous refraction behavior and observed a very wide tunability in the beam propagation direction. This concept provides a means to achieve real-time, dynamic control of photonic band structure and will thus expand the utility of photonic crystal structures in advanced nanophotonic systems.
We are looking back on 30 years development of periodic space partitioners (PSP) and their relations to their periodic relatives, i.e. minimal surfaces (PMS), zero potential surfaces (P0PS), nodal surfaces (PNS), and exponential scale surfaces. Hans-Georg von Schnering and Sten Andersson have pioneered this field especially in terms of applications to crystal chemistry. This review relates the early attempts to approximate periodic minimal surfaces which established a systematic classification of all PSP in terms space group symmetry and consecutive applications in a variety of different fields. A consistent nomenclature is outlined and different methods for deriving PSP are described. Characteristic structure factor sets which solely define PNS by can be used to discriminate structure types of a given symmetry or even to determine complicated crystal structures. The concept of PSP relates space group symmetry, topology, and chemical bonding in an intriguing way and tessellations on PSP which can be generated in a straight forward way allow to predict new framework types. Through transformation of such continuous topological forms a new entry has been found for understanding and interpreting reconstructive phase transitions. Finally we indicate the importance of PSP models for soft matter science.