biomimetics

Article Photonic Crystal Characterization of the Cuticles of Chrysina chrysargyrea and Chrysina optima Jewel Scarab Beetles

William E. Vargas 1,2,*, Esteban Avendano 1, Marcela Hernández-Jiménez 1, Daniel E. Azofeifa 1, Eduardo Libby 3, Ángel Solís 4 and Cynthia Barboza-Aguilar 5 1 Centro de Investigación en Ciencia e Ingeniería de Materiales, Escuela de Física, Universidad de Costa Rica, San José 2060-11501, Costa Rica; [email protected] (E.A.); [email protected] (M.H.-J.); [email protected] (D.E.A.) 2 Academia Nacional de Ciencias de Costa Rica, San José 1367-2050, Costa Rica 3 Centro de Investigación en Ciencia e Ingeniería de Materiales, Escuela de Química, Universidad de Costa Rica, San José 2060-11501, Costa Rica; [email protected] 4 Departamento de Historia Natural, Museo Nacional de Costa Rica, San José 749-1000, Costa Rica; [email protected] 5 Centro de Investigación en Estructuras Microscópicas, Universidad de Costa Rica, San José 2060-11501, Costa Rica; [email protected] * Correspondence: [email protected]



Received: 31 July 2018; Accepted: 27 September 2018; Published: 11 October 2018
 Abstract: A unified description involving structural morphology and composition, dispersion of optical constants, modeled and measured reflection spectra and photonic crystal characterization is devised. Light reflection spectra by the cuticles of scarab beetles (Chrysina chrysargyrea and Chrysina optima), measured in the wavelength range 300–1000 nm, show spectrally structured broad bands. Scanning electron microscopy analysis shows that the pitches of the twisted structures responsible for the left-handed circularly polarized reflected light change monotonically with depth through the cuticles, making it possible to obtain the explicit depth-dependence for each cuticle arrangement considered. This variation is a key aspect, and it will be introduced in the context of Berreman’s formalism, which allows us to evaluate reflection spectra whose main features coincide in those displayed in measurements. Through the dispersion relation obtained from the Helmholtz’s equation satisfied by the circular components of the propagating fields, the presence of a photonic band gap is established for each case considered. These band gaps depend on depth through the cuticle, and their spectral positions change with depth. This explains the presence of broad bands in the reflection spectra, and their spectral features correlate with details in the variation of the pitch with depth. The twisted structures consist of chitin nanofibrils whose optical anisotropy is not large enough so as to be approached from modeling the measured reflection spectra. The presence of a high birefringence substance embedded in the chitin matrix is required. In this sense, the presence of uric acid crystallites through the cuticle is strongly suggested by frustrated attenuated total reflection and Raman spectroscopy analysis. The complete optical modeling is performed incorporating the wavelength-dependent optical constants of chitin and uric acid.

Keywords: circular polarization; structural color; natural photonic material; photonic band gap; photonic crystal

1. Introduction Reflection of light by cuticles of scarab beetles has attracted the attention of researchers since the beginning of the 20th Century, even more so after the circularly polarized nature of the reflected

Biomimetics 2018, 3, 30; doi:10.3390/biomimetics3040030 www.mdpi.com/journal/biomimetics Biomimetics 2018, 3, 30 2 of 20 light was established [1]. Natural systems from bird feathers and butterfly wings to scarab cuticles, displaying what is referred to as structural color, were previously considered throughout the 19th Century by brilliant minds like the third and the fourth Lord Rayleigh [2,3] and Isaac Newton [4]. With the work of Robert Hook, optical microscopy contributes to a first approach to the structure of some of these iridescent natural systems [5]. Regarding scarab beetles, detailed descriptions of the self-assembled cuticular structures have been available since the use of electron microscopes [6]. Constructive interference between reflected light rays propagating through micron-sized structures composed of organized nano-sized elements is responsible for the color of these natural systems. Application of radiative transfer models has allowed characterization of the relationship between cuticular structures and corresponding reflection spectra. For instance, the iridescent green and purple colors of the elytra of the Japanese beetle Chrysochroa fulgidissima have been correlated with the presence of corresponding multilayered structures through its cuticle [7]. In this case, successive layers differ slightly in refractive index, and each one is assumed as optically homogeneous in the context of the radiative transfer model used to calculate reflection spectra consistent with the observed colors and linear polarization of the reflected light. Higher complexity optically anisotropic chitin-based natural arrangements have been considered in the last few decades, since the pioneering work of Neville and Caveney [8]. As in the cuticle of many scarab species, optical anisotropy is the result of a twisted or helical structure where each layer of chitin nanofibrils is slightly rotated with respect to the previous one until completion of several cycles throughout the cuticle; the thickness of these helicoidal stacks is usually between 10 and 20 µm. The circular polarization of the reflected light is determined by the chirality of the twisted structure. Most of the scarab beetles considered reflect left-handed circularly polarized light [9]. These kinds of structures, at larger scales, have also been found in crustaceans [10], in some fruits where the fibrils are made of cellulose [11], as well as in some plants’ leaves [12]. The role played by the circularly polarized reflected light in aspects such as thermal regulation, mating behavior, signaling, camouflage, etc., is a current theme of research [13,14], as well as the development of methods to produce functional polymer-based or cholesteric materials with similar twisted structures [15–17]. Regarding the twisted arrangements found through the cuticle of scarab beetles, structures characterized by a single pitch value with a small variation of the pitch from a certain depth through the cuticle and helicoidal arrangements with various pitches have been considered in connection with the spectral properties of the reflected light [18,19]. Both spectrophotometric- and ellipsometry-based analyses have been reported [20,21]. Several works have considered the optical properties of the cuticle of Chrysina scarabs. Photometric and ellipsometric measurements were reported by Goldstein for Chrysina resplendens, Chrysina clypealis and Chrysina gloriosa scarabs [22]. The silver-like appearance of Chrysina chrysargyrea has been qualitatively explained in terms of an assumed chirped structure through its cuticle [23], with no modeling or measurements. The cuticle surface of C. gloriosa has been studied by optical microscopy [24], and its polarizing properties analyzed through ellipsometric measurements [25,26]. Calculated reflection spectra by cuticles of Chrysina aurigans and Chrysina optima are reported [27], with no specification of the depth dependence of the pitch and with no comparisons with experimental measurements. Co- and cross-polarized measured reflection spectra by the cuticle of Chrysina resplendens have been compared with calculated ones with the incorporation of a scaled depth dependence of the pitch [28]. A photonic crystal characterization of the cuticle of Hoplia coerulea has been performed to correlate the presence of fluorophores with the density of states available for the photons emitted by fluorescence [29]. In the context of our research work, scanning electron images have shown that scarabs of the Chrysina genus are characterized by monotonously depth-dependent pitches, i.e., the spatial period gradually changes with the depth throughout the cuticle. For each specific species and varieties considered, when the depth dependence of the pitch is introduced in a radiative transfer model appropriate to describe the propagation of electromagnetic radiation through anisotropic uniaxial media, the calculated reflection spectrum is very similar to the measured one. This has been done for the silver-like and red C. aurigans and for the golden- and silver-like C. chrysargyrea beetles [30–35], Biomimetics 2018, 3, 30 3 of 20 including a photonic crystal (PC) characterization of C. aurigans varieties. These works introduced for the first time the explicit incorporation of a depth-dependent pitch in the radiative transfer formalism, dispersion in the optical constants of the involved materials, together with a PC characterization correlated with the presence of broad bands in the reflection spectra of these natural systems. In this work, we consider the optical properties of anisotropic twisted arrangements found in the cuticle of Chrysina scarab beetles through the application of Berreman’s radiative transfer formalism. Sections2 and3 include details about the optical, morphological and composition characterization of the elytra whose optical properties and PC behavior will be considered, for three scarab beetles of the Chrysina genus: the golden-like C. chrysargyrea, the silver-like C. chrysargyrea and the silver-like C. optima. Spectrophotometric measurements of light reflection and scanning electron microscopy (SEM) were used to optically and morphologically characterize the cuticles of Chrysina scarab beetles. Additionally, frustrated attenuated total reflection of infrared light and Raman spectroscopy were used to carry out the compositional characterization of the elytra of C. optima specimens. Section3 briefly describes the so-called 4 × 4 matrix approach, with some introductory applications focused on synthetic structures with a single pitch, a pitch linearly dependent on the depth through the cuticle and a pitch with a quasi-parabolic dependence on depth. The method followed to carry out a PC characterization of helicoidal arrangements is also described in this section, with application to a linearly graded arrangement and a structure with a quasi-parabolic dependence of the pitch on depth. The modeling of the photometric and photonic characterization of the chiral structures in nature includes graphics displaying both calculated reflection spectra and the depth dependence of the photonic band gap (PBG), its local limits and the effective spectral limits of the reflection band. Correlations between depth dependences of the band gaps and features of the reflection spectra are discussed.

2. Materials and Methods

2.1. Specimens and Sample Preparation This research was developed with the approval of the Institutional Biodiversity Commission of the University of Costa Rica, resolution number 40. C. optima specimens used through this research were captured alive in the Tapantí National Park rainforest in Costa Rica. They were collected according to the permissions in the document “Resolución-SINAC-ACLAP-GMRN-INV-129-2016”. The collection was performed during the new moon period between April and May in 2017 and 2018. The specimens were attracted by means of a high intensity mercury lamp placed in from of a white screen faced towards the hillside of the mountain. After collection, the scarabs were put in a freezer to avoid degradation of the material. The C. chrysargyrea specimens were obtained through the material transfer agreement, from the collection of the former National Institute of Biodiversity (INBio), document number MTA-BP-001-11. Specimens were dried in a oven for preservation purposes. Samples for SEM were prepared following the method reported in [35] to determine the pitch of the elytra. For Raman spectroscopy and Fourier-transform infrared spectroscopy in frustrated attenuated total reflection configuration (FTIR-ATR), samples were prepared from the elytra upper surface of eight non-cured specimens carefully scraped with a steel blade to produce a fine micron-sized powder. Two reference samples were used: a low humidity and high purity uric acid (>99%) purchased from Fisher Scientific (Hampton, NH, USA) and a finely grained chitin powder extracted from shrimp shells. Raman spectra were recorded with an Alpha300R confocal Raman microscope (WiTec, Ulm, Germany) using a 785 nm excitation laser. Each spectrum was recorded with an integration time of 500 ms and an average of 100 scans. The infrared spectra were measured with a Universal ATR sampling accessory installed on a Frontier FIR/MIR spectrometer, both from Perkin Elmer (Waltham, MA, USA). Resolution was set to 0.5 cm−1 for an average of 50 scans per sample. The powder samples were covered with a gold foil and pressed against the diamond crystal, maintaining the same reading in the pressure gauge for each sample. Biomimetics 2018, 3, 30 4 of 20

2.2. Visual appearance Biomimetics 2018, 3, x FOR PEER REVIEW 4 of 20 Figure1 shows pictures of representative specimens of the jewel scarabs (golden- and silver-like C. chrysargyrea2.2. Visual appearanceand C. optima ) use in this study. Pictures where taken with a Nikon D7200 digital camera andFigure AF-S 1 shows 105 f/2.8pictures lens of representative (Nikon Corporation, specimens Tokyo, of the jewel Japan). scarabs Exposure (golden- forand all silver-like the images was normalizedC. chrysargyrea by and spot-measuring C. optima) use in the this white-matte study. Pictures background where taken to thewith side a Nikon of the D7200 specimens digital and settingcamera it to and 1.33 AF-S f/stops 105 f/2.8 above lens the (Nikon meter Corporation, reading. Tokyo, This exposure Japan). Exposure setting for was all chosenthe images so was none of the imagenormalized RGB by channels spot-measuring became the oversaturated. white-matte back Theground visual to appearance the side of the of specimens the scarabs and is setting shown in Figureit1 toA,D,G. 1.33 f/stops Figure above1B,E,H the meter shows reading. photographs This exposure taken setting when thewas lightchosen reflected so none byof the the image elytra RGB passes throughchannels a left-handed became oversaturated. circular polarizer The visual (LHCP) appearance (HOYA of PL-CIR, the scarabs Hoya is shown Corporation, in Figure Tokyo, 1A,D,G. Japan) beforeFigure reaching 1B,E,H the shows objective photographs of the camera, taken when and athe right-handed light reflected circular by the polarizerelytra passes (RHCP) through (HOYA a left- Pro1 MC PL-C,handed Hoya circular Corporation) polarizer (LHCP) was used(HOYA to PL-CIR take the, Hoya pictures Corporation, shown Tokyo, in Figure Japan)1C,F,I. before As reaching previously the objective of the camera, and a right-handed circular polarizer (RHCP) (HOYA Pro1 MC PL-C, reported, the appearance of the scarabs when using a RHCP is determined by a background of Hoya Corporation) was used to take the pictures shown in Figure 1C,F,I. As previously reported, the non-coherentappearance reflected of the scarabs radiation when associated using a withRHCP the is presencedetermined of defectsby a background (deviations of fromnon-coherent the gradual variationreflected in the radiation orientation associated of the with chitin the nanofibrils) presence of defects through (deviations the chiral from structure the gradual [31,33 variation]. These defectsin are nottherelated orientation to the of the presence chitin nanofibrils) of a ripple through structure the superimposed chiral structure on[31,33]. the broadThese defects band of are reflection not displayedrelated for to some the presence of the Chrysina of a ripplebeetles structure like superi the goldenmposedC. on aurigans the broadand bandC. chrysargyrea of reflection[ 36displayed]. When this non-coherentfor some componentof the Chrysina of beetles the reflected like the radiation golden C. isaurigans partially and removed C. chrysargyrea by the [36]. LHCP, When the this appearance non- of thecoherent cuticle component is more intense. of the reflecte A visuald radiation comparison is partially of the removed first two by columns the LHCP, shows the appearance that most of of the reflectedthe cuticle radiation is more is left-handed intense. A circularlyvisual comparison polarized. of the The first reflection two columns spectra shows were that measured most of usingthe an reflected radiation is left-handed circularly polarized. The reflection spectra were measured using an Avaspec 3648 fiber optic spectrometer (Avantes, Apeldoom, The Netherlands) in the wavelength range Avaspec 3648 fiber optic spectrometer (Avantes, Apeldoom, The Netherlands) in the wavelength 300–1000 nm and using a halogen deuterium lamp AvaLight DHc (Avantes). A flat aluminum mirror range 300–1000 nm and using a halogen deuterium lamp AvaLight DHc (Avantes). A flat aluminum was usedmirror as was a reflectance used as a standard reflectance STAN-SSH standard STAN-S (OceanSH Optics, (Ocean Winter Optics, Park, Winter FL, USA)Park, forFL, normalizationUSA) for 2 of thenormalization measurements. of the An measurements. area of approximately An area of 2 mmapproximatelywas illuminated 2 mm2 was with illuminated non-polarized with normallynon- incidentpolarized radiation. normally Details incident on the radiation. procedure Details used on to the measure procedure the used spectra to measure and to ensure the spectra reproducibility and to are reportedensure reproducibility elsewhere [30 are]. reported elsewhere [30].

FigureFigure 1. AppearanceAppearance and and circularly circularly polarized polarized light light reflec reflectiontion from fromelytra elytraof three of jewel three scarabs jewel scarabsof the Chrysina of the Chrysinagenus. (A–genus.C) Golden- (A– Cand) Golden- (D–F) silver-like and (D –C.F )chrysargyrea silver-like, andC. chrysargyrea (G–I) silver-like, and C. (optimaG–I) silver-likespecimens. TheC. optima visual specimens.appearance of The (A) visual golden appearance C. chrysargyrea of, ((AD)) goldensilvery C.C. chrysargyrea chrysargyrea, and,(D (G)) silvery silvery C.C. chrysargyreaoptima is shown, and on (theG) silveryleft column.C. optima The middleis shown column on the(B,E left,H) shows column. photographs The middle taken column with a (LHCPB,E,H between) shows the photographs illuminated takenelytra and the objective of the camera. A RHCP was used for the photographs shown on the right column (C,F,I). with a LHCP between the illuminated elytra and the objective of the camera. A RHCP was used for the photographs shown on the right column (C,F,I).

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3.3. Results Results and and Discussion Discussion

3.1.3.1. Measured Measured Reflection Reflection Spectra Spectra FigureFigure 22 depictsdepicts thethe correspondingcorresponding reflectionreflection spectraspectra throughthrough thethe ultravioletultraviolet (UV),(UV), visiblevisible andand near-infrarednear-infrared (NIR) (NIR) wavelength wavelength ranges. ranges. The The elytron elytron of of the the golden golden C.C. chrysargyrea chrysargyrea showsshows a a spectrum with a reflection reflection band from ≈525525 to to 1000 1000 nm nm (containing (containing a a ripple ripple structure structure beyond beyond 600 600 nm), nm), and and it goesgoes from from 350 to 1000 nm for the silver-like scar scarabsabs whose spectra have have a a broad reflection reflection band at NIRNIR wavelengths. wavelengths. It It also also shows shows a aflattened flattened shoulder shoulder just just after after the the reflection reflection edge. edge. For For the the silvery silvery C. chrysargyreaC. chrysargyrea, several, several peaks peaks are are depicted depicted in inthe the short short wave wavelengthslengths side side of of the the visible visible range, range, with with a a plateau for wavelengths between 540 and 610 nm. The The spectrum spectrum of the the C.C. optima optima hashas additionally additionally two two broadbroad peaks inin thethe visible visible range. range. Similar Similar measured measured spectra, spectra, in thein the wavelength wavelength range range 450–1000 450–1000 nm, havenm, havebeen reportedbeen reported for these for two these scarab two beetles scarab [ 37beetles]. The [3 presence7]. The ofpresence shoulders of orshoulders plateaus or is aplateaus consequence is a consequenceof a range of depthsof a range through of depths the cuticle through where the cuticle the pitch where is almost the pitch constant is almost (see Sectionconstant 3.5 (see). Typically, Section 3.5).the reflectionsTypically, spectrathe reflections gradually spectra decrease gradually when decrease approaching when 1000 approaching nm in wavelength. 1000 nm in wavelength.

FigureFigure 2. 2. MeasuredMeasured reflection reflection spectra spectra of of elytra elytra from from (A ()A golden-like) golden-like C. C.chrysargyrea chrysargyrea, (B,() Bsilver-like) silver-like C. chrysargyreaC. chrysargyrea, and, and (C ()C silver-like) silver-like C.C. optima optima scarabsscarabs illuminated illuminated with with normally normally incident incident non-polarized non-polarized light.light. NIR: NIR: Near Near infrared; infrared; UV: UV: Ultraviolet. 3.2. Scanning Electron Microscopy Analysis and Morphology of the Cuticle 3.2. Scanning Electron Microscopy Analysis and Morphology of the Cuticle Depth dependence of the apparent pitch was measured by SEM to characterize each twisted Depth dependence of the apparent pitch was measured by SEM to characterize each twisted structure in the cuticles of the beetles under study. This was previously reported for the C. chrysargyrea structure in the cuticles of the beetles under study. This was previously reported for the C. scarabs [35]. Their apparent thicknesses are close to 11.5 and 10.9 µm for the golden and silvery chrysargyrea scarabs [35]. Their apparent thicknesses are close to 11.5 and 10.9 μm for the golden and C. chrysargyrea scarabs, respectively. The apparent thickness of the C. optima’s elytron is the largest one, silvery C. chrysargyrea scarabs, respectively. The apparent thickness of the C. optima’s elytron is the ≈17.2 µm. Following a similar method as described in [35] to determine how the pitch of the C. optima largest one, ≈17.2 μm. Following a similar method as described in [35] to determine how the pitch of changes with depth through the cuticle, Figure3 shows a cut through the cuticle with the added violet the C. optima changes with depth through the cuticle, Figure 3 shows a cut through the cuticle with lines coinciding with those planes where the chitin nanofibrils are parallel to the cut. The plane of the the added violet lines coinciding with those planes where the chitin nanofibrils are parallel to the cut. cut could be inclined with respect to the plane normal to the surface, with β as the angle of inclination. The plane of the cut could be inclined with respect to the plane normal to the surface, with β as the Changes in the orientation of the chitin nanofibrils, every 180◦, can be correlated with the depth z angle of inclination. Changes in the orientation of the chitin nanofibrils, every 180°, can be correlated through the cuticle, and as a consequence of this, the discrete depth dependence of the apparent pitch with the depth z through the cuticle, and as a consequence of this, the discrete depth dependence of can be established. From this set of z-values, whose uncertainties are close to δz = 5 nm, a smoothed the apparent pitch can be established. From this set of z-values, whose uncertainties are close to δz = curve is obtained and used to interpolate when applying Berreman’s formalism. Determination of 5 nm, a smoothed curve is obtained and used to interpolate when applying Berreman’s formalism. these parameters from SEM images allows us to depict the depth dependence of the apparent pitches Determination of these parameters from SEM images allows us to depict the depth dependence of (Figure4) corresponding to the cuticles of the scarabs shown in Figure1. The depth dependence of the apparent pitches (Figure 4) corresponding to the cuticles of the scarabs shown in Figure 1. The the golden-like C. chrysargyrea shows an extended quasi-parabolic behavior, and as commented on depth dependence of the golden-like C. chrysargyrea shows an extended quasi-parabolic behavior, before, this fact is directly correlated with the ripple-structured broad band displayed in its reflection and as commented on before, this fact is directly correlated with the ripple-structured broad band spectrum. The pitches of the silver-like beetles show small decreases near the surface of the structures, displayed in its reflection spectrum. The pitches of the silver-like beetles show small decreases near followed by monotonously increasing values showing some shoulders for certain ranges of depth. the surface of the structures, followed by monotonously increasing values showing some shoulders for certain ranges of depth.

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Figure 3. Scanning electron microscopy image of a cross-section through the cuticle of a C. optima scarab.Figure The 3. Scanning added violet electron lines, microscopy which cover image image a depth of of closea cross-section to 17.2 μm, through indicate the those cuticle planes of a where C. optima the μ chitinscarab. fibrils The areadded parallel violet to lines, the cut which of the cover twisted a depth structure. close toScale 17.2 bar: μµm, 5 indicatem. those planes where the chitin fibrilsfibrils are parallel toto thethe cutcut ofof thethe twistedtwisted structure.structure. ScaleScale bar:bar: 5 µμm.

FigureFigure 4. 4. DepthDepth dependences dependences of ofthe the apparent apparent pitches pitches of the of thecuticles cuticles of (A of) golden (A) golden C. chrysargyreaC. chrysargyrea, (B) , (B) silvery C. chrysargyrea, and (C) silvery C. optima scarab beetles. Maximum (P ) and minimum (P ) silveryFigure C. 4. chrysargyreaDepth dependences, and (C )of silvery the apparent C. optima pitches scarab of beetles.the cuticles Maximum of (A) golden (PMM) and C. chrysargyreaminimum (P, (mBm) ) values of the apparent pitches are indicated. valuessilvery of C. the chrysargyrea apparent pitches, and ( Care) silvery indicated. C. optima scarab beetles. Maximum (PM) and minimum (Pm) 3.3. Compositionvalues of the apparent pitches are indicated. 3.3. Composition Chitin is a natural polymer with a low birefringence. Besides the twisted structure of chitin 3.3. ChitinComposition is a natural polymer with a low birefringence. Besides the twisted structure of chitin nanofibrils, the existence of a high birefringent substance embedded between the arrangement of chitin nanofibrils,Chitin theis aexistence natural polymerof a high with birefringe a lownt birefringence. substance embedded Besides the between twisted the structure arrangement of chitin of is required to approach the measured reflection spectra from modeling. The occurrence of crystallites chitinnanofibrils, is required the existence to approach of a thehigh measured birefringe reflnt ectionsubstance spectra embedded from modeling. between theThe arrangement occurrence of of of such a material through twisted structures of chitin nanofibrils in cuticles of Chrysina scarabs was crystalliteschitin is required of such ato material approach through the measured twisted streflructuresection ofspectra chitin from nano modeling.fibrils in cuticles The occurrence of Chrysina of established some time ago, particularly when considering C. resplendens and C. optima specimens. scarabscrystallites was ofestablished such a material some timethrough ago, twisted particularly structures when of considering chitin nano C.fibrils resplendens in cuticles and of C. Chrysina optima Our choice of uric acid for this strongly birefringent substance follows the original determinations of specimens.scarabs was Our established choice of some uric timeacid ago,for thisparticularly strongly when birefringent considering substance C. resplendens follows andthe C.original optima Caveney [38], who recognized the presence of absorption bands characterizing the UV spectrum of uric determinationsspecimens. Our of choiceCaveney of [38],uric wh acido recognized for this strongly the presence birefringent of absorption substance bands follows characterizing the original the determinations of Caveney [38], who recognized the presence of absorption bands characterizing the

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Biomimetics 2018, 3, 30 7 of 20 UV spectrum of uric acid. Caveney’s slow extraction of uric acid, accompanied by loss of the metallic reflectivity, when using 70% alcohol or with 1% ammonia, is consistent with a polar and acidic acid.substance Caveney’s (uric slowacid extractionpKa1 = 5.4). of uric There acid, are accompanied many reports by loss of the of the occurrence metallic reflectivity, of uric acid when in usinginsect 70%cuticles. alcohol For or example, with 1% it ammonia, is present is in consistent the white with stripes a polar of the and armyworm acidic substance Pseudaletia (uric acidseparata pKa1 [39] = 5.4and). Therein the arereflecting many reports cuticle ofof thetheoccurrence light organ of of uric fireflies acid in[40]. insect However, cuticles. exists Forexample, some controversy it is present with in theregard white to stripesCaveney’s of the chemical armyworm extractionPseudaletia experiments separata performed[39] and in in the the reflecting 1970s that cuticle may not of the support light organthis claim of fireflies [7,41]. [40 ]. However, exists some controversy with regard to Caveney’s chemical extraction experimentsInitially, performed Raman and in theFTIR-ATR 1970s that spectra may notwere support measured this claimdirectly [7 ,41from]. the elytra for both non- curedInitially, samples Raman obtained and FTIR-ATRfrom recently spectra captured were measured specimens directly and fromcured the samples elytra forfrom both a non-curedcollection. samplesCured samples obtained showed from recentlya reduced captured Raman specimenssignal by a andfactor cured of 10 samples with respect from to a collection.the fresh samples. Cured samplesIn addition, showed the aspectra reduced showed Raman a signal broadening by a factor and of changes 10 with in respect position to the of freshthe vibration samples. modes. In addition, The theFTIR-ATR spectra spectra showed showed a broadening significant and differences changes in in position water content of the (structural vibration modes.water embedded The FTIR-ATR on the spectrachitin arrangement) showed significant and degradation differences of in organic water contentcompounds. (structural To minimize water embedded those effects, on thethe chitinelytra arrangement)upper surface andof eight degradation non-cured of organicspecimens compounds. was carefully To minimizescraped with those a effects,steel blade the elytrato produce upper a surfacefine micron-sized of eight non-cured powder like specimens that shown was in carefullythe insets scraped of Figure with 5A. aThe steel two blade reference to produce samples a were fine micron-sizedmeasured; chitin powder powder like (red that line) shown can inbe the easily insets dist ofinguished Figure5A. from The that two of reference the uric acid samples (blue were line), measured;as shown in chitin Figure powder 5B. The (red chitin line) and can uric be easily acid distinguishedpowder standards from used that ofare the in uricexcellent acid (blueagreement line), aswith shown previously in Figure reported5B. The studies chitin [42,43]. and uric Figure acid powder5A shows standards two spectra used measured are in excellent from the agreement powder of withC. optima previously cuticlereported (PCOC); studiesthe sample [42,43 obtained]. Figure from5A shows eight twoelytra spectra specimens measured presented from thetwo powder distinct ofparticulates:C. optima cuticle (i) a white (PCOC); powder the sample(lower-right obtained inset from in Figure eight elytra5A) that specimens resembles presented chitin powder two distinct (inset particulates:in Figure 5B); (i) aand white (ii) powder a colored (lower-right particulate inset (upper-left in Figure5 A)inset that in resembles Figure 5A) chitin that powder appears (inset more in Figurecrystalline5B); andthan (ii) the a other colored agglom particulateerates (upper-leftjudging from inset the in narrow Figure 5bandsA) that and appears strong more signal crystalline measured thanin comparison the other agglomerates with the white judging crysta fromls. There the narrowis a distribution bands and of strong these signaltypes of measured crystals inobtained comparison from withthe elytra the white cuticle crystals. as reported There isin a [38]. distribution Figure 5 of shows these typesthe Raman of crystals bands obtained for thefrom PCOC the sample elytra cuticleat 497 as(501) reportedc, 630 (624) in [38ac,]. 999 Figure (897)5 cshows, 1002 the(998) Ramanac, 1043 bands (1060) forc, 1045 the PCOC(1037)ac sample, 1113 (1108) at 497c, (501) 1338c ,(1236) 630 (624)c, 1384ac, 999(1376) (897)c, 1429c, 1002 (1406) (998)acac, 1607, 1043 (1596) (1060)acc ,and 1045 1648 (1037) (1650)ac, 1113ac (in (1108) parenthesis,c, 1338 (1236) the positionc, 1384 (1376) of thec, chitin 1429 (1406) (c) andac, 1607uric acid (1596) (ac)ac and standards; 1648 (1650) all dataac (in in parenthesis, relative units the of position cm−1). The of the band chitin spectra (c) and are uric a close acid match (ac) standards; for those allof datathe uric in relative acid standard; units of cmnonetheless,−1). The band many spectra of these are vibration a close match modes for are those also of present the uric in acid many standard; other nonetheless,ring compounds many [42]. of these vibration modes are also present in many other ring compounds [42].

FigureFigure 5. SpectralSpectral dependence dependence of ofthe the Raman Raman scattering scattering intensity. intensity. (A) Raman (A) Raman spectra spectra of white of (lower- white (lower-rightright inset) and inset) colored and colored(upper-left (upper-left inset) powd inset)ers powders obtained obtained by scraping by scrapingof the cuticles of the of cuticles C. optima of C.specimens. optima specimens. (B) A reference (B) A reference spectrum spectrum of uric acid of uric is sh acidown is showntogether together with the with spectrum the spectrum of chitin of chitinpowder powder obtained obtained from shrimp from shrimp shells shells(inset). (inset). a.u.: Arbitrary a.u.: Arbitrary units. units.

Because the PCOC sample contains at least one known component, chitin, and an unknown Because the PCOC sample contains at least one known component, chitin, and an unknown number of other organic compounds, it was not possible to obtain an exact matching of the vibration number of other organic compounds, it was not possible to obtain an exact matching of the vibration modes with respect to the standards. Moreover, an exact reconstruction of the spectra from the modes with respect to the standards. Moreover, an exact reconstruction of the spectra from the standards is not possible due to the lack of information regarding the nature of the environment in

Biomimetics 2018, 3, 30 8 of 20 Biomimetics 2018, 3, x FOR PEER REVIEW 8 of 20 whichstandards the moleculesis not possible are embedded. due to the Thelack positionof inform ofation the vibrationregarding modes the nature may varyof the depending environment on the in whichchemical the environment molecules are and embedded. composition The ofposition the samples. of the Fromvibration the Ramanmodes may analysis, vary wedepending concluded on thatthe chemicalit is likely environment that PCOC may and containcomposition a uric of acid-type the sample compounds. From the and, Raman thus, analysis, we will we use concluded the term “uric that itacid” is likely to refer that to PCOC it. may contain a uric acid-type compound and, thus, we will use the term “uric acid”Additionally, to refer to it. absorbance measurements were performed by FTIR-ATR. Figure6A shows the measuredAdditionally, infrared absorbance absorbance measurements spectrum of the were two standards,performed uricby FTIR-ATR. acid and chitin; Figure both 6A coincideshows the in measuredtheir spectral infrared details absorbance with those spectrum reported inof thethe literaturetwo standards, [44,45 ].uric For acid wavenumbers and chitin; betweenboth coincide 500 and in 1800their cmspectral−1, both details display with absorption those reported peaks in with the overlapping literature [44,45]. spectral For positions. wavenumbers From 1800 between to 2800 500 cm and−1, −1 −1 1800the light cm absorption, both display by chitin absorption is negligible peaks [with46],with overlapping a decreasing spectral absorption positions. tail From approaching 1800 to 28002800 cmcm−1,. theThe light full spectrum absorption of theby PCOCchitin measuredis negligible under [46], the with same a decreasing conditions isabsorption also shown. tail At approaching≈3000 cm−1 ,2800 uric −1 cmacid. presents The full a spectrum stretching of vibration the PCOC mode measured for the N–H unde bondr the [ 47same] that conditions it is not present is also in shown. chitin. ThereAt ≈3000 are −1 cmno vibration, uric acid modes presents of chitin a stretching at this spectral vibration position, modeand for the perpendicularN–H bond [47] stretching that it isvibration not present mode in chitin.for the N–HThere bond are isno reported vibration in themodes vicinity of chitin of 3264 at cm this−1 [spectral44,47], as position, indicated and in Figure the perpendicular6A. Figure6B −1 stretchingshows the vibration absorption mode spectra for of the the N–H uric acidbond standard, is reported chitin in powderthe vicinity standard, of 3264 the cm PCOC [44,47], sample as indicatedand three in different Figure homogeneous6A. Figure 6B mixtures shows the of uricabsorp acidtion and spectra chitin of (standards) the uric acid for volumestandard, fractions chitin powderof uric acid standard, of 0.500, the 0.250 PCOC and sample 0.125. Inand the three range different 2400–3600 homogeneous cm−1, the absorbance mixtures of contributions uric acid and of chitinuric acid (standards) and the naturalfor volume polymer fractions can of be uric distinguished. acid of 0.500, At 0.250≈3000 and cm 0.125.−1, the In chitinthe range standard 2400–3600 does −1 cmnot present, the absorbance a vibration contributions mode different of uric from acid the and pure the uric natural acid, aspolymer shown can in Figure be distinguished.6B. The PCOC At −1 ≈sample3000 cm shows,, the chitin in the standard vicinity of does 3000 not cm present−1, a strong a vibrat absorbanceion mode thatdifferent resembles from thethe convolutionpure uric acid, of −1 aschitin shown and in uric Figure acid. 6B. The The additional PCOC sample measurements shows, in the infraredvicinity of strongly 3000 cm suggest, a strong the presence absorbance of a thaturic acid-typeresembles compound, the convolution in agreement of chitin with andthe uric Raman acid. The spectra. additional Without measurements a careful chemical in the extraction, infrared stronglyit is not possible suggest tothe confirm presence that of the a uric compound acid-typ ise purecompound, uric acid. in However,agreement from with the the vibration Raman spectra. spectra Withoutpresented, a careful it is possible chemical to conclude extraction, that it theis not compound possible isto aconfirm ring compound that the compound very closely is associated pure uric withacid. uricHowever, acid. from the vibration spectra presented, it is possible to conclude that the compound is a ring compound very closely associated with uric acid.

Figure 6. SpectralSpectral dependence dependence of of the the infrared infrared absorb absorbanceance by by chitin, chitin, uric uric acid, acid, and and powder powder from from C. optimaC. optima cuticle.cuticle. (A ()A Infrared) Infrared absorption absorption of ofsamples samples of of chitin chitin powder, powder, uric uric acid acid and and powder powder from from the cuticle of a CC.. optima specimen (PCOP). ( (B)) Infrared Infrared absorbance absorbance within within a a smaller smaller wavenumber wavenumber range, range,

including the absorption of chitin samples containing differentdifferent volumevolume fractionsfractions ofof uricuric acidacid ((FFuaua).). A key point of this discussion is the birefringence nature of the compound associated with the A key point of this discussion is the birefringence nature of the compound associated with the metallic-like structural color of these beetles [30–35], which should be deposited within the chitin metallic-like structural color of these beetles [30–35], which should be deposited within the chitin structure. There are many reports of doping or functionalized uric acid [48–52], but not all of them structure. There are many reports of doping or functionalized uric acid [48–52], but not all of them present a birefringence [48]. The chemical extraction of the PCOC sample was attempted by using the present a birefringence [48]. The chemical extraction of the PCOC sample was attempted by using method suggested by Caveney [38]. The method was shown to be an extremely slow reaction, and the method suggested by Caveney [38]. The method was shown to be an extremely slow reaction, limitations were found regarding a sufficient amount of mass to perform a nuclear magnetic resonance and limitations were found regarding a sufficient amount of mass to perform a nuclear magnetic (NMR) analysis. This will be a subject of future investigations, in the case that a sufficient amount resonance (NMR) analysis. This will be a subject of future investigations, in the case that a sufficient amount of sample is produced for analysis. By using the absorbance values at 3000 cm−1 and by

Biomimetics 2018, 3, 30 9 of 20 of sample is produced for analysis. By using the absorbance values at 3000 cm−1 and by assuming that the uric acid-type compound has a mass density equal to the pure uric acid, we calculated the average volume fraction for the cuticle of a C. optima specimen by linear regression as Fua ± ∆Fua = 0.17 ± 0.01. We neglected any other source of error in this estimation, because of the difficulty of assessing this in terms of statistical methods; that is, the limitations in the preparation of more samples for comparison due to the lack of specimens. This value will be used in the context of Berreman’s formalism [53] to evaluate the average values of the ordinary and extraordinary refractive indices of the structure, as well as its effective birefringence. It is important to mention that the PCOC was taken from non-cured samples obtained from recently captured specimens, and the amount of water present inside the structure is evident because of the increase in the absorbance at the end of the spectral range (Figure6B). Furthermore, the use of the calculated volume fraction ( Fua = 0.17) on the calculation of the reflection spectrum allows us to obtain a good fitting with the measured one (see Figure2C and Figure 13A). This fact can be used to assess the quality of the method followed to determine the volume fraction of uric acid. The only drawback of this method is the difficulty in obtaining sufficient “fresh” samples for other species.

3.4. Modeling Synthetic Reflection Spectra with Berreman’s Formalism Regarding the modeling of photometric measurements, Berreman’s formalism is suitable to describe the propagation of electromagnetic radiation through uniaxial anisotropic media [53]. In this approach, a plane parallel anisotropic structure, whose thickness is H, is divided into successive thin layers, each one of thickness h. The h-value is set small enough to ensure numerical convergence in the reflection spectra: H = Nh, with N the number of thin layers. The continuous tangential components of the electric and magnetic fields at successive interfaces of these thin layers are related through the layer transfer-matrix P = exp(−iko∆h), where ko = 2π/λ is the wavenumber of the incident radiation, λ its wavelength and with the elements of Berreman’s propagation ∆ matrix depending on the angle of incidence (ϕ), the refractive index of the medium covering the structure (nc), the refractive index of the substrate beneath the chiral structure (ns), the chirality of the helical arrangement (γ), the extraordinary 2 and ordinary refractive indices (ne and no, respectively) or the respective dielectric functions (εe = ne 2 and εo = no ), as given elsewhere [35]. The birefringence is given by ∆n = ne − no and the average refractive index is nav = (ne + no)/2. The ∆ matrix also depends on the angle φ specifying the orientation of the polarizable units: cholesteric macromolecules or chitin nanofibrils, for instance. This angle depends on the pitch P through the relation φ = 2πz/P, where P can be a constant (P = Po) or dependent on z, the depth through the twisted arrangement measured from its illuminated interface (P = P(z)). Our computational implementation of this approach follows the formulation of Wöhler et al. [54] to evaluate the layer transfer-matrices and that of Brink et al. [19] to compute the co- and cross-polarized complex amplitude reflection coefficients for circularly polarized light [55]: rLL and rRR, and rLR 2 2 and rRL, respectively; and the corresponding reflections: RLL = |rLL| , RRR = |rRR|, RLR = |rLR| 2 and RRL = |rRL| . Under non-polarized incident radiation, the total reflection RT is calculated as follows: RT = (RLL + RLR)/2 + (RRL + RRR)/2. This means that when doing the measurements and the calculations, there are no polarizers between the reflecting surface and the objective of the sensor receiving the reflected light. In the Wöhler approach, successive layer transfer-matrices are evaluated from the eigenvalues of Berreman’s propagation ∆ matrix. We will apply Berreman’s formalism following a gradual procedure, in terms of how the pitch depends on depth through the cuticle, going from the simplest case to those found in nature. In this regard, our results can be compared with the literature on synthetic structures. On the other hand, this approach allows us to show the correlation of some of the optical, structural and PC properties with features of the reflection spectra. First, we consider the evaluation of the reflection spectrum of a single-pitch cholesteric right-handed liquid crystal (γ = 1) with the following specification: Po = 330 nm, H = 16Po, ∆n = 0.40 and no = 1.5 (ne = no + ∆n). The sample is normally illuminated (ϕ = 0) with non-polarized radiation, and Biomimetics 2018, 3, 30 10 of 20

Biomimeticsthe calculated 2018, 3 total, x FOR reflection PEER REVIEW spectrum is shown in Figure7A. This system, with a high birefringence,10 of 20 has been considered by Hong et al. [56] with their calculations performed by Berreman’s formalism, Figureas well 4 asin a[56]) finite is provided, element method. with coincidence A very goodin the agreementnumber of ofpeaks our and results their with amplitudes those reported at both sides(see Figure of the 4reflection in [56]) is band. provided, The withoptical coincidence band gap inis thecentered number at ofλo peaks= navPo and = 560 their nm, amplitudes with nav = at1.70 both as o thesides average of the reflectionrefractiveband. index Theand optical bandwidth band of gap Δλ is = centered ΔnP = 132 at λ nm.o = navPo = 560 nm, with nav = 1.70 as the average refractive index and bandwidth of ∆λ = ∆nPo = 132 nm.

Figure 7. ReflectionReflection byby chiral chiral structures structures when when normally normally illuminated illuminated with with non-polarized non-polarized light. light. (A) Total (A)

Totalreflection reflection spectrum spectrum of a cholesteric of a cholesteric liquid crystal liquid withcrystal the with following the following specification: specification:Po = 330 nm, Po =H 330=16 nm,Po,

H∆n = =16 0.40Po, Δ andn = n0.40o = 1.5and [56 no]. = ( B1.5) Reflection[56]. (B) Reflection spectrum spectrum of a linearly of gradeda linearly left-handed graded left-handed twisted cholesteric twisted cholestericliquid crystal, liquid whose crystal, pitch whose is given pitch by is Pgiven(z) = byPm P(1(z) + =az/H Pm (1) with+ az/Ha) =with 0.458, a = H0.458,= 24 HPm =, 24PmPm=, P 240m = nm,240

nm,∆n = Δ 0.40,n = 0.40, and andno = n 1.5.o = 1.5. Normal Normal illumination illumination of non-polarized of non-polarized radiation radiation is assumed. is assumed. For wavelengths within the optical band gap, 50% of the incident radiation is reflected as For wavelengths within the optical band gap, 50% of the incident radiation is reflected as right- right-handed circularly polarized light. The larger the birefringence, the higher the top of the reflection handed circularly polarized light. The larger the birefringence, the higher the top of the reflection band, which approaches 50%, and the wider its width (see Figure 3 in [57]). Our second example band, which approaches 50%, and the wider its width (see Figure 3 in [57]). Our second example corresponds to a linearly graded left-handed pitch (γ = −1) given by P(z) = Pm (1 + az/H), with Pm corresponds to a linearly graded left-handed pitch (γ = −1) given by P(z) = Pm (1 + az/H), with Pm as as the minimum value of the pitch, a = (PM − Pm)/Pm = ∆P/Pm, where PM is the maximum value of the minimum value of the pitch, a = (PM − Pm)/Pm = ΔP/Pm, where PM is the maximum value of the pitch the pitch (chirped structure). The following values are assumed: Pm = 240 nm, PM = 350 nm, a = 0.458, (chirped structure). The following values are assumed: Pm = 240 nm, PM = 350 nm, a = 0.458, H = 24Pm, H = 24Pm, ∆n = 0.4 and no = 1.60. By assuming normally non-polarized incident radiation, Figure7B Δn = 0.4 and no = 1.60. By assuming normally non-polarized incident radiation, Figure 7B shows the shows the calculated broad band total reflection spectrum. This is in agreement with the spectrum calculated broad band total reflection spectrum. This is in agreement with the spectrum shown in shown in Figure 6 in [56], which was calculated for a right-handed helical arrangement. The graded Figure 6 in [56], which was calculated for a right-handed helical arrangement. The graded pitch pitch widens the reflection band. Both reflection spectra, the reported and the calculated, must coincide widens the reflection band. Both reflection spectra, the reported and the calculated, must coincide for for non-polarized incident light, although their circular polarizations correspond to those of the chiral non-polarized incident light, although their circular polarizations correspond to those of the chiral structures. The values of λo and ∆λ indicated in the figure were calculated as explained below, in the structures. The values of λo and Δλ indicated in the figure were calculated as explained below, in the context of the PC characterization of the helicoidal stack. context of the PC characterization of the helicoidal stack. 3.5. Photonic Crystal Characterization of Twisted Structures with Graded Pitches 3.5. Photonic Crystal Characterization of Twisted Structures with Graded Pitches In this section, the link between Berreman’s formalism and a PC characterization of the twisted In this section, the link between Berreman’s formalism and a PC characterization of the twisted structure is introduced by considering two chiral arrangements with assumed depth dependences of structure is introduced by considering two chiral arrangements with assumed depth dependences of the pitches. A chiral twisted structure behaves like one-dimensional PC for that incident light whose the pitches. A chiral twisted structure behaves like one-dimensional PC for that incident light whose circular polarization coincides with the chirality of the arrangement. At least for sufficiently thick circular polarization coincides with the chirality of the arrangement. At least for sufficiently thick structures, no photons with this chirality will be transmitted through the arrangement, for energies structures, no photons with this chirality will be transmitted through the arrangement, for energies within the spectral location of the reflection band. As we have reported in previous works [31,33], within the spectral location of the reflection band. As we have reported in previous works [31,33], when the pitch depends on the depth z through the arrangement, the spectral position of the PBG also when the pitch depends on the depth z through the arrangement, the spectral position of the PBG depends on depth, i.e., both the spectral limits of the local band gap λ − = λ −(z) and λ + = λ +(z) also depends on depth, i.e., both the spectral limits of the local band gap λλ−−= ()z and depend on z. This fact explains why the reflection band is significantly broader than the PBG. For a λλ= linearly + + () gradedz depend pitch, on applicationz. This fact explains of the formalism why the reflection devised in band [34,35 is ],significantly with the dispersion broader than relation the PBG. For a linearly graded pitch, application of the formalism devised in [34,35], with the dispersion relation obtained from Hemholtz’s wave equation satisfied by the two orthogonal left- and right- handed circularly polarized components of the propagating electric field, gives for the spectral limits of the PBG:

Biomimetics 2018, 3, 30 11 of 20 obtained from Hemholtz’s wave equation satisfied by the two orthogonal left- and right-handed circularly polarized components of the propagating electric field, gives for the spectral limits of the PBG: √ √ 2 ε 2 1 − K λ ±(z) = [P(z)] p , (1) Pm [1 ∓ 1 − (1 − K2)(1 + Γ)] 2 where ε = (εe + εo)/2, Γ = [P(z)∆P/πPm H] and K = (εe − εo)/(εe + εo). The z-dependent spectral position of the PBG is λo(z) = [λ+(z) + λ−(z)]/2, and its local width is ∆λ(z) = λ+(z) − λ−(z). The effective width of the reflection band is obtained from the minimum value of λ−(z) and the maximum of λ+(z), i.e., min[λ−(z)] ≡ λmin and max[λ+(z)] ≡ λmax. The center of the reflection band is at λo = (λmin + λmax)/2, and its effective width is ∆λ = λmax − λmin. For a helicoidal arrangement with a linearly graded pitch, the reflection band is characterized by the following limits: √ √ √ 2 √ 2 2 1 − K PM 1 − K λ = εPm , λmax = ε , (2) min p 2 p 2 [1 + 1 − (1 − K )(1 + Γm)] Pm [1 − 1 − (1 − K )(1 + ΓM)]

2 2 where ΓM = (∆PPM/πHPm) and Γm = (∆P/πH) . The pitch values are of the order of tenths of a micrometer, and the thickness of the structures is around a few tens of micrometers. As a consequence of this, Γm  1 and ΓM  1. The values of λmin and λmax can be approximated from the previous Equation (2) and the spectral position of the center of the reflection band, as well as its effective width becomes: 2 2 2 2 nePM + no Pm nePM − no Pm λo = , ∆λ = , (3) 2Pm Pm 2 with λmin = noPm and λmax = nePM /Pm. Equation (3) is the extended version of those equations valid for a single pitch structure (λo = navPo and ∆λ = ∆nPo, respectively), when considering chiral chirped arrangements. It is conceptually erroneous to apply the equations λo = navPo and ∆λ = ∆nPo when considering helical structures with graded pitches, as reported in [58], where λo was estimated from navPo to show that the depth-dependent pitch values obtained for the cuticle of silver-like C. chrysargyrea scarabs, based on the analysis of SEM images, are too small to justify the presence of a reflection band extending towards the NIR [35,58]. In these cases, the correct way to explain the effective width of the reflection band is by application of Equations (4)–(6) to obtain the minimum value of λ− and the maximum value of λ+ for a specific depth dependence of the pitch. Namely,

 z dP  Q(z) = q(z) 1 − , (4) P(z) dz q 2 2 4  ω± 2 1 1 ± 1 − (1 − K )(1 + Γ /Q ) ε = , (5) c Q2 1 − K2 " # q(z) 2z  dP 2  dP  d2P Γ = − 2 − z , (6) P(z) P(z) dz dz dz2 where q(z) = 2πγ/P(z), c is the speed of light in vacuum, and ω = 2πc/λ is the angular frequency of the incident radiation whose wavelength is λ, as described in [35]. When we apply Equation (3) to the linearly graded structure considered in Section 3.4, the following results are obtained: λo = 702.5 nm and ∆λ = 636.8 nm, in good agreement with the reflection spectrum shown in Figure7B. With no approximations, by application of Equation (1) or following the method reported in [35], the corresponding values are: λo = 702.0 nm and ∆λ = 634.0 nm. Figure8 shows the depth dependence of the local PBG ∆λ(z), its depth-dependent spectral limits λ+(z) and λ−(z) and its spectral position. Biomimetics 2018, 3, x FOR PEER REVIEW 12 of 20 characteristics, the parabolic section is calculated from P(z) = Pm + C (z − zo)2, with zo = αH (with α < 1) and C = ΔP/(αH)2 to ensure that P(z = 0) = PM. From z1 = μH (with α < μ < 1), a linear dependence holds: P(z) = A + B(z − zo) with B = 2C(z1 − zo) to match the slopes at z1 and A = Pm + C(z1 − zo)2 − B(z1 − zo) to ensure continuity of the P(z) function at z = z1.The following input values were used: Pm = 210 nm, PM = 350 nm, H = 18Pm, no = 1.60, Δn = 0.40. The values α = 0.5 and μ = 0.60 were assumed. Figure 9A shows the depth dependence of the pitch that we use to evaluate the spectral reflectance displayed in Figure 9B, which displays a broad structured reflection band from 282 to 918 nm. From Equation (1), with the application of Equations (4)–(6), the PC characterization depicted in Figure 10 is obtained. The visual silvery appearance of this hypothetical structure depends on Bragg reflection occurringBiomimetics 2018in layers, 3, 30 between a 0.5 and a 2.25 μm depth, as can be deduced from the analysis of the12 ofPC 20 behavior shown in Figure 10.

Biomimetics 2018, 3, x FOR PEER REVIEW 12 of 20 characteristics, the parabolic section is calculated from P(z) = Pm + C (z − zo)2, with zo = αH (with α < 1) and C = ΔP/(αH)2 to ensure that P(z = 0) = PM. From z1 = μH (with α < μ < 1), a linear dependence holds: P(z) = A + B(z − zo) with B = 2C(z1 − zo) to match the slopes at z1 and A = Pm + C(z1 − zo)2 − B(z1 − zo) to ensure continuity of the P(z) function at z = z1.The following input values were used: Pm = 210 nm, PM = 350 nm, H = 18Pm, no = 1.60, Δn = 0.40. The values α = 0.5 and μ = 0.60 were assumed. Figure 9A shows the depth dependence of the pitch that we use to evaluate the spectral reflectance displayed in Figure 9B, which displays a broad structured reflection band from 282 to 918 nm. From Equation (1), with the application of Equations (4)–(6), the PC characterization depicted in Figure 10 is obtained. The visual silvery appearance of this hypothetical structure depends on Bragg reflection occurring in layers between a 0.5 and a 2.25 μm depth, as can be deduced from the analysis of the PC behavior shown in Figure 10. FigureFigure 8. 8. DepthDepth dependence dependence of of the the photonic photonic band band gap gap ( (Δ∆λλ(z)), its spectral limits ((λ++(z) and λ−((zz)))) and and z centralcentral position position ( (λλoo((z)).)). The The spectral spectral limits limits of of the the reflection reflection band band ( (λλminmin andand λλmaxmax) are) are also also indicated. indicated.

The pitch in cuticles of some Chrysina scarab beetles has shown a predominantly quasi-parabolic

depth dependence with a linear behavior in the deeper helicoidal layers (see Figure 6A in [35]). The minimum value of the pitch corresponds to the vertex of the parabola, with the maximum value close to the illuminated surface of the structure. With the aim of generating a pitch with these 2 characteristics, the parabolic section is calculated from P(z) = Pm + C (z − zo) , with zo = αH (with α < 1) 2 and C = ∆P/(αH) to ensure that P(z = 0) = PM. From z1 = µH (with α < µ < 1), a linear dependence 2 holds: P(z) = A + B(z − zo) with B = 2C(z1 − zo) to match the slopes at z1 and A = Pm + C(z1 − zo) − B(z1 − zo) to ensure continuity of the P(z) function at z = z1.The following input values were used: Pm = 210 nm, PM = 350 nm, H = 18Pm, no = 1.60, ∆n = 0.40. The values α = 0.5 and µ = 0.60 were assumed. Figure9A shows the depth dependence of the pitch that we use to evaluate the spectral reflectance displayed in Figure9B, which displays a broad structured reflection band from 282 to 918 nm. From Equation (1), with the application of Equations (4)–(6), the PC characterization depicted in FigureFigure 10 8. is Depth obtained. dependence The visual of the silvery photonic appearance band gap ( ofΔλ this(z)), hypotheticalits spectral limits structure (λ+(z) and depends λ−(z)) onand Bragg reflectioncentral occurring position (λ ino(z layers)). The betweenspectral limits a 0.5 of and the a reflection 2.25 µm band depth, (λ asmin canand beλmax deduced) are also fromindicated. the analysis of the PC behavior shown in Figure 10.

Figure 9 Dependence of pitch on depth z and corresponding reflection spectrum of a chiral structure.

(A) Quasi-parabolic depth dependence of a helicoidal structure. Maximum (PM) and minimum (Pm) values of the pitches are indicated. (B) Reflection spectrum of the structure by assuming normally incident non-polarized light. The reflection band is centered at λo = 600 nm, and its width is Δλ = 636 nm.

Color coordinates, evaluated with the standard procedure established by the Commission Internationale de l’Éclairage (CIE), which is based on the use of the color-matching functions as commented elsewhere [32,59] and by assuming the AM1.5 solar spectrum (which corresponds to a

FigureFigure 9 9. DependenceDependence of of pitch pitch on on depth depth zz andand corresponding corresponding reflection reflection spectrum spectrum of of a a chiral chiral structure. structure.

((A)) Quasi-parabolic Quasi-parabolic depth depth dependence dependence of of a ahelicoidal helicoidal structure. structure. Maximum Maximum (PM) ( PandM) andminimum minimum (Pm) values(Pm) values of the ofpitches the pitches are indicated. are indicated. (B) Reflection (B) Reflection spectrum spectrum of the structure of the structureby assuming by assumingnormally incidentnormally non-polarized incident non-polarized light. The light.reflection The reflectionband is centered band is at centered λo = 600 at nm,λo = and 600 its nm, width and is its Δ widthλ = 636 is nm.∆λ = 636 nm.

Color coordinates, evaluated with the standard procedure established by the Commission Internationale de l’Éclairage (CIE), which is based on the use of the color-matching functions as commented elsewhere [32,59] and by assuming the AM1.5 solar spectrum (which corresponds to a

Biomimetics 2018, 3, x FOR PEER REVIEW 13 of 20 solar zenith angle of 48.2°), are x = 0.337 and y = 0.335 with a luminous reflection Y = 42.2. The corresponding RGB values are: R = 190, G = 169, and B = 164. The deeper layers contribute to the NIR reflection. The reflection band displays a ripple structure for wavelengths between 370 and 620 nm, which is produced by Bragg reflections at two ranges of depth: from the top of the structure to 0.8 μm of depth and from ≈1.9 to 2.6 μm of depth. For depths between ≈0.8 and 1.9 μm, the PBG is in the ultraviolet range, being responsible for the shoulder or narrow reflection band spectrally located between the reflection edge and the beginning of the ripple structure. The presence of this shoulder is determined by Bragg reflections at layers close to a 1.4 μm depth, where there is a range of depths with quasi-constant PBG. The presence of the ripple structure is determined by enhanced Bragg reflection due to a graded pitch with a parabolic or quasi-parabolic dependence on depth through

Biomimeticssome extended2018, 3, 30section of the elytron. Chiral chirped arrangements do not display any 13ripple of 20 structure in their reflection spectra.

Figure 10. Variation withwith depthdepth through thethe cuticlecuticle ofof thethe locallocal photonicphotonic band gap ( Δ∆λ(z)) and of its limits (λ+((zz)) and and λ−(z()).z)). The The effective effective values values of of the the central central position position of of the the band band and and its its width are

indicated as λo andand Δ∆λλ..

3.6. OpticalColor Characterization coordinates, evaluated of the Cuticle with of theC. chrysargyrea standard procedure Scarabs established by the Commission Internationale de l’Éclairage (CIE), which is based on the use of the color-matching functions as commentedThis section elsewhere is focused [32,59 ]on and modeling by assuming the reflection the AM1.5 spectra solar spectrum by the elytra (which of correspondsboth the golden- to a solar and zenithsilver-like angle C. of chrysargyrea 48.2◦), are x =beetles. 0.337 and They = correlation 0.335 with a between luminous optical reflection propertiesY = 42.2. Theand corresponding the cuticle’s RGBmorphology values are: has Rbeen = 190, investigated G = 169, and during B = 164. the Thelast deeperfew years layers by contributeseveral research to the NIRgroups, reflection. involving samplesThe taken reflection from band beetles displays of the aChrysina ripple structure genus. For for example, wavelengths the optical between properties 370 and620 of seven nm, which species is producedof scarab beetles by Bragg (C reflections. macropus, atC. two peruviana ranges, ofC. depth:argenteola from, C. the resplendens top of the, C. structure woodii, toC. 0.8gloriosa,µm of and depth C. andchrysargyrea from ≈1.9) have to 2.6 beenµm ofconsidered depth. For through depths betweenellipsomet≈ry0.8 measurements and 1.9 µm, the [21]. PBG Our is in main the ultraviolet purpose range,when modeling being responsible the reflection for the spectra shoulder will be or to narrow reproduce reflection the main band spectral spectrally features located displayed between in the reflectionoptical measurements edge and the beginningperformed of thewith ripple normally structure. incident Thepresence non-polarized of this shoulderradiation. is determinedAccording byto BraggEquation reflections (1), λmin atis layersproportional close to to a 1.4Pm. µThemdepth, minimum where value there of isthe a rangepitch is of correlated depths with with quasi-constant the spectral PBG.position The of presence the reflection of the edge. ripple When structure using is Berreman’s determined formalism by enhanced to calculate Bragg reflection reflection due spectra, to a graded with pitchγ = −1, with the aspectral parabolic positions or quasi-parabolic of the reflection dependence edge at on short depth wavelengths through some and extended of the main section reflection of the elytron.peaks are Chiral numerically chirped sensitive arrangements to the angle do not of display inclination any ( rippleβ). Moreover, structure this in theirangle reflection modifies the spectra. depth dependence of the pitch from apparent to real values through the relation P(z) → P(z)/cosβ [35]. In 3.6.this Opticalway, we Characterization optimized the ofthe β-value, Cuticle ofobtaining C. chrysargyrea 26° and Scarabs 20° for the golden and the silvery C. chrysargyrea, respectively. With these β-values, the thicknesses of the twisted structures are 12.7 and This section is focused on modeling the reflection spectra by the elytra of both the golden- 11.6 μm for the golden and silvery scarabs, respectively. The corresponding number of pitches is the and silver-like C. chrysargyrea beetles. The correlation between optical properties and the cuticle’s same for both chiral structures, i.e., 29. The use by Finlayson et al. of a scaled depth-dependent pitch morphology has been investigated during the last few years by several research groups, involving in their simulations of the co- and cross-polarized light reflections by the cuticle of a C. resplendens samples taken from beetles of the Chrysina genus. For example, the optical properties of seven species scarab can be alternatively interpreted as an implicit geometrical correction through a β-angle close of scarab beetles (C. macropus, C. peruviana, C. argenteola, C. resplendens, C. woodii, C. gloriosa, and to 25° [28]. Application of Berreman’s method required the optical constants of chitin and uric acid C. chrysargyrea) have been considered through ellipsometry measurements [21]. Our main purpose when modeling the reflection spectra will be to reproduce the main spectral features displayed in the optical measurements performed with normally incident non-polarized radiation. According to Equation (1), λmin is proportional to Pm. The minimum value of the pitch is correlated with the spectral position of the reflection edge. When using Berreman’s formalism to calculate reflection spectra, with γ = −1, the spectral positions of the reflection edge at short wavelengths and of the main reflection peaks are numerically sensitive to the angle of inclination (β). Moreover, this angle modifies the depth dependence of the pitch from apparent to real values through the relation P(z) → P(z)/cosβ [35]. In this way, we optimized the β-value, obtaining 26◦ and 20◦ for the golden and the silvery C. chrysargyrea, respectively. With these β-values, the thicknesses of the twisted structures are 12.7 and 11.6 µm for the golden and silvery scarabs, respectively. The corresponding number of pitches is the same for both chiral structures, i.e., 29. The use by Finlayson et al. of a scaled Biomimetics 2018, 3, 30 14 of 20

depth-dependentBiomimetics 2018, 3, x FOR pitch PEER in REVIEW their simulations of the co- and cross-polarized light reflections by14 of the 20 cuticle of a C. resplendens scarab can be alternatively interpreted as an implicit geometrical correction ◦ through[60,61], incorporating a β-angle close their to 25 wavelength[28]. Application dependence. of Berreman’s For the substrate method of required the chiral the structure, optical constants we have ofassumed chitin andns = n uricav. An acid optically [60,61 ],homogenous incorporating layer their of wax wavelength covers the dependence. structures whose For the refractive substrate index of thenc is chiral calculated structure, from we the have model assumed reportedns in= n[62].av. AnThe optically calculations homogenous were performed layer of with wax N covers = 3 × the104. structuresThe optimized whose volume refractive fractions index ofnc uricis calculated acid are the from same the modelfor both reported scarabs: in F [ua62 =]. 0.40, The to calculations obtain, as 4 weremuch performed as possible, with similarN = 3relative× 10 . heights The optimized of the main volume reflection fractions peaks of uric to acidthose are measured. the same The for bothbirefringence scarabs: Fofua chitin= 0.40, is tosmall obtain, (Δn asc = much0.035 [63]) as possible, as compared similar with relative the birefringence heights of the of main uric reflectionacid (Δnua peaks= 0.31 to[50]). those The measured. heights of The the birefringence peaks in the of ca chitinlculated is small reflection (∆nc =spectra 0.035 [are63]) determined as compared by with the theeffective birefringence birefringence. of uric The acid presence (∆nua = 0.31of flattened [50]). The sh heightsoulders ofor theplateaus peaks in in the the reflections’ calculated reflectionspectra is spectraan indication are determined of high effective by the effectivebirefringence birefringence. values. We The use presence this fact of to flattened optimize shoulders the volume or plateaus fraction inof theuric reflections’ acid, to approach, spectra isas anmuch indication as possible, of high the effectivemain spectral birefringence features values.displayed We in use the this measured fact to optimizereflection the spectra. volume The fraction calculated of uric total acid, reflect to approach,ion spectra as much are asshown possible, in Figure the main 11 spectral for the features two C. displayedchrysargyrea in scarabs, the measured which were reflection considered spectra. in a The previous calculated study total [35]. reflectionOnly β and spectra Fua are used are shown as fitting in Figureparameters. 11 for Here, the two we C.report chrysargyrea a better scarabs,fitting of whichthe reflection were considered spectra, particularly in a previous that study of the [ 35silvery]. Only C. βchrysargyreaand Fua are at used short as wavelengths, fitting parameters. as well Here, as the we PC report characterizations, a better fitting which of the were reflection not included spectra, particularlypreviously. thatThe ofprimary the silvery reflectionC. chrysargyrea by the waxyat short coating wavelengths, of the cuticle, as well which as the is PC around characterizations, 3% at short whichvisible were wavelengths, not included was previously. not included The in primary the di reflectionsplayed calculated by the waxy reflection coating ofspectra. the cuticle, Comparing which isFigure around 11A,B 3% atwith short the visible corresponding wavelengths, experiment was notal included measurements in the displayed reported calculatedin Figure reflection2A,B, we spectra.observed Comparing some similarities Figure in11 A,Bthe spectra with the with corresponding respect to the experimental main features: measurements spectral position reported of the in Figurefirst reflection2A,B, we peak observed or shoulder, some similarities ripple structure in the or spectra plateau with around respect theto middle the main of the features: reflection spectral band, positionand decreasing of the first values reflection when approaching peak or shoulder, the NIR. ripple Figure structure 11 shows or plateau the width around of the the reflection middle of band the reflection(Δλ) centered band, at and λo, decreasingwhose values values were when calculated approaching as explain the NIR.ed in FigureSection 11 3.5. shows Figure the 12 width shows of thethe reflectionbehaviors band with ( ∆depthλ) centered through at λtheo, whosecuticle valuesof the werelocal calculatedPBGs (Δλ( asz)), explained of its limit in Section(λ−(z) and 3.5 .λ Figure+(z)), and 12 showsthe limits the of behaviors the effective with width depth of through the reflection the cuticle bands of ( theλmin local and λ PBGsmax). From (∆λ(z Figure)), of its 12A, limit we (λ conclude−(z) and λthat+(z )),the and visual the limitsgolden of appearance the effective of width the C. of chrysargyrea the reflection is bands due to (λ Braggmin and reflectionsλmax). From at layers Figure of 12 theA, wecuticle conclude whose that depths the visualare between golden 1.7 appearance and 8.0 μm: of the the yellowC. chrysargyrea contributionis due is produced to Bragg by reflections reflections at layersat depths of the between cuticle 2.5 whose and depths7.0 μm, are and between the red 1.7component and 8.0 µ arisesm: the fr yellowom reflections contribution between is produced 1.7 and 2.5 by reflectionsμm, and 7.0 at and depths 8.0 μ betweenm. The layers 2.5 and located 7.0 µm, close and to the the red surface, component up to arises1.7 μm, from and reflections those from between 8.0 μm 1.7to the and bottom 2.5 µm, of and the 7.0structure and 8.0 areµm. responsible The layers for located the NIR close reflection. to thesurface, up to 1.7 µm, and those from 8.0 µm to the bottom of the structure are responsible for the NIR reflection.

FigureFigure 11.11. CalculatedCalculated total total reflection reflection spectra spectra ofof cuticles cuticles of of(A ()A golden-like) golden-like C. chrysargyreaC. chrysargyrea andand (B) (silver-likeB) silver-like C. chrysargyreaC. chrysargyrea illuminatedilluminated with non-polarized with non-polarized normally normally incident incident light. NIR: light. Near NIR: infrared; Near infrared;UV: Ultraviolet. UV: Ultraviolet.

Biomimetics 2018, 3, 30 15 of 20 Biomimetics 2018, 3, x FOR PEER REVIEW 15 of 20

FigureFigure 12. Variation 12. Variation with depth with depththrough through the cuticle the cuticleof the local of the photonic local photonic band gap band (Δλ( gapz)) and (∆λ of(z ))its and limits of (λ+(z)its and limits λ−(z), (λ solid+(z) andblueλ lines),−(z), solid for the blue two lines), photonic for the crysta twols photonic considered crystals and correlated considered with and the correlated cuticles of (A)with golden the C. cuticles chrysargyrea of (A) goldenand (B)C. silvery chrysargyrea C. chrysargyreaand (B) silveryscarabsC. whose chrysargyrea calculatedscarabs reflection whose spectra calculated are displayedreflection in Figure spectra 11. are The displayed red line indicates in Figure th11e. Thecentral red position line indicates of the the photonic central band position gap, of λ theo. NIR: photonic Near infrared;band UV: gap, Ultraviolet.λo. NIR: Near infrared; UV: Ultraviolet.

The reflection reflection spectrum shows that the the UV, UV, violet, blue, bluish and and green green light light are are not not reflected. reflected. This fact agrees with the information provided by the PC diagram in Figure 12A,12A, where the minimum λ of the effective reflectionreflection bandband ((λminmin = 513 513 nm) nm) is is above above the mentioned spectral range. Regarding the silver-like C. chrysargyrea, there is a small fraction of UV light reflectedreflected by superficialsuperficial layers, and all visible tonestones areare reflectedreflected withwith the the bluish bluish colors colors emerging emerging from from layers layers beginning beginning with with the the surface surface up up to 1.5to 1.5µm μm (see (see Figure Figure 12 12B).B). The The green green and and yellow yellow colors colors are are due due to to Bragg Bragg reflectionsreflections inin layerslayers between 1.5 and 6.5 µμmm inin depth.depth. The next micrometer in depth produces the red contribution, and the NIR reflectedreflected light emerges from layers located from 7.5 to 11.5 µμm. Similar correlations, showing how to change thethe spectrum spectrum and and corresponding corresponding color color with with the number the number of pitches of contributingpitches contributing to the reflection, to the wasreflection, performed was performed for C. aurigans for C.scarabs aurigans [33 scarabs]. [33].

3.7. Optical Characterization of the Cuticle of C. optima Scarabs 3.7. Optical Characterization of the Cuticle of C. optima Scarabs The total reflection spectrum by the cuticle of a C. optima specimen has also been measured The total reflection spectrum by the cuticle of a C. optima specimen has also been measured for for normally incident non-polarized radiation (see Figure2C). Three main peaks are distinguished, normally incident non-polarized radiation (see Figure 2C). Three main peaks are distinguished, with with some superimposed irregular spectral structure. A similar spectrum, in the wavelength range some superimposed irregular spectral structure. A similar spectrum, in the wavelength range 450−1000 nm, has been previously reported [64]. The monotonous depth dependence of the pitch is not 450−1000 nm, has been previously reported [64]. The monotonous depth dependence of the pitch is incorporated in the modeling of the reflection spectrum by these authors. Using the depth-dependent not incorporated in the modeling of the reflection spectrum by these authors. Using the depth- pitch shown in Figure4C, the reflection spectrum of the chiral structure has been calculated, with β = 10◦ dependent pitch shown in Figure 4C, the reflection spectrum of the chiral structure has been and with the average volume fraction of uric acid previously estimated as described in Section 3.3 calculated, with β = 10° and with the average volume fraction of uric acid previously estimated as (Fua = 0.17). The thickness of the structure is H = 17.5 µm, and the number of pitches is 40.5. Figure 13A described in Section 3.3 (Fua = 0.17). The thickness of the structure is H = 17.5 μm, and the number of shows the main three reflection peaks, with two smaller peaks between those spectrally located in the pitches is 40.5. Figure 13A shows the main three reflection peaks, with two smaller peaks between visible range. The spectral positions of the main peaks and those of the measured ones match very well. those spectrally located in the visible range. The spectral positions of the main peaks and those of the The fraction of uric acid estimated from the infrared absorbance spectra leads to peak heights close to the measured ones match very well. The fraction of uric acid estimated from the infrared absorbance observed ones. The calculated spectrum was obtained by assuming a normal distribution in the depth spectra leads to peak heights close to the observed ones. The calculated spectrum was obtained by dependence of the pitch around the mean value displayed in Figure4C. The standard deviation was set assuming a normal distribution in the depth dependence of the pitch around the mean value to 5 nm, which is equal to the uncertainty in the determinations of z- and P(z)-values from SEM images. displayed in Figure 4C. The standard deviation was set to 5 nm, which is equal to the uncertainty in Thethe determinations relations between of heightsz- and ofP(z the)-values reflection from peaks SEM have images. been The improved relations in thebetween fitting byheights assuming of the a f C/P z pitchreflection dependence peaks have of the been uric improved acid volume in the fraction, fitting according by assuming to the a pitch assumed dependence relation uaof =the uric( ) withacid the average volume fraction given by Fua = C/Pav. Then, fua = FuaPav/P(z) with the average value of volume fraction, according to the assumed relation fua = C/P(z) with the average volume fraction given by Fua = C/Pav. Then, fua = FuaPav/P(z) with the average value of the pitch evaluated from Pav = (Pm + PM)/2cosβ with Pm = 250 nm and PM = 424 nm (see Figure 4C). The minimum value of fua is 0.14, close

Biomimetics 2018, 3, x FOR PEER REVIEW 16 of 20

to the back side of the structure, and the maximum value is 0.23, close to the illuminated surface. The mechanism involved in the incorporation of uric acid crystallites through the protein–chitin matrix of the chiral structure is basically unknown. The high birefringence required to approach the measured reflection spectra from modeling indicates that the orientation of the crystallites is not at random. The protein–chitin matrix is probably permeated by liquid uric acid, perhaps containing nanocrystals, being conducted throughout the submicron-sized pore canals distributed across the chiral structure and nearly perpendicular to the planes containing the oriented chitin nanofibrils. This uric acid could be conducted from each pore canal to the interstitial space between chitin nano-fibril, Biomimetics 2018, 3, 30 16 of 20 where it could grow to form oriented larger crystals. The larger the pitch of the structure is, the larger the available space between planes of chitin nanofibrils. This means that as the pitch increases with thedepth, pitch it evaluated would be from expectedPav = (toPm have+ PM larger)/2cos embeddedβ with Pm =uric 250 acid nm andcrystallites.PM = 424 Beyond nm (see a Figurecertain4 C).size, Thearound minimum 10 nm, value the oflargerfua is the 0.14, size close of tothe the crystallites back side, ofthe the larger structure, the amount and the of maximum space free value of uric is 0.23, acid, closei.e., tothe the space illuminated between surface.crystallites. The Consequently, mechanism involved the volume in the fraction incorporation of uric ofacid uric will acid decrease crystallites as the throughpitch of the the protein–chitin structure increases. matrix of It the is chiralbased structureon this analysis is basically that unknown. we assumed The highan inverse birefringence relation requiredbetween to the approach volume thefraction measured of uric reflection acid and spectrathe spatial from period modeling or pitch. indicates that the orientation of the crystallitesAccording to is the not PC at random.diagram in The Figure protein–chitin 13B, the reflection matrix is edge probably is displayed permeated at λmin by = liquid388 nm. uric The acid,PBG perhaps is displayed containing up to λ nanocrystals,max = 1209 nm, being as shown conducted in Figure throughout 13C, which the depicts submicron-sized the PC characterization pore canals distributedin the last acrossmicrometer the chiral of the structure twisted andstructure. nearly The perpendicular effective width to the of planes the reflection containing band the is orientedthen Δλ = chitin821 nm. nanofibrils. In this case, This a uricnovel acid feature could is beobserved: conducted the fromPBG eachdisappears pore canal for thicknesses to the interstitial between space 17.06 betweenand 17.17 chitin μm, nano-fibril, and for wavelengths where it could between grow λ tomax form= 1209 oriented and λmin,2 larger = 1270 crystals. nm. This The λ largermin,2 becomes the pitch the ofspectral the structure edge is,of thea secondary larger the PBG. available The spacefirst reflecti betweenon planespeak, labeled of chitin 1 nanofibrils.within the violet-blue This means colors that as(Figure the pitch 13B), increases is due withto the depth, locali itzed would quasi-parabolic be expected dependence to have larger of embeddedthe pitch through uric acid the crystallites. superficial Beyondlayers whose a certain depths size, are around from10 the nm, illuminated the larger surface the size up of to the 1.8 crystallites,μm in depth. the The larger second the peak, amount labeled of space2 and free with of a uric maximum acid, i.e., in thethe spaceyellowish between colors, crystallites. is associated Consequently, with the shoulder the volume displayed fraction in the of depth uric aciddependence will decrease of the as thepitch pitch for ofdepths the structure between increases. 3.0 and 5.5 It isμm. based The on broader this analysis structured that wepeak assumed in the NIR, an inverselabeled relation 3, is due between to the shoulder the volume of fractionthe pitch’s of uricdepth acid dependence and the spatial for z-values period orbetween pitch. 8 and 13 μm.

Figure 13. Reflection spectrum and photonic crystal characterization of the cuticle of the C. optima Figure 13. Reflection spectrum and photonic crystal characterization of the cuticle of the C. optima scarab. (A) Calculated total reflection spectra of the cuticles of C. optima illuminated with non-polarized scarab. (A) Calculated total reflection spectra of the cuticles of C. optima illuminated with non- normally incident light. (B) Variation with depth through the cuticle of the local photonic band polarized normally incident light. (B) Variation with depth through the cuticle of the local photonic gap (∆λ(z)) and its limits (λ+(z) and λ−(z)), for the photonic crystal correlated with the cuticle of band gap (Δλ(z)) and its limits (λ+(z) and λ−(z)), for the photonic crystal correlated with the cuticle of C. optima scarab. The limits of the reflection band, λmin and λmax, are also indicated. Labels 1, 2, and 3 C. optima scarab. The limits of the reflection band, λmin and λmax, are also indicated. Labels 1, 2, and 3 correlate the spectral positions of the reflection peaks with the local depth dependence of the pitch. correlate the spectral positions of the reflection peaks with the local depth dependence of the pitch. (C) Photonic crystal characterization in the last micrometer of the twisted structure. NIR: Near infrared; (C) Photonic crystal characterization in the last micrometer of the twisted structure. NIR: Near UV: Ultraviolet. infrared; UV: Ultraviolet.

According to the PC diagram in Figure 13B, the reflection edge is displayed at λmin = 388 nm. The PBG is displayed up to λmax = 1209 nm, as shown in Figure 13C, which depicts the PC characterization in the last micrometer of the twisted structure. The effective width of the reflection band is then ∆λ = 821 nm. In this case, a novel feature is observed: the PBG disappears for thicknesses between 17.06 and 17.17 µm, and for wavelengths between λmax = 1209 and λmin,2 = 1270 nm. This

λmin,2 becomes the spectral edge of a secondary PBG. The first reflection peak, labeled 1 within the violet-blue colors (Figure 13B), is due to the localized quasi-parabolic dependence of the pitch through the superficial layers whose depths are from the illuminated surface up to 1.8 µm in depth. The second peak, labeled 2 and with a maximum in the yellowish colors, is associated with the shoulder displayed in the depth dependence of the pitch for depths between 3.0 and 5.5 µm. The broader structured peak in the NIR, labeled 3, is due to the shoulder of the pitch’s depth dependence for z-values between 8 and 13 µm. Biomimetics 2018, 3, 30 17 of 20

4. Conclusions The optical properties of cuticles of Chrysina scarab beetles have been considered from spectrophotometric measurements and modeled with Berreman’s formalism, which incorporates the anisotropy in the optical constants of the materials: the natural polymer chitin nanofibrils and the uric acid high birefringent embedded crystals. In addition to the optical constants with their wavelength dependences, variations with depth of the pitches characterizing the chiral structures found through the cuticles have been provided to the model. This dependence has been obtained from analysis of SEM images of cross-sections of the cuticles. Fourier-transform infrared and Raman spectroscopies were used to characterize the composition of the cuticles, particularly to corroborate, with a high degree of certainty, the presence of uric acid in the cuticle of C. optima. With only one or two fitting parameters (uric acid volume fraction and inclination angle), the main spectral features of the measured total reflection spectra are reproduced from the application of the mentioned radiative transfer matrix formalism, when considering reflection spectra by cuticles of golden C. chrysargyrea, silvery C. chrysargyrea, and silvery C. optima scarab beetles. A method described previously in [35] has been devised to characterize the PC behavior of the twisted structures, for that circular polarization component matching the chirality of the arrangement. Using this method, the PBG is obtained as a function of the depth through the cuticle, its spectral limits, as well as the limits of the broad reflection band displayed both in the measured reflection spectra and in the calculated ones. We expect that the developed methodology reported in this article can be used to predict the optical properties of other natural systems with chirality and simulated or synthetized functional chiral arrangements.

Author Contributions: Capture and characterization of the samples, E.A., M.H.-J., D.E.A., E.L., Á.S and C.B.-A.; Formal analysis, W.E.V. and E.A.; Writing—original draft preparation, W.E.V., E.A., M.H.-J. and D.E.A; Writing—review and editing, W.E.V. Funding: This research received no external funding. Acknowledgments: The authors would like to thank the support given by the Universidad de Costa Rica to conduct this research. They also express their gratitude to the Tapantí National Park staff for their assistance. Conflicts of Interest: The authors declare no conflict of interest.

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