Exploring optics of beetle cuticles with Mueller-matrix ellipsometry

Materials Today: Proceedings 1S ( 2014 ) 155 – 160

2214-7853 © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).Selection and Peer-review under responsibility of Physics Department, University of Namur.doi: 10.1016/j.matpr.2014.09.016

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Exploring optics of beetle cuticles with Mueller-matrix ellipsometry

Hans Arwina,∗, Roger Magnussona, Lía Fernandez del Ríoa, Christina Åkerlinda,b, EloyMunoz-Pinedac, Jan Landina, Arturo Mendoza-Galvana,c, Kenneth Järrendahla

aDepartment of Physics, Chemistry and Biology, Linköping University, SE-581 83 Linköping, SwedenbDivision of Sensor and EW systems, Swedish Defence Research Agency, SE-581 11 Linköping, Sweden

cCinvestav-IPN, Unidad Querétaro, Libramiento Norponiente 2000, 76230 Querétaro, Mexico

Abstract

Spectroscopic Mueller-matrix ellipsometry at variable angles of incidence is applied to beetle cuticles using a small (50 -100 μm)spot size. It is demonstrated how ellipticity and degree of polarization of the reflected light can be derived from a Mueller matrixproviding a detailed insight into reflection properties. Results from Cetonia aurata, Chrysina argenteola and Cotinis mutabilisare presented. The use of Mueller matrices in regression analysis to extract structural and optical parameters of cuticles is brieflydescribed and applied to cuticle data from Cetonia aurata whereby the pitch of the twisted layered structure in the cuticle isdetermined as well as the refractive indices of the epicuticle and the exocuticle.c© 2014 The Authors. Published by Elsevier Ltd.Selection and Peer-review under responsibility of Physics Department, University of Namur. This is an open access article underthe CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).

Keywords: Beetle cuticles; Twisted layered structures; Mueller matrices; Ellipsometry; Electromagnetic modeling

1. Introduction

Biological reflectors exhibit many optical features including scattering, structural colors, metallic shine and po-larization phenomena. Extensive investigations have been performed by many research groups using various opticaltechniques to explore these phenomena and in combination with microscopy the knowledge about the relation betweenstructure and optical properties is steadily increasing. Prominent investigations have been performed in the researchgroups of Vigneron [1], Vukusic [2], Parker [3], Hodgkinson [4] and more.

Here we specifically discuss Mueller-matrix spectroscopic ellipsometry (MMSE) for studies of specular reflectionfrom beetle cuticles. A major advantage with MMSE compared to reflectance measurements is that not only the basicspectral reflection properties of cuticles are obtained but also their polarizing and depolarizing capabilities. From aMueller matrix we can derive polarization properties in reflection for arbitrary polarization of incident light. We can,

∗ Corresponding author. Tel.: +46-13-281215 ; fax: +46-13-137568.E-mail address: [email protected]

© 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).Selection and Peer-review under responsibility of Physics Department, University of Namur.

156 Hans Arwin et al. / Materials Today: Proceedings 1S ( 2014 ) 155 – 160

for example, obtain the wavelength and angular dependence of ellipticity, handedness and degree of polarization inreflection under illumination with unpolarized light.

A Mueller matrix can also be used in electromagnetic modeling of the structure from which the optical featuresoriginate. We demonstrate how chirality in the scarab beetle Cetonia aurata (Linnaeus, 1758) can be modeled with atwisted layered structure and how structural and optical parameters of the epicuticle and exocuticle can be extracted.

Beetle cuticles are in many cases depolarizing and may also exhibit interference oscillations in the Mueller matrixelements. These effects can be addressed by further analyses of Mueller matrices and will provide deeper insight intocuticle optics and structure. As an example, a sum decomposition into non-depolarizing matrices provides informationabout the basic optical character of cuticles. In this way a Mueller matrix for C. aurata can be decomposed into a planemirror and a circular polarizer [5]. Beetles with broad-band reflectors are more complex and additional componentsmay be needed in decomposition. Further possibilities with Mueller matrices are that the interference patterns in theelements of a Mueller matrix allow determination of cuticle thickness as well as studies of allowed optical modes ofpropagation in the cuticles [6].

Our objective in this report is to illustrate the use of MMSE for a detailed characterization of beetle cuticles. Resultsfrom beetles in the Scarabaeidae subfamilies Cetoniinae and Rutelinae will be presented. We limit the discussion toa brief presentation of the first two aspects mentioned above, i.e. derived parameters from a Mueller matrix andelectromagnetic modeling. Decomposition and optical modes will be discussed elsewhere.

2. Methodology

The experimental results are presented as 4×4 Mueller matrices M which represent the full linear optical responseof samples, in our case the reflection properties of beetle cuticles. In the Stokes-Mueller formalism, M is determinedfrom So =MSi, where So = (Io,Qo,Uo,Vo)T and Si = (Ii,Qi,Ui,Vi)T are Stokes vectors of the emerging and incidentlight, respectively, and T indicates transpose. In a Stokes vector S, I is the total irradiance, Q and U are irradiances forthe part of the light with preference for x or y and +45◦ or −45◦ linear polarization, respectively, and V with preferencefor left- or right-handed circular polarization. We will here use Si normalized by setting Ii = 1. With a Mueller-matrixellipsometer, M is determined by measuring So for a set of Si and most instruments will deliver a normalized M forwhich all elements are normalized to element m11. In this work a dual-rotating compensator ellipsometer (RC2, J. A.Woollam Co., Inc.) was used to record Mueller matrices for beetle cuticles at angles of incidence θ in the range 20 -75◦ and in the spectral region 300-900 nm. Long-focus optics were used to reduce spot size to 100 μm or smaller.

The polarizing and depolarizing properties for light with any incoming state of polarization can be derived fromthe elements mi j (i, j = 1, 2, 3, 4) of M [7]. In particular for Si = (1, 0, 0, 0)T , i.e. unpolarized (natural) light, we obtainthe ellipticity angle ε and degree of polarization P of the reflected light as

ε =12

arcsinm41√

m221 + m2

31 + m241

and P =√

m221 + m2

31 + m241 (1)

A measured Mueller matrix M also contains information about the structure of the reflecting sample and can beanalyzed using regression analysis. A model Mueller matrix Mmod is determined by forward calculations of reflectionproperties using an optical model based on the knowledge about cuticle structure, e.g. from electron microscopyimages. By minimizing the difference ||M −Mmod || by varying structural and optical parameters in the model, e.g.layer thicknesses and refractive indices, these parameters can be quantified. Further details can be found in Ref. [8].

Results from three species of beetles are presented including two specimens of C. aurata collected in Sweden. Oneof them has a red and the other a green appearance. The specimen of Cotinis mutabilis (Gory and Percheron, 1833)was collected in Mexico, whereas Chrysina argenteola (Bates, 1888) was on loan from Museum of Natural Historyin Stockholm. Three of the specimens are shown in Fig. 1.


Fig. 1. Photos of the studies beetles Chrysina argenteola (left, photo J. Birch), Cetonia aurata (middle, photo J. Birch) and Cotinis mutabilis (right)with lengths 29, 19 and 23 mm, respectively.

3. Results

3.1. Primary data

Figure 2 shows an example of primary data measured on C. aurata at three angles of incidence. At small θ, thenarrow-band character is seen in several elements as a peak or a dip centered around 550 nm (green light). At largerθ a shift to shorter wavelengths is seen in accordance with visual observations on this iridescent cuticle structure.Several symmetries in M can be observed, e.g. that m12 = m21 and m33 = m44 for wavelengths below and abovethe feature around 550 nm. In addition the off-diagonal blocks are zero. This corresponds to that the cuticle appearsas an isotropic mirror in these spectral ranges. An isotropic reflector also has m34 = −m43 but as the cuticle isdielectric these elements are zero. Additional symmetries like m14 = m41, m13 = −m31 and m24 = m42 are expected forchiral non-depolarizing systems and have been discussed explicitly for C. mutabilis [6] in the case of depolarization.By inspection of M, we can also immediately conclude that this beetle reflects unpolarized light as near-circularlypolarized light in the 500-600 nm spectral range at small θ because m41 is non-zero whereas m21 and m31 are small.The polarization is also left-handed as m41 < 0.

Fig. 2. Example of primary data from C. aurata measured by MMSE. Only Mueller matrices measured at θ = 20◦, θ = 45◦ and θ = 75◦ are shownfor clarity.

3.2. Derived parameters

Figure 3a shows the ellipticity angle derived from Eq. 1 for a few selected beetles. Two of the beetles are C.aurata specimens with red and green appearance, respectively. These beetles represent narrow-band reflectors and


reflect almost circularly polarized light as the ellipticity angle is close to -45◦ in their respective color bands. AlsoC. mutabilis is a narrow-band reflector, whereas the gold-colored C. argenteola is a broad-band reflector and reflectsleft-handed circularly polarized light in the whole visible spectral range. Notice the interference oscillations in thedata, especially for C. argenteola and C. mutabilis. These oscillations can be used to determine cuticle thickness [6].From Fig. 3b we also find that the degree of polarization, as derived from Eq. 1, is high and in the range 0.7-0.9 in thespectral range in which circularly polarized light is reflected.

C. argenteola

C. auratagreen

C. auratared

C. mutabilisC. argenteola

C. mutabilis

C. aurata red

C. aurata green

(°)

(a) (b)

De

gre

e o

f p

ola

riza

tio

n

Elli

pticity a

ng

le (

°)

Wavelength (nm)Wavelength (nm)

Fig. 3. (a) Ellipticity angle and (b) degree of polarization of natural (unpolarized) light reflected at θ = 20◦ from C. argenteola, C. mutabilis, a redC. aurata and a green C. aurata. The horizontal dashed line in (a) indicates ε = −45◦ corresponding to circularly polarized light.

3.3. Modeling

Figure 4 shows a structural model used in regression analysis of M from C. aurata. The assumption is thatthe structure is a twisted layered structure here subdivided into 360 sublayers (lamellae) representing a Bouligandstructure [9]. The parameters evaluated are the pitch Λ and its distribution, the epicuticle thickness depi and theuniaxial refractive index of the epicuticle and the biaxial index of the exocuticle lamellae. The value of Λ dependson the color of the cuticle [10]. For a green C. aurata Λ ≈ 380 nm and depi ≈ 500 nm. In Fig. 4 an example ofthe biaxial refractive index of the cuticle lamellae are shown. In this type of analysis, which is focused on resolvingchiral features, spectral data from multiple angles are used, e.g. from 20◦ to 60◦ in steps of 5◦. For θ larger than60◦, the surface reflection is dominating and may introduce systematic errors in the results. Methodology and generalprocedures for modeling of ellipsometric data are found in [7,11] whereas further details for the specific approachused here are given in [8].

4. Discussion

Relatively few reports on Muller-matrix studies of beetle cuticles are found, probably due to the complexity inrecording high-quality data. A typical cuticle sample is small, curved and has many inhomogeneities. To get a rea-sonably complete description it is necessary to perform spectroscopy at several angles of incidence which meansthat instruments have to be very sophisticated. Some early work was performed by Goldstein [12] who did normal-incidence Mueller-matrix polarimetry. He confirmed that right-handed circular polarization can result e.g. in lightreflected from Chrysina resplendens. Hodgkinson [4] developed a Mueller-matrix ellipsometer and presented near-normal incidence results and polarization analysis for several beetles. Similar studies including angle-resolved MMSEhave been performed by us [13]. Imaging Muller-matrix ellipsometry has been employed on beetle cuticles but onlyat single wavelength [14]. Imaging ellipsometry allows qualitative studies of patterned surfaces and also facilitatesdecomposition of Mueller matrices for a deeper insight into cuticle optics [15]. Recently Mueller-matrix spectro-scopic ellipsometers have become available commercially. Among the advantages are easy operation, small spot size(<100 μm), a large spectral range extending outside the visible range and including ultraviolet and near-infrared light,possibilities to measure at multiple angles of incidence and powerful software for analysis. It should be pointed outthat each beetle is an individual and unique and specimen to specimen variations in color and polarization featuresare observed as revealed in MMSE-data [10]. Differences are also found between measurements on the elytra and


400 600 800

1.3

1.4

Re

fra

cti

ve

ind

ex

Wavelength (nm)

�

dexo

depiEpicuticle

Exocuticle

Endocuticle

Ambient

360 sublayers in total

Ambient

400 600 8001.4

1.5

1.6

Re

fra

cti

ve

ind

ex

Wavelength (nm)

nz

ny

nx

nz

nxy

Fig. 4. Structural model for the cuticle of C. aurata and the refractive index of the epicuticle and the exocuticle lamellae obtained from a regressionanalysis of Mueller-matrix data. (Reprinted from [8]).

the scutellum on the same specimen. However, when MMSE-measurements are repeated on the same position on acuticle, the repeatability is very high and differences among data are typically not visible on scales as used in Fig. 2.

Only results from beetle cuticles with small scattering and a dominating specular reflection are presented here.However, scattering may occur and may be diffuse like for the white beetle Cyphochilus insulanus [16,17]. Interestingscattering phenomena are also found in Chrysina gloriosa which has stripes being either gold-colored or green [18].The gold-colored stripes exhibit specular reflection at oblique incidence with pronounced left-handed circular polar-ization, whereas the green stripes in specular reflection can be described as dielectric mirrors. However, on the greenareas, the incident light is scattered towards the normal and is left-handed circularly polarized. As an example, θ = 45◦

results in left-handed circularly polarized light at 30◦ from the normal [18].In summary we conclude that the accuracy of MMSE is very high and of the order of 0.01 or better for the Mueller-

matrix elements. The studies are complicated by variations among individuals, cuticle inhomogeneities, spot size andmodeling possibilities of the data. However, methodology with spot size below 50 μm is under development whichwill facilitate studies of individual scales in butterfly wings for example. The presented modeling of MMSE-data isdone in regression mode and is not simulation-based as often seen in reflectance studies. So far models are based onplanar structures utilizing the Fresnel formalism but numerical modeling is used frequently in simulations and willsoon be implemented in regression mode. In our opinion MMSE will have a large impact on the understanding ofbiological reflectors in the future.

Acknowledgements

This work is supported by a grant from the Swedish Research Council. Knut and Alice Wallenberg foundationis acknowledged for support to instrumentation. Jens Birch is acknowledged for providing photos in Fig. 1. ArturoMendoza-Galvan acknowledges financial support from the Swedish Government Strategic Research Area in MaterialsScience on Functional Materials at Linköping University (Faculty Grant SFO-Mat-LiU 2009-00971).


References

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[2] P. Vukusic, R. Sambles, Nature 424(2003)852–855.[3] A.R. Parker, H.E. Townley, Nature Nanotechn. 2(2007)347–353.[4] I. Hodgkinson, S. Lowrey, L. Bourke, A. Parker, M.W. McCall, Appl. Opt. 49(2010)4558-4567.[5] H. Arwin, R. Magnusson, E. Garcia-Caurel, C. Fallet, K. Järrendahl, A. De Martino, M. Foldyna, R. Ossikovski, in manuscript.[6] E. Munoz-Pineda, K. Järrendahl, H. Arwin, A. Mendoza-Galvan, Thin Solid Films, http://dx.doi.org/10.1016/j.tsf.2013.11.144.[7] R.M.A. Azzam, N.M. Bashara, Ellipsometry and Polarized Light, North-Holland, Amsterdam, 1977.[8] H. Arwin, T. Berlind, B. Johs, K. Järrendahl, Opt. Expr. 21(2013)22645–22656.[9] Y. Bouligand, Tissue & Cell 5(1972)189–217.

[10] H. Arwin, L. Fernandez del Río, K. Järrendahl, Thin Solid Films, http://dx.doi.org/10.1016/j.tsf.2014.02.012.[11] H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications, John Wiley & Sons, Ltd, 2007.[12] D.H. Goldstein, Appl. Opt. 45(2006)7944–7950.[13] H. Arwin, R. Magnusson, J. Landin, K. Järrendahl, Phil. Mag. 92(2012)1583–1599.[14] C. Fallet, Angle Resolved Mueller Polarimetry, Applications to Periodic Structures, Ph D thesis, École polytechnique/CNRS (2011).[15] R. Ossikovski, M. Foldyna, C. Fallet, A. De Martino, Opt. Lett. 34(2009)2426–2428.[16] P. Vukusic, B. Hallam, J. Noyes, Science 4315(2007)348.[17] C. Åkerlind, H. Arwin, T. Hallberg, J. Landin, J. Gustafson, K. Järrendahl, in manuscript.[18] L. Fernandez del Río, H. Arwin, K. Järrendahl, Thin Solid Films, http://dx.doi.org/10.1016/j.tsf.2013.11.149.

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Exploring optics of beetle cuticles with Mueller-matrix ellipsometry