accepted article preview · network metamaterials henning galinski, gael favraud , hao dong, juan s...

Accepted Article Preview: Published ahead of advance online publication

Scalable, ultra-resistant structural colors based on network metamaterials

Henning Galinski, Gael Favraud, Hao Dong, Juan S Totero Gongora, Grégory Favaro, Max Döbeli, Ralph Spolenak, Andrea Fratalocchi and Federico Capasso

Cite this article as: Henning Galinski, Gael Favraud, Hao Dong, Juan S Totero Gongora,

Grégory Favaro, Max Döbeli, Ralph Spolenak, Andrea Fratalocchi and Federico

Capasso. Scalable, ultra-resistant structural colors based on network metamaterials.

Light: Science & Applications accepted article preview 27 September 2016; doi:

10.1038/lsa.2016.233.

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resistant structural colors based on network metamaterials

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accepted article preview

Henning Galinski, Gael Favraud, Hao Dong, Juan S Totero Gongora,



Henning Galinski, Gael Favraud, Hao Dong, Juan S Totero Gongora,

, Ralph Spolenak, Ralph Spolenak, Totero

ACCEPTED ARTICLE PREVIEW

© 2016 Changchun Institute of Optics, Fine Mechanics and Physics (CIOMP), Chinese Academy of Sciences (CAS). All rights reserved.

1

Scalable, ultra-resistant structural colors based on network

metamaterials

Henning Galinski1,2‡ , Gael Favraud3,‡ , Hao Dong1,2, Juan S. Totero Gongora3, Gregory

Favaro4, Max Dobeli5, Ralph Spolenak2, Andrea Fratalocchi3,* and Federico Capasso1,†

1John A. Paulson School of Engineering and Applied

Sciences, Harvard University, Cambridge 02138, USA 2Laboratory for Nanometallurgy, ETH Zurich, Vladimir-

Prelog-Weg 1-5/10, Zurich, Switzerland3PRIMALIGHT, King Abdullah University of Science and

Technology (KAUST), Thuwal 23955-6900, Saudi Arabia 4Anton Paar TriTec SA, CH-2034 Peseux, Switzerland

5Ion Beam Physics, ETH Zurich, Otto-Stern-Weg 5, Zurich,

Switzerland

(Dated: April 17, 2016)

Running title: Scalable, ultra-resistant structural colors

Abstract

Structural colors have drawn wide attention for their potential as a future printing technology for

various applications, ranging from biomimetic tissues to adaptive camouflage materials. However, an

efficient approach to realize robust colors with a scalable fabrication technique is still lacking,

hampering the realization of practical applications with this platform. Here, we develop a new

approach based on large-scale network metamaterials that combine dealloyed subwavelength structures

at the nanoscale with lossless, ultra-thin dielectric coatings. By using theory and experiments, we

show how subwavelength dielectric coatings control a mechanism of resonant light coupling with

epsilon-near-zero (ENZ) regions generated in the metallic network, generating the formation of

saturated structural colors that cover a wide portion of the spectrum. Ellipsometry measurements

support the efficient observation of these colors, even at angles of 70 degrees. The network-like

architecture of these nanomaterials allows for high mechanical resistance, which is quantified in a series

of nano-scratch tests. With such remarkable properties, these metastructures represent a robust design

technology for real-world, large-scale commercial applications.

Keywords: nanophotonics; plasmonics; structural colors

†[email protected], * [email protected] ; ‡ These authors contributed equally to the work.

saturated structural colors that cover a wide

support the efficient observation of these colors, even at angles of 70 degrees. The network-like

architecture of these nanomaterials allows for high mech


epsilon-near-zero (ENZ) regions generated in th

saturated structural colors that cover a wide


at the nanoscale with lossless, ultr




at the nanoscale with lossless, ultr


efficient approach to realize robust colors with



Structural colors have drawn wide attention fo


efficient approach to realize robust colors with

Structural colors have drawn wide attention fo


Scalable, ultra-resistant structural colors

Abstract

Switzerland


Scalable, ultra-resistant structural colors

Switzerland


Anton Paar TriTec SA, CH-2034 Peseux, Switzerland

Otto-Stern-Weg 5, Zurich,

23955-6900, Saudi Arabia

Anton Paar TriTec SA, CH-2034 Peseux, Switzerland

PRIMALIGHT, King Abdullah University of Science and

23955-6900, Saudi Arabia

egory



2

INTRODUCTION 1

2

3

Billions of years ago, green algae originated life, changing the face of the earth from gray to 4

green and paving the way for the life forms we see today 1. Since then, living organisms 5

have extensively used color for a variety of purposes, ranging from communication to self-6

defense, from reproduction to camouflage 2. The enormous variety of colors, such as the 7

sapphire blue wings of the Morpho butterfly 3, 4 and the thermochromic coloration of the 8

chameleon 5, has stimulated the interest of researchers dating back to the 17th century, when 9

Hooke theorized about the origin of color in the brilliant feathers of peacocks and ducks 6. Many 10

of these colors do not originate from pigments or dyes but are ‘structural’, resulting from the 11

interaction of light with self-assembled structures of living organisms 4, 7, 8. 12

The engineering of structural colors from artificial photonic structures has attracted 13

conspicuous interest in research due to the many applications that can potentially be opened 14

by this technology 5, 9–17. Structural colors based on photonic crystals and metamaterials have 15

been explored, showing very promising results, including the possibility to create colors at the 16

diffraction limit 15. A major challenge is overcoming the problems of limited scalability and 17

lack of robustness, which affect the real-world applicability of photonic crystals and classical 18

metamaterials. It is therefore highly desirable to investigate new approaches that can transform 19

these initial breakthroughs into real world applications. 20

In the following, we describe a new biomimetic material that overcomes the 21

aforementioned challenges, introducing a new type of structural coloration that is highly 22

scalable and extremely robust. This nanomaterial takes inspiration from s u b w a v e l e n g t h 23

n a n o s c a l e n e t w o r k s i d e n t i f i e d i n t h e f e a t h e r s of Cotinga maynana, a South 24

American bird 18. The non-iridescent blue color of the feathers is produced by an aperiodic 25

nanoporous keratin network with a typical feature size smaller than 200 nm. This lightweight 26

network has extraordinary optical properties that cannot be explained by classical 27

R a y l e i g h / M i e scattering and are strongly related to the short-range order of the nano-28

network of the barbs19. The interaction of light waves with complex materials has already 29

been reported to have a series of fascinating dynamics, ranging from energy harvesting to 30

ultra-dark nanomaterials and beyond 7, 11, 20–27. Taking inspiration from the Cotinga maynana 31

feathers as an example in nature of a network-based optical nanomaterial, we create complex 32

nano-photonic structures that combine a cellular metallic network 28, 29 with subwavelength 33

network has extraordinary optical properties

R a y l e i g h / M i e scattering and are strongly relate

network of the barbs

American bird

nanoporous keratin network with a

network has extraordinary optical properties

n a n o s c a l e n e t w o r k s i d e n t i f i e d i n t h e f e a t h e r s of

American bird 18

scalable and extremely robust. This nanomat

n a n o s c a l e n e t w o r k s i d e n t i f i e d i n t h e f e a t h e r s of

In the following, we describe a new biomimetic material that overcomes the

aforementioned challenges, intr

scalable and extremely robust. This nanomat

these initial breakthroughs in

In the following, we describe a new biomimetic material that overcomes the

metamaterials. It is therefore highly desirable to investigate ne

to real world applications.

. A major challenge is overcoming th

lack of robustness, which affect the real-world

ghly desirable to investigate ne

due to the many applications

. Structural colors based on photonic

been explored, showing very promising results, including the possibility to create colors at the

. A major challenge is overcoming th

due to the many applications

. Structural colors based on photonic

bled structures of living organisms

artificial photonic structures has attracted

due to the many applications that can potentially be opened

or dyes but are ‘structural’, resulting from the

bled structures of living organisms 4, 7, 8

the brilliant feathers of peacocks and ducks

or dyes but are ‘structural’, resulting from the

c coloration of the

researchers dating back to the 17 century, when

the brilliant feathers of peacocks and ducks

. The enormous variety of colors, such as the

c coloration of the

century, when

purposes, ranging from communication to self-purposes, ranging from communication to self-


c coloration of the

. Since then, living organisms

purposes, ranging from communication to self-


changing the face of the earth from gray to

. Since then, living organisms



3

coatings made by lossless dielectrics. This material combination provides significant advantages 1

for real world applications: it is suited for large-scale fabrication and is lightweight and 2

mechanically robust, combining the high yield strength to low density ratio of a cellular 3

metallic network with the resistance to wear that alumina offers 30. Optically, the interface of 4

such a metallic nanoscale network and the lossless dielectric can be considered as 5

electromagnetically “weakly” rough and an inhomogeneous mixture of dielectric/metal and 6

dielectric/air regions. In this scenario, the component of the wavevector parallel to the 7

interface is not conserved, resulting in a highly spatially dependent electromagnetic response. 8

Taking advantage of such a complex light-matter interaction, we illustrate here how to create 9

colors with remarkable properties. 10

11

12

MATERIALS AND METHODS 13

14

15

Sample Preparation and Characterization 16

17

PtYAl layers of 300 nm thickness were deposited at room temperature by magnetron co-18

sputtering onto SiNx/Si substrates that were pre-cleaned using isopropanol and acetone. 19

Subsequently, the films were dealloyed in 4 M NaOH at room temperature for 60 s and t h e n 20

rinsed with deionized water. The morphological analysis of the samples was studied via scanning 21

electron microscopy (SEM) assisted by focused ion beam etching (FIB). The compositional 22

analysis was performed by Rutherford backscattering spectrometry. Detailed information is 23

given in the Supplementary Information. In this work, the Savannah atomic layer deposition 24

(ALD) from Ultratech/Cambridge NanoTech (Waltham, Massachusets, USA) was used to deposit 25

Al2O3 coatings on the dealloyed metal nanowire networks. During the ALD deposition of 26

Al2O3, a pulse time of 0.15 s and a purge time of 30 s for both TMA and water were used. The 27

base pressure was 500 mTorr, and the working temperature was 250°C. The growth rate was 28

approximately 0.1 nm per cycle. For creating colored graphic arts, the 60 nm thick Al2O3 29

film was deposited via radio frequency (RF) sputtering at room temperature using a sputtering 30

tool (AJA International, Scituate, MA, USA). The electromagnetic reflectance of the coated 31

samples was measured using a variable-angle spectroscopic ellipsometer from J.A. Woollam Co 32

(Lincoln, NE, USA) and a NanoCalc thin film reflectrometry setup (Ocean Optics Inc., 33

Al2O3, a pulse time of 0

base pressure was 500 mTorr, and the working

approximately 0

(ALD) from Ultratech/Cambridge NanoTech (Waltham, Massachusets, USA) was used to deposit

2O3 coatings on the dealloyed metal nanowire networks. During the ALD deposition of

, a pulse time of 0

given in the Supplementa

(ALD) from Ultratech/Cambridge NanoTech (Waltham, Massachusets, USA) was used to deposit

analysis was performed by Rutherford backscattering spectrometry. Detailed information is

given in the Supplementa

rinsed with deionized water. The morphological an

electron microscopy (SEM) assisted by focuse

analysis was performed by Rutherford backscattering spectrometry. Detailed information is

Subsequently, the films were d

rinsed with deionized water. The morphological an

sputtering onto SiNx/Si substrates that were

Subsequently, the films were dealloyed in 4 M NaOH at room

PtYAl layers of 300 nm thickness were depos

sputtering onto SiNx/Si substrates that were

Sample Preparation and Characterization

ting in a highly spatially dependent electromagnetic response.

teraction, we illustrate here how to create

e wavevector parallel to the


teraction, we illustrate here how to create

ure of dielectric/metal and



lossless dielectric can be considered as

ure of dielectric/metal and



. Optically, the interface of

lossless dielectric can be considered as



4

Dunedin, FL, USA). The dielectric constant of the Al2O3 coating deposited by ALD was 1

determined using a Cauchy model by analyzing a 53 nm thick Al2O3 coating deposited on a Si 2

wafer. The scratch tests were performed using an Anton Paar TriTec Nano Scratch Tester 3

(Anton Paar TriTec SA, Peseux, Switzerland). 4

5

Finite-Difference Time-Domain (FDTD) simulations. 6

Numerical simulations were carried out using our parallel code NANOCPP, which is a highly 7

scalable (up to hundreds of thousands CPU) Maxwell equation solver, able to include 8

dispersive materials with arbitrary dispersion curves20. To build a realistic model for our 9

sample, we considered a metallic structure whose profile was extracted from the 10

morphological analysis of the samples (FIB) shown in Fig. 1a. The dispersion parameters 11

of the various materials were taken from direct measurements. Light impinging on the 12

sample was simulated within the Transmitted Field/Scattered Field formulation20, which 13

allows the detailed modelling of plane wave input excitations on the samples. 14

15

RESULTS AND DISCUSSION 16

17

18

Material design and color characterization 19

20

We selected dealloying to assemble a nanoscale metallic network with controllable features. 21

This method, first proposed by Raney to synthesize metal catalysts 31, utilizes the selective 22

dissolution of the less noble constituent of an alloy during wet etching. In our experiments, 300 23

nm thick Pt.14Y.06Al.80 thin films were deposited on an amorphous Si3N4/Si substrate. 24

While immersing the film in a 4 M aqueous solution of NaOH for 60 s, the less noble Al in the 25

Pt-alloy thin film is subsequently removed, and the remaining metal reorganizes into a 26

network with an open porosity. Characteristic geometrical features of the network can be 27

altered by changing the etching time, the etchant concentration or the initial composition of the 28

thin film 32–36. 29

In a second step, the nanomaterial is coated with an ultra-thin layer of Al2O3 using ALD. The 30

coating thickness is increased stepwise in a range from 7 to 53 nm. We characterized the 31

growth of the subwavelength Al2O3 coatings by Rutherford backscattering spectroscopy and 32

Pt-alloy thin film is subsequently removed, and the remaining metal reorganizes into a 26

network with an open porosity. Characteristic

altered by changing the etching time, the etchant concentration or the initial composition of the

While immersing the film in a 4 M aqueous solu

Pt-alloy thin film is subsequently removed, and the remaining metal reorganizes into a

nm thick Pt 14Y

While immersing the film in a 4 M aqueous solu

This method, first proposed by Rane

dissolution of the less noble constituent of an a

Al

We selected dealloying to assemble a nanoscale metallic network with controllable features.

This method, first proposed by Rane

dissolution of the less noble constituent of an a

We selected dealloying to assemble a nanoscale metallic network with controllable features.

Material design and color characterizationMaterial design and color characterization

ve input excitations

in the Transmitted Field/Scattered Field formulation


direct measurements. Light impinging on the

in the Transmitted Field/Scattered Field formulation


samples (FIB) shown in Fig. 1a. The dispersion parameters

direct measurements. Light impinging on the

ile was extracted from the

. The dispersion parameters

tion solver, able to include

. To build a realistic model for our

ile was extracted from the

, which is a highly


, which is a highly


, which is a highly



5

FIB assisted SEM (see Supplementary Information). A three-dimensional image of the 1

Pt.56Y.26Al.18 network, experimentally obtained using FIB thin film tomography, is displayed 2

in Fig. 1a. 3

In a final series of experiments, we characterized the optical response of the network 4

metamaterial for different thicknesses of the dielectric layer Al2O3. These experiments 5

unveiled a very interesting mechanism of structural coloration from the nanowire network, as 6

shown in Fig. 1b. By changing the coating thickness, we observed the formation of a multitude 7

of colors spanning from yellow, orange, and red to, finally, blue. T h e s a m e p h y s i c a l 8

e f f e c t w i t h t h e o p t i c a l r e s p o n s e b l u e - s h i f t e d a n d s m a l l e r c o l o r r a n g e 9

w a s o b s e r v e d f o r a P t - A l n e t w o r k (see Supplementary Information and 10

Supplementary Fig. S 9). Conversely, when the same coatings were deposited on a dense 11

PtYAl metal thin film, no particular color was produced (see Supplementary Information and 12

Supplementary Fig. S 5). The colors observed in the metallic network were saturated and go 13

even slightly beyond the Red Green Blue (RGB) gamut in the CIE chromaticity diagram (Fig. 14

1c). 15

To illustrate that these colors were consistently observed by varying Al2O3 layer thickness, 16

we compared experimental results with theoretical predictions based on Finite Difference 17

Time-Domain (FDTD) simulations. For the latter, we used a 2D section of the FIB 18

tomography of the sample illustrated in Fig. 1a. Our FDTD simulations, shown in Fig. 1c 19

as a dotted line, reproduced the experimental results well, confirming the possibility of 20

achieving such a large variety of colors by tuning the thickness of the Al2O3 layer. Figure 1b 21

shows experimental images of samples characterized by different thicknesses of Al2O3. 22

Remarkably, despite the existence of the metallic nanoscale network below the Al2O3 layer, 23

the samples demonstrated a highly uniform color in all different configurations. A comparison 24

with FDTD calculations is provided in Fig. 1d, which illustrates the color palette that can be 25

observed when the thickness of Al2O3 increases. 26

To emphasize that the structural coloration in these nanoplasmonic structures can be achieved 27

by various deposition techniques, we also fabricated a structural colored graphic arts by using 28

physical vapor deposition. Figure 2 depicts an example created by combining a dealloyed 29

network metamaterial with an RF-sputtered 60 nm thick Al2O3 coating and photolithography 30

using a Heidelberg µPG501 optical direct writing system. The bicolored graphic art combines a 31

highly uniform structural color (blue) with a metallic white color (dense film). The material 32

26

To emphasize that the structural coloration in th

by various deposition techniques,

with FDTD calculations is provided in Fig. 1d,

observed when the thickness of Al

the samples demonstrated a highly uniform color in all different configurations. A comparison

with FDTD calculations is provided in Fig. 1d,

shows experimental images of samples ch

Remarkably, despite the existence of the metallic nanoscale network below the Al

the samples demonstrated a highly uniform color in all different configurations. A comparison

achieving such a large variety of colors by tuning the thickness of the Al

shows experimental images of samples ch

Remarkably, despite the existence of the metallic nanoscale network below the Al

as a dotted line, reproduced the experimental

achieving such a large variety of colors by tuning the thickness of the Al

tomography of the sample illustrated in Fig.

as a dotted line, reproduced the experimental

we compared experimental results with theo

Time-Domain (FDTD) simulations. For the la

tomography of the sample illustrated in Fig.

even slightly beyond the Red Green Blue (RGB) gamut in the CIE chromaticity diagram (Fig.

To illustrate that these colors were consistently observed by varying Al

we compared experimental results with theoretical predictions base

) gamut in the CIE chromaticity diagram (Fig.

PtYAl metal thin film, no particular color was produced (see Supplementary Information and

the metallic network we

) gamut in the CIE chromaticity diagram (Fig.

ely, when the same coatings were deposited on a dense

PtYAl metal thin film, no particular color was produced (see Supplementary Information and

w a s o b s e r v e d f o r a P t - A l n e t w o r k (see Supplementary Information and

ely, when the same coatings were deposited on a dense

of colors spanning from yellow, orange, and red to, finally, blue. T h e s a m e p h y s i c a l

u e - s h i f t e d a n d s m a l l e r c o l o r r a n g e

w a s o b s e r v e d f o r a P t - A l n e t w o r k (see Supplementary Information and

kness, we observed the formation of a mu


u e - s h i f t e d a n d s m a l l e r c o l o r r a n g e

ural coloration from the nanowire network, as ural coloration from the nanowire network, as

kness, we observed the formation of a multitude


. These experiments

ural coloration from the nanowire network, as

ltitude

acterized the optical response of the network

. These experiments



6

choice for the coating layer is not limited to Al2O3 a lossless dielectric. Dielectric coatings with 1

and without losses could, in principle, be used to alter the plasmonic response and finally change 2

the structural coloration. Another approach to altering the color impression, especially its 3

saturation, is to change the number of trapping sites within the network metamaterial, for example, 4

by reducing the metamaterial thickness. 5

6

Robustness of structural colors from metamaterial networks 7

8

9

To quantify the mechanical robustness of these colors, we resort to nano-scratch resistance 10

testing (Fig. 3a), which is an ideal technique to characterize the adhesion failure of coatings. A 11

detailed description of the experimental procedure we used is given in the supplemental 12

material. Figure 3b reports optical micrographs of four representative nano-scratch tests. The 13

wear resistance of a dense PtYAl film with and without a 28 nm thick Al2O3 coating is 14

compared to a porous nanoscale Pt network coated with 28 nm and 53 nm of Al2O3, 15

respectively. The critical load causing delamination of the coated network metamaterial is 16

almost 2 times higher than the corresponding dense metallic film (Fig. 2b) and 20% higher 17

than the dense metallic film coated with 28 nm thick Al2O3. Considering the 53% porosity in 18

the nanoscale network, the observed increase in wear resistance is remarkable and indicates an 19

enhanced strength-to-density ratio 37 corresponding to a significant reduction of overall weight 20

of the coating. Figure 4 illustrates s-polarized reflectivity spectra at normal (Fig. 4a) and 21

oblique (Fig. 4b-e) incidence for different alumina coating thickness. Figure 4a demonstrates 22

that the formation of colors originates from a large red shift of the reflectivity response of the 23

nanomaterial, observed when the Al2O3 layer changes thickness. The corresponding FDTD 24

results are reported in Fig. 4f. FDTD simulations quantitatively reproduce well the 25

experimental results, confirming the principal role of the Al2O3 coating layer in red-shifting the 26

spectral response of the material. A small variation of only 30 nm in the Al2O3 thickness shifts 27

the reflectivity minimum of approximatively 350 nm. Reflectivity spectra of the material are 28

stable and do not show significant variations up to incident angles of 70°, which still provide 29

reflectivity minima as low as < 1% (Fig. 4b-e). The mean angular dispersion of the reflectance 30

minimum has been determined from the reflectance spectra obtained by ellipsometry. The 31

mean angular dispersion is independent of the coating thickness and the reflectance minimum blue 32

spectral response of the material. A sma

the reflectivity minimum of approximatively 350 nm

results are reported in Fig. 4f. FDTD si

experimental results, confirming

spectral response of the material. A sma

nanomaterial, observed when the Al

results are reported in Fig. 4f. FDTD si

that the formation of colors originates from a

nanomaterial, observed when the Al

of the coating. Figure 4 illustrates s-polarized

oblique (Fig. 4b-e) incidence fo

that the formation of colors originates from a

enhanced strength-to-density ratio

of the coating. Figure 4 illustrates s-polarized

the nanoscale network, the observed increase in w

enhanced strength-to-density ratio corresponding to a significant reduction of overall weight

almost 2 times higher than the corresponding de

coated with 28 nm thick Al

the nanoscale network, the observed increase in w

compared to a porous nanoscale Pt network coated with 28 nm and 53 nm of Al

respectively. The critical load causing delamination of the coated network metamaterial is

almost 2 times higher than the corresponding dense metallic film (Fig. 2b) and 20% higher

with and without a 28 nm thick Al

ork coated with 28 nm and 53 nm of Al

perimental procedure we used

of four representative nano-scratch tests. The

with and without a 28 nm thick Al

characterize the adhesion failure of coatings. A

is given in the supplemental

of four representative nano-scratch tests. The

to nano-scrat

characterize the adhesion failure of coatings. A

to nano-scratch resistance

twork metamaterial, for example,



7

shifts with −1.0 ± 0.3 nm/°. These experiments show that the structural colors observed in Fig. 1 1

are non-iridescent, that is, robust against large changes of the incident angle. 2

3

4

Structural coloration from localized surface states in complex epsilon-near-zero (ENZ) 5

materials 6

7

8

In this section, we analyze in more detail the mechanisms by which structural colors are 9

created and observed in the metallic network of Fig. 1. When polychromatic light impinges on 10

the structure of Fig. 1a, the interaction between light and matter generates surface plasmon 11

polaritons (SPP)38, which are surface waves localized at the metal-dielectric interface of the 12

structure7. In our samples (Fig. 5a), the motion of SPP develops along complex trajectories in 13

space due to a strongly disordered metallic profile, (Fig. 5a, inset). It is convenient to study 14

this motion in a new curvilinear system, whose axes are parallel to the spatial trajectories of 15

SPP. To this extent, we introduce a new set of coordinates. (ψ,ϕ ), which are conformal to 16

the disordered surface of the metal. Figure 5a shows how these coordinates appear in the 17

original space. (x,y), whereas Fig. 5b shows how the original structure appears in the space 18

(ψ,ϕ ) , which we identify as the ‘plasmonic reference.’ In the plasmonic reference, the 19

motion of the surface plasmons is extremely simple and composed of straight lines at ψ = 0 20

(Fig. 5b, inset). When we change spatial coordinates in any electromagnetic system, 21

Maxwell equations remain invariant if we introduce an inhomogeneous refractive index 22

distribution that makes the two reference systems equivalent39, 40. The pseudocolor plot in Fig. 23

5b shows the spatial distribution of the inhomogeneous index, n (ψ,ϕ ) , computed by using 24

transformation optics ( see Supplementary In format ion) . The index, n (ψ,ϕ ) , is 25

associated with the coordinate transformation introduced in Fig. 5b and acts as a counterpart 26

of the metallic geometry of Fig. 5a, which does not exist in Fig. 5b, as the metal surface is 27

flattened out. The two structures of Fig. 5a and Fig. 5b are exactly equivalent: when light 28

propagates in one or another, it follows the same dynamics. This is an exact result of Maxwell 29

equations that contains no approximation. This result also implies that when light impinges on 30

the structure of Fig. 5a, it happens to propagate in the medium of Fig. 5b. The calculation of a 31

conformal grid for the disordered surface of Fig. 5a requires a new formulation of optical 32

associated with the coordinate transformation introduced in Fig. 5b and acts as a counterpart 26

of the metallic geometry of Fig. 5a, which does

flattened out. The two structur

transformation optics ( see Supplementary In format ion) . The index, n

associated with the coordinate transformation introduced in Fig. 5b and acts as a counterpart

distribution that makes the two reference systems equivalent

5b shows the spatial distributi

transformation optics ( see Supplementary In format ion) . The index, n

Maxwell equations remain invariant if we


(Fig. 5b, inset). When we change spatial coordinates in any electromagnetic system,

Maxwell equations remain invariant if we


, which we identify as the ‘plasmonic refe

motion of the surface plasmons is extremely si

(Fig. 5b, inset). When we change spatial coordinates in any electromagnetic system,


motion of the surface plasmons is extremely si

of the metal. Figure 5a shows how these coordinates appear in the

, whereas Fig. 5b shows how the original structure appears in the space


space due to a strongly disordered metallic profile

this motion in a new curvilinear system, whose axes are parallel to the spatial trajectories of

oduce a new set of coordinates. oduce a new set of coordinates. oduce a new set of

of the metal. Figure 5a shows how these coordinates appear in the

SPP develops along complex trajectories in

, (Fig. 5a, inset). It is convenient to study

es are parallel to the spatial trajectories of

calized at the metal-diel

SPP develops along complex trajectories in

, (Fig. 5a, inset). It is convenient to study

Fig. 1. When polychromatic light impinges on

matter generates surface plasmon

calized at the metal-diel

e mechanisms by which structural colors are

Fig. 1. When polychromatic light impinges on

matter generates surface plasmon

e mechanisms by which structural colors are

ce states in complex epsilon-near-zero (ENZ)



8

conformal mapping, which we recently developed, and allows for the generation of conformal 1

grids for arbitrary structures with arbitrary-large numerical precision. This approach is 2

relatively involved, and it will be discussed in a future work. 3

The plasmonic reference of Fig. 5b illustrates in clear form the effects of disorder, which 4

introduce a strong modulation of the refractive index in the proximity of the metallic surface 5

at ψ = 0, generating a network of epsilon-near-zero (ENZ) regions, separated by areas of 6

high refractive index (Fig. 5b). As observed in the insets of Fig. 5a and Fig. 5b (dashed lines), 7

ENZ regions are created in the points where the metallic surface is convex, whereas high 8

dielectric permittivities originate in the points where the surface is concave. When waves 9

propagate into an ENZ material, the phase velocity diverges, thus creating standing waves 10

with infinite wavelengths 41–43. When SPP waves propagate in the nanowire network of Fig. 11

5a, they ‘see’ the equivalent medium illustrated in Fig. 5b and become trapped in the ENZ 12

regions, thereby generating a set of quasi-localized states. We illustrated these dynamics by a 13

series of FDTD simulations. Figure 6a presents a magnified version of Fig. 4a, showing 14

FDTD-calculated reflectivity spectra for different thicknesses of the Al2O3 layer. FDTD 15

results corresponding to different combinations of alumina thicknesses and input wavelengths 16

are summarized in Figs. 6b-l. When light impinges on the disordered metallic structure (Fig. 17

6b), some energy is scattered back, generating components along all directions in space, 18

whereas the remainder is coupled into SPP waves. As illustrated in Figs. 6c-e, which show 19

FDTD-calculated electromagnetic energy density distributions, SPP waves are completely 20

localized in the proximity of different convex points of the surface, exactly where the ENZ 21

regions are formed. FDTD simulations show that different wavelengths are trapped in 22

different ENZ regions of the metal, demonstrating that the ENZ network formed in Fig. 5b 23

does not possess a particular length scale and that it traps equivalently all input wavelengths. 24

The absence of a characteristic scale is expected from the strongly disordered surface 25

modulation of the sample, which possesses an abundant variety of different curvatures (Fig. 5a) 26

and therefore of ENZ regions with different extensions (Fig. 5b). The combinations of all of these 27

ENZ regions traps polychromatic light very efficiently, as observed from the flat reflectivity 28

response of Fig. 6a (solid green line). To further characterize the energy propagation in the 29

structure, we also plotted the flow of electromagnetic energy in the structure, computed from the 30

Poynting vector of the electromagnetic field (Fig. 6f). This is represented with a specific line 31

integral convolution (LIC) technique, which clearly visualizes the energy flow, characterized by 32

complex patterns with a nontrivial vorticity. 33

and therefore of ENZ regions with 27

ENZ regions traps polychromatic light very efficiently, as observed from the flat reflectivity

response of Fig. 6a (solid gree

The absence of a characteristic scale is expected from the strongly disordered surface

modulation of the sample, which modulation of the sample, which

and therefore of ENZ regions with

does not possess a particular

The absence of a characteristic scale is expected from the strongly disordered surface

modulation of the sample, which

different ENZ regions of the metal, demonstra


localized in the proximity of different convex points of the surface,

regions are formed. FDTD simulations show

different ENZ regions of the metal, demonstra


FDTD-calculated electromagnetic energy density


whereas the remainder is coupled into SPP waves.

FDTD-calculated electromagnetic energy density


are summarized in Figs. 6b-l. When light impinges on the disordered metallic structure (Fig.

back, generating components al

whereas the remainder is coupled into SPP waves.

for different thicknesses of the Al

combinations of alumina thicknesses and input wavelengths

are summarized in Figs. 6b-l. When light impinges on the disordered metallic structure (Fig.

gure 6a presents a magnified

for different thicknesses of the Al

ted in Fig. 5b and become trapped in the ENZ

of quasi-localized states. We illustrated these dynamics by a

gure 6a presents a magnified

the nanowire network of Fig.

ted in Fig. 5b and become trapped in the ENZ

illustrated these dynamics by a

locity diverges, thus creating standing waves

the nanowire network of Fig.

e the metallic surface is convex, whereas high

where the surface is concave. When waves

locity diverges, thus creating standing waves

e insets of Fig. 5a and Fig. 5b (dashed lines),


where the surface is concave. When waves

s, separated by areas of



mity of the metallic surface

s, separated by areas of



in clear form the effects of disorder, which

mity of the metallic surface



9

When we deposited a small layer of Al2O3 on top of the metal, the scattering dynamics 1

changed abruptly (Fig. 6g). In this situation, a portion of scattered wavevectors were reflected 2

inside the alumina layer, thus generating a series of additional scattering events in the Al2O3. 3

Wavevectors propagating at an angle, θ , (see Fig. 6g) larger than the critical angle, 4

θc = arcsin nAIR

nAl 2O3

, formed by the interface of air and alumina were totally reflected back and 5

do not radiate energy outside the alumina, surviving the dynamics for many scattering 6

events. These components existed at any given thickness of alumina, as the critical angle depends 7

only on the difference in the refractive index between alumina and air. Reflected wavevectors 8

create a flow of energy in the layer of Al2O3, inducing a preferential localization of SPP 9

inside ENZ regions that exists within the film of Al2O3. This process is clearly illustrated in 10

Figs. 6h-i, which show the presence of a resonant coupling around the wavelength of 425 nm 11

(Fig. 6l). Resonant light localization in ENZ regions within the alumina layer is observed in 12

Fig. 6i, which demonstrates light trapping at the wavelength of 425 nm at different points of 13

convex metallic curvature located inside the Al2O3. F i g u r e 6 h - i a n d 14

s u p p l e m e n t a r y F i g . S 7 s h o w e l e c t r o m a g n e t i c e n e r g y 15

d i s t r i b u t i o n s c a l c u l a t e d f r o m t h e r e s o n a n c e , d e m o n s t r a t i n g 16

t h a t o u t s i d e t h e r e f l e c t i v i t y m i n i m u m l o c a t e d a r o u n d t h e 17

w a v e l e n g t h o f 4 5 0 n m , no surface localization is formed, and no energy is 18

trapped in the alumina layer. Figure 6m presents LIC images of the Poynting flux clearly 19

showing the flux of energy originated inside the Al2O3, from the light backscattered from the 20

random metallic surface of the sample. By using arguments from wave theory and scale 21

invariance of Maxwell equations (see Supplementary Information), we obtained a simple 22

relationship for the wavelength shift, Δλ ( Δd ), as a function of the thickness variation of 23

alumina, Δλ , 24

Δλ = λ0

d0

Δd , (1) 25

where λ0 is the wavelength of a reflectivity minimum corresponding to a coating thickness, d0. 26

Figure 6n compares experimental measures with the results of Eq. (1). By applying 27

experimental values for both λ0 and d0, we obtained a coefficient λ0/d0 ≅ 12, which implies a 28

wavelength shift of 12 nm for every 1 nm increment of coating thickness. The results of Eq. 29

(1) show a good agreement with experimental results, predicting the large red shift that is 30

25

where

alumina,

relationship for the wavelength shift,

Δλ ,

random metallic surface of the sample. By us

invariance of Maxwell equations (see Supplemen

relationship for the wavelength shift,

showing the flux of energy originated inside the Al

random metallic surface of the sample. By us

invariance of Maxwell equations (see Supplemen

w a v e l e n g t h o f 4 5 0 n m , no surf

trapped in the alumina layer. Figure 6m pres

showing the flux of energy originated inside the Al


trapped in the alumina layer. Figure 6m pres

s u p p l e m e n t a r y F i g . S 7 s

d i s t r i b u t i o n s c a l c u l a t e d f r o m

f l e c t i v i t y m i n i m u


Fig. 6i, which demonstrates light trapping at the wavelength of 425 nm at different points of

convex metallic curvature located inside the Al

s u p p l e m e n t a r y F i g . S 7 s h o w e l e c t r o m a g n e t i c e n e r g y

t h e r e s o n a n c e , d e m o n s t r a t i n g

gions within the alumina layer is observed in

e wavelength of 425 nm at different points of

convex metallic curvature located inside the Al2

sonant coupling around the wavelength of 425 nm

gions within the alumina layer is observed in

e wavelength of 425 nm at different points of

. This process is clearly illustrated in

sonant coupling around the wavelength of 425 nm

, inducing a preferential localization of SPP

. This process is clearly illustrated in

a, as the critical angle depends

between alumina and air. Reflected wavevectors

al localization of SPP

dynamics for many scattering

a, as the critical angle depends

umina were totally reflected back and


umina were totally reflected back and


, (see Fig. 6g) larger than the critical angle,



10

the basis of the structural colors formed in the system. 1

2

3

CONCLUSIONS 4

5

We have experimentally demonstrated a new design concept to create robust and 6

saturated structural colors in metasurfaces composed of metallic nanowire networks with 7

ultra-thin, lossless dielectric coatings. Using a combination of analytical and numerical 8

techniques, we illustrated that these colors are the result of the resonant coupling of light 9

with surface plasmons that are localized in equivalent epsilon-near-zero regions formed in the 10

metallic network. This mechanism is not constrained for large angles as high as 70°, allowing 11

for efficient trapping of light over a broad wavelength range in the visible region. The 12

combination of mechanical robustness and color saturation in an extremely lightweight 13

structure makes these structural colors suitable for real world industrial applications, such as 14

automotive vehicles or airplanes, for which the weight is directly related to the fuel economy. 15

As discussed in the introduction, achieving a scalable fabrication is a key problem in structural 16

color printing. On the basis of our experiments, it is evident that our metasurfaces have 17

shown a wide color capability without the need for electron beam lithography (EBL) or other 18

complex fabrication procedures. Our structures, in fact, are based on simple wet-chemistry and 19

coating technologies, which can produce robust colors on large spatial scales. In addition to 20

such fundamental advances, our design concept has the potential to enrich the application of 21

metasurfaces to areas in which large active regions are mandatory, such as efficient light 22

trapping layers in photovoltaic cells. Although a deeper discussion of this topic is beyond the 23

scope of this paper, we can introduce some important points. On the basis of our theory and 24

experiments, we demonstrated that it is possible to control the response of an optical material 25

by ‘engineering’ the connectivity of a network of ENZ nanostructures created in a random 26

metallic structure. From the results of Fig. 6, we observed that this approach allows for 27

strong localization of optical radiation in nanoscale regions located well outside the metal, 28

completely absorbing incoming optical photons in a specific bandwidth (Fig. 6l-m). This 29

approach can potentially enhance the absorption power of ultra-thin absorbers, which can 30

take advantage of the formation of localized spots and harvest a significant portion of light 31

energy in nm-thick film structures. The current photovoltaic technology employs Si absorbers 32

of approximatively 100 µm thickness, whereas other solution- processed materials with high 33

metallic structure. From the results of Fig. 6, we observed that this approach allows for 27

strong localization of optical ra

completely absorbing incoming optical photons in a specific bandwidth (Fig. 6l-m). This

by ‘engineering’ the connectiv

metallic structure. From the results of Fig. 6, we observed that this approach allows for

scope of this paper, we can introduce some impor

experiments, we demonstrated that it is possible to control the response of an optical material

by ‘engineering’ the connectiv

trapping layers in photovoltaic


metasurfaces to areas in which large active re

trapping layers in photovoltaic


coating technologies, which can pr

such fundamental advances, our

metasurfaces to areas in which large active re

complex fabrication procedures. Our structures, in fact, are ba

coating technologies, which can produce robust colors on large spatial scales. In addition to

such fundamental advances, our design concept has the potential

color printing. On the basis of our experiment

shown a wide color capability without the need

Our structures, in fact, are ba

automotive vehicles or airplanes, for which the weight is directly related to the fuel economy.

ieving a scalable fabrication is a key problem in structural

color printing. On the basis of our experiments, it is evident that our metasurfaces have

for electron beam lithography (EBL) or other

colors suitable for real world

ight is directly related to the fuel economy.

ieving a scalable fabrication is a key problem in structural

obustness and color saturation in an extremely lightweight

colors suitable for real world industrial applications, such as

metallic network. This mechanism is not constrained for large angles as high as 70°, allowing

wavelength range in the visible region. The

obustness and color saturation in an extremely lightweight

localized in equivalent epsilon-near-zero regions formed in the

metallic network. This mechanism is not constrained for large angles as high as 70°, allowing

e the result of the resonant coupling of light

localized in equivalent epsilon-near-zero regions formed in the

composed of metallic nanowire networks with

a combination of analytical and numerical

e the result of the resonant coupling of light

to create robust and



to create robust and





11

manufacturability and low cost, such as quantum dots, require film thickness larger than 1 1

µm to efficiently absorb all incoming photons. Our metastructures can considerably scale down 2

these thicknesses, stimulating new research aimed at developing innovative materials for 3

renewable energy harvesting. 4

5

6

Acknowledgments 7

8

For computing, we used the resources of the KAUST Supercomputing Laboratory and the Redragon 9

cluster of the Primalight group. 10

F Capasso acknowledges the Air Force Office of Scientific Research (MURI: FA9550-14-1-0389) for 11

financial support. Part of the nano-fabrication was performed at the Center for Nanoscale Systems 12

(CNS), a member of the National Nanotechnology Coordinated Infrastructure (NNCI), which is 13

supported by the National Science Foundation under NSF award no. 1541959. CNS is part of Harvard 14

University. 15

A Fratalocchi thanks P Magistretti for fruitful discussions on brain functions. A Fratalocchi 16

acknowledges financial support from KAUST (Award CRG-1-2012-FRA-005). 17

H Galinski acknowledges the financial support of the ‘Size matters’ project (TDA Capital Ltd, London, 18

UK). H Dong acknowledges the financial support by the Master Thesis Grant of 19 the Zeno Karl 19

Schindler Foundation (Switzerland).20

21

22

23

FIGURE LEGENDS 24

25

26

Fig. 1. Observation of structural colors in random metallic networks with 27

subwavelength dielectric coatings. (a) Schematic illustration of an Al2O3 coated PtYAl 28

nanomaterial, based on a 3D reconstruction of a completely dealloyed PtYAl thin film 29

obtained via FIB assisted thin film tomography. (b) Photographs of deposited, dealloyed, and 30

Al2O3 coated PtYAl metamaterial networks, illustrating the formation of vibrant colors and the 31

continuous color change with increasing coating thickness. The photographs were taken under 32

illumination from ceiling lights. Each image is 2 × 2 mm2. (c) Experimental and FDTD 33

simulated structural color reported in a standard CIE 1931 (x, y) space, depicting the 34

subwavelength dielectric coatings28

nanomaterial, based on a 3D reconstruction of a completely dealloyed PtYAl thin film

obtained via FIB assisted thin film tomography. (

Fig. 1.

subwavelength dielectric coatings

Observation of structural colors in random metallic networks with

FIGURE LEGENDS

Schindler Foundation (Switzerland).

H Galinski acknowledges the financial support of the

UK). H Dong acknowledges the financial support by

A Fratalocchi thanks P Magistretti for fruitful discussions on brain functions. A Fratalocchi

acknowledges financial support from KAUST (Award CRG-1-2012-FRA-005).

H Galinski acknowledges the financial support of the ‘Size matters’ project (TDA Capital Ltd, London,

r NSF award no. 1541959. CNS is part of Harvard

A Fratalocchi thanks P Magistretti for fruitful discussions on brain functions. A Fratalocchi

Coordinated Infrastructure (NNCI), which is

r NSF award no. 1541959. CNS is part of Harvard

F Capasso acknowledges the Air Force Office of Scientific Research (MURI: FA9550-14-1-0389) for

was performed at the Center for Nanoscale Systems

Coordinated Infrastructure (NNCI), which is

F Capasso acknowledges the Air Force Office of Scientific Research (MURI: FA9550-14-1-0389) for

UST Supercomputing Laboratory and the Redragon UST Supercomputing Laboratory and the Redragon



12

chromaticity visible to the average person. The RGB color space is marked by the triangle 1

area. The chromaticity is calculated directly from reflectance spectra obtained either 2

experimentally (circles markers) or by FDTD simulations (dashed line). The edges of the 3

tongue-shaped plane correspond to color values of maximal saturation. d, Color palette 4

calculated by FDTD simulations for increasing thickness of Al2O3. 5

6

Fig. 2. Examples of different graphic arts designs with structural colors from 7

metamaterial networks. Photograph and optical micrograph of a colored graphic art 8

designed by combining a RF-sputtered Al2O3 coated network metamaterial and photolithography. 9

The inset shows an optical micrograph illustrating a detail of the graphic art and the 10

uniformity of the color. 11

12

Fig. 3. Wear properties of the structural colors. (a) Schematic illustration of the basic 13

principle of the scratch testing technique. A diamond stylus is used to scratch the film with 14

progressively increasing load. (b) Optical micrographs of progressive load scratches (0.4−15 15

mN) on a dense PtYAl thin film with and without coating, and PtYAl nanoscale networks 16

coated with 28 and 53 nm thick Al2O3, respectively. The critical load characterizing the 17

adhesion failure of the films is indicated by a pink arrow. 18

19

Fig. 4. Optical properties of the network metamaterials: reflectivity spectra. (a) 20

Experimental normal incidence reflectance spectra as a function of the Al2O3 coating thickness, 21

d. (b-e) Experimental reflectance spectra of nanoporous PtYAl thin films coated with 18 nm, 22

28 nm, 45 nm, and 53 nm Al2O3, respectively, as a function of the incidence angle (20°–85°). 23

The value of reflectance is indicated by the color bar. (f) FDTD-calculated normal incidence 24

reflectance spectra as function of the Al2O3 coating thickness, d. 25

26

Fig. 5. Generation of an equivalent ENZ material in the metallic nanowire network of 27

Fig. 1a. (a) 2D cross section profile of the metallic nanowire network, as obtained from 28

experimental FIB images of polished samples (Fig. 1a). When light impinges on this structure, 29

it excites the propagation of surface plasmon polariton waves (SPP), which move along the 30

complex surface of the metal (Panel a, inset). This motion is conveniently described in a 31

reflectance spectra as function of the Al25

28 nm, 45 nm, and 53 nm Al

The value of reflectance is indicated by the co

reflectance spectra as function of the Al

. (b-e) Experimental reflectance spectra of

28 nm, 45 nm, and 53 nm Al

Experimental normal incidence reflecta


Optical properties of the network metamaterials: reflectivity spectra.

Experimental normal incidence reflecta


adhesion failure of the films is indicated by a pink arrow.

mN) on a dense PtYAl thin film with and w

coated with 28 and 53 nm thick Al2O3, respectively. The critical load characterizing the

adhesion failure of the films is indicated by a pink arrow.

principle of the scratch testing technique. A diamond stylus is used to scratch the film with

) Optical micrographs of progressive load scratches (0

mN) on a dense PtYAl thin film with and without coating, and PtYAl nanoscale networks

Wear properties of the structural colors. (a) Schematic illustration of the basic

principle of the scratch testing technique. A diamond stylus is used to scratch the film with

) Schematic illustration of the basic

The inset shows an optical micrograph illustrating a detail of the graphic art and the

coated network metamaterial and photolithography.

The inset shows an optical micrograph illustrating a detail of the graphic art and the

aph of a colored graphic art

coated network metamaterial and photolithography.

signs with structural colors from

aph of a colored graphic art

signs with structural colors from signs with structural colors from

of maximal saturation. d, Color palette



13

curvilinear reference ϕ,ψ( ) , which provides a conformal map of the metallic surface of the 1

sample (solid red line). In the transformed space, ϕ,ψ( ) (panel b), SPP waves appear to 2

propagate inside an inhomogeneous material with refractive index, n ϕ,ψ( ) , on the line at 3

ψ = 0 (c, inset). The material, n ϕ,ψ( ) , models the effects of the metallic geometry of 4

panel (a), which is flattened out in transformed space, ϕ,ψ( ) . The two systems of panels (a-b) 5

are exactly the same for light propagation. The equivalent structure of (b) demonstrates a 6

complex network of ENZ structures (panel b, dark blue area), which are created by points of 7

convex metallic curvature (right inset). 8

9

Fig. 6. Mechanisms of structural color formation in the PtYAl cellular network. (a) 10

Normal incidence reflectance spectra obtained from FDTD simulations of the nanoscale Pt 11

network of Fig. 1a with different thickness of Al2O3. Panels (b-f) analyze the case with no 12

Al2O3 deposited on top of the metal, while panels (g-m) summarize the results for an Al2O3 13

layer of 33 nm. Panels (b,g) provide a pictorial illustration of light-matter interactions with 14

the sample, without (b) and with (g) Al2O3. In the presence of Al2O3, a portion of scattered 15

waves are reflected back in the Al2O3 layer, thus creating an energy flow in the coating layer 16

and a resonant coupling with ENZ regions located in the Al2O3. Panels (c-e) and (h-l) present 17

FDTD- c a l c u l a t e d spatial energy distributions in the structure by considering an input 18

wavelength indicated by the corresponding letter in panel (a). Energy distributions are 19

averaged over one optical cycle at steady state. Panel (f,m), conversely, provides a zoomed 20

view of the pink area of panel (e,l) and illustrates the electromagnetic energy flow in the 21

structure (arrow colored lines). The flow is superimposed with the corresponding averaged 22

spatial energy distribution. Panel (n), finally, compares the reflectivity minimum shift observed 23

in experiments (Fig. 4) with theoretical predictions based on the model illustrated in panel (g). 24

25 26

27

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in experiments (Fig. 4) with theoretical predic

structure (arrow colored lines). The flow is

spatial energy distribution. Panel (n), finally, co

in experiments (Fig. 4) with theoretical predic

view of the pink area of panel


averaged over one optical cycle at steady state.

view of the pink area of panel


FDTD- c a l c u l a t e d spatial energy distributions in the structure by considering an input

wavelength indicated by the corresponding lette

averaged over one optical cycle at steady state.

ENZ regions located in the Al

FDTD- c a l c u l a t e d spatial energy distributions in the structure by considering an input

wavelength indicated by the corresponding lette

the sample, without (b) and with (g) Al

O3 layer, thus creating an energy

ENZ regions located in the Al

deposited on top of the metal, while panels (g-m) summarize the results for an Al

layer of 33 nm. Panels (b,g) provide a pictorial illustration of light-matter interactions with

. In the presence of Al

layer, thus creating an energy

O3. Panels (b-f) analyze the case with no

deposited on top of the metal, while panels (g-m) summarize the results for an Al

l illustration of light-matter interactions with

from FDTD simulations of the nanoscale Pt

. Panels (b-f) analyze the case with no

ion in the PtYAl cellular network.

from FDTD simulations of the nanoscale Pt

ion in the PtYAl cellular network.

blue area), which are created by points of

are exactly the same for light propagation. The equivalent structure of (b) demonstrates a

blue area), which are created by points of

. The two systems of panels (a-b)


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. Porous gold with a nested-



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