Chapter 3: Polarisation effects in natural photonic structures and their applications – Optical Biomimetics

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Polarisation effects in natural photonic structures and their applications

S. Berthier,     Université Paris-Diderot, France and Facultés Universitaires Notre Dame de la Paix, Belgium

Abstract:

Electromagnetic waves, unlike those which are generated mechanically, are transverse and introduce polarisation into optic phenomena. Many organisms have photosensitive sensors which enable them to respond to this. Most insects are sensitive to the polarisation of light and are capable of distinguishing two different states of polarisation. This is not the case in primates in general and in hominids in particular. This natural handicap has proved to be a source of bio-inspired innovation, as the use of simple instruments has made it possible to reveal what was previously hidden. Polarisation is used by many animals and may be adapted for use as a means of detecting forgeries. The first part of this chapter deals with fundamental theories on the polarisation of light and with experimental techniques. The photonic structures of insects are also considered. The chapter concludes with a presentation of a transfer bio-generated anti-counterfeiting mechanism used for documents or banknotes.

Key words

polarisation

bio-photonic

polarising structures

bio inspiration

insects

3.1 Introduction

Vision is an important and dominant sense in human beings but is relatively atrophied when compared with other animal groups. Many of the electromagnetic signals received by humans escape due to the transverse nature of the wave. However, the light environment, even when restricted to the visible spectrum, is very strongly polarised. Many animals and insects in particular, are sensitive to linear polarisation of the electromagnetic wave and have developed means of making this phenomenon an integral part of their inter- and intra-specific communication systems (Gabor and Dezso, 2004) .The basic principles of this development constitute an important source of ideas and are presented in this chapter.

3.2 Principles of polarisation

Following sections present outlines of the principles of polarisation. The topics that are covered are: the electromagnetic wave, Stokes vector and Mueller matrix representation, linear polarisation and circular polarisation.

3.2.1 The electromagnetic wave

In wave form, a beam of light consists of two fields: an electric field E and a magnetic field H. These are perpendicular to each other and to the direction of propagation. The spatio-temporal dependency of these fields was determined during the 19th century and summarised by J.C. Maxwell in the equations which bear his name (Jackson, 1975; Lipson et al., 1995). All the examples include the handling of monochromatic plane waves. However, this is not restrictive as any electromagnetic wave may be decomposed into an infinite number of monochromatic fields of pulsation ω, each of which has an infinite number of plane waves with vector k. The Maxwell equations for macroscopic fields in an area with a macroscopic bound charge can be written as follows:

[3.1]

and

[3.2]

E and B represent the electric field (in units of V/m) and magnetic induction (T) respectively, which are connected to the electric displacement D (V) and magnetic field H (A/m) by the following linear relations:

[3.3]

where P and M represent the electric and magnetic polarisation phenomena induced in matter by the wave. ∇ symbolises the vector operator ‘nabla’ and × the vector product. The rotationals indicate that E and B are perpendicular to each other. In looking for plane wave solutions, these fields may be represented as in Fig. 3.1.

3.1 The electric field and magnetic induction of a plane wave are perpendicular to each other and to the direction of propagation.

By omitting details of the calculation which, although long, are simple and classic, and seeking monochromatic equations, these equations lead to the following pairs of solutions:

[3.4]

and

[3.5]

where Ex, Ey, Bx and By are the components along ox and oy of fields E and B respectively. These equations show some of these components to be intimately linked: Bx and Ey and By and Ex form two plane waves totally independent of each other which can be separated spatially, creating polarised light. There is no imposed direction of vibration in natural light, so the wave is not defined as polarised. Fields E and H, which are always perpendicular to each other, may vibrate in any direction in the plane wave. However, it is possible to impose a direction of vibration to the fields, or to modify a pre-existing direction, making waves interact with various devices. The polariser and polarising films are the most common of such devices.

3.2.2 Stokes vector and Mueller matrix representation

The general polarisation state of a given wave may be determined by a set of parameters involving only measurable quantities as determined from the intensities of different components. These are known as the Stokes parameters (Gel’fand and Shapiro, 1956; Huard, 1994; Schalz et al., 1999). These parameters are usually grouped in a vector quantity with four components and are known as the Stokes vector S. Natural light does not generally present in any particular state of polarisation and may be seen as the superposition of all possible states, both linear and circular. The wave may be decomposed on these bases to define the intensities of the different elements.

If Ix and Iy are the intensities of the components of the electric vector along the ox and oy directions, I+ 45 and I− 45 those of the components at ± 45° of the same directions, and IG and ID the respective intensities of the left and right circularly polarised components, the Stokes parameters will be defined by:

[3.6]

In any optical device which amends the optical polarisation state of the incident radiation, the emergent Stokes vector S′ will differ from the incident vector S. The 4 × 4 matrix between these two vectors is called the Mueller matrix [M] and characterises the effect of the optical device.

The 16 elements of the matrix which link linearly measurable quantities, can be determined experimentally and represented by maps (Kusceri and Rubaric, 1959). Each element of the matrix is obtained by the linear combination of a number of measures of intensity (Fig. 3.2). VH, for example, corresponds to a vertically polarised (V) incident wave and a horizontally (H) detected wave. M11 is the total backscattered light intensity when the sample is illuminated with non-polarised light and is used as a standardisation for the other 15 elements. Symmetry in the Mnm and Mmn elements is obtained simply by reversing the optical incident or emerging polarisation devices and is the signature of an isotropic medium.

3.2 16 elements of the Mueller matrix. 49 measures are needed to determine them. Each letter corresponds to an intensity of the wave: O: unpolarised; H and V polarised horizontally and vertically, P and M polarised to + 45° and − 45°; and L and R, circularly polarised left and right respectively.

3.2.3 Linear polarisation

It should be noted that when a wave, even if un-polarised, falls on a surface, particular directions will appear ipso facto. The plane defined by the incident and emergent beam is termed the ‘plane of incidence’, regardless of the direction of the incident field and may be broken down into two vectors, one perpendicular to the plane of incidence, Es (from the German senkrecht), and one Ep parallel to that plane (parallel in German). Note that other decompositions of the wave are possible, as for example, in transverse electric (TE) and transverse magnetic (TM) adapted to the study of gratings, which will be presented later.

These two fields define two perpendicular polarised waves which, if following the Snell–Descartes laws concerning their directions of propagation, may interact differently with matter. One of the most remarkable properties (often found in butterflies) is the angular dependence of reflected intensity. The s-wave and its electric field which is always in the level plane, regardless of the incidence, depends very little upon the latter, but the second, the p-wave, presents surprising variations in angle. There is a specific angle, known as the Brewster angle, for which the reflectance of the p-wave is equal to 0. If a surface is illuminated under the incidence of Brewster θB, the reflected light is strictly s-polarised (Abeles, 1967). A practical consequence of this, which is well known to photographers, is that this incidence makes it possible to remove the reflection of a surface. Under these conditions, the light reflected by certain butterflies may be very strongly polarised. The Brewster angle depends only on the refraction indices of materials which constitute the diopter:

[3.7]

When in contact with air of index n0 = 1, biological materials with an index varying schematically from 1.5 to 1.8 will give Brewster angles between 50 and 60° (see Fig. 3.3).

3.3 (a) The electric field of a non-polarised wave falling on a diopter can be decomposed into two perpendicular vectors Es and Ep which are reflected differently depending on the angle of incidence (b).

3.2.4 Circular polarisation

Circular polarisation is not often encountered in nature, although it is generated by the carapace of beetles and merits specific attention. A wave is circularly polarised when the electric vector E rotates around the direction of propagation as it moves along this direction (Fig. 3.4).

3.4 Schematic representation of a dextrorotatory wave.

It should be noted that any linear polarised wave may be seen as the sum of two circularly polarised waves turning in phase in opposite directions: a levorotatory and a dextrorotatory wave. These polarised waves can be created by introducing a phase equal to a quarter of the wavelength between two perpendicular polarised waves, due to a thin layer known as a ‘quarter wave layer’. Many insects have developed a particular structure which produces the same effect in reflection as this transmission device. This imposes a stratified medium and it is necessary to consider how a given electromagnetic wave is propagated in such a medium.

Relation of dispersion

To understand how an electromagnetic wave or a photon propagates in a material, the relation of dispersion is calculated (Fox, 2001). This function establishes the relation between the energy of the particle E (or any quantity linked to the energy such as the frequency u, the angular frequency m) and its momentum p (or any quantity linked to it such as the wave vector k).

[3.8]

Which leads to:

[3.9]

In a homogeneous media with index n, this relation takes the form of a continuous straight line, indicating that any wave, whatever its frequency, can propagate in the medium with a velocity equal to the slope of the line (Fig. 3.5a). The situation is completely different in a periodically structured medium (Fig. 3.5b). It may be shown that each time the vector of the electromagnetic wave is equal to that of the structure, or to a subdivision.of it, the straight line is broken and frequency gaps are opened in the spectrum, indicating that waves of this frequency cannot propagate in the medium. They will therefore be reflected and cause a colour to appear (Ziman, 1979).

3.5 In a continuous medium with refractive index n (a), any electromagnetic wave, whatever its frequency, propagates with a velocity given by the slope of the relation (b). In a stratified medium, (c) the straight line is broken when the frequency or the harmonics of the two waves – the electromagnetic and the material ones – match (d). At these frequencies, the electromagnetic wave cannot propagate and is reflected

3.3 Experimental techniques to study polarisation

In addition to the classical spectroscopic techniques used to determine the reflectivity and transmissive qualities of insect wings and integuments, there are specific methods of polarimetric analysis such as various ellipsometric and polarimetric imaging techniques.

3.3.1 Ellipsometry

Ellipsometry has a long history of use in science and technology. However, it is only recently – with the exception of the precursory works of Michelson (Michelson, 1911) – that it has been used to characterise natural photonic structures. The spectra of these structures are extremely sensitive to surface conditions and are complex and difficult to interpret.

Principle

The principle of measurement is to determine the change of state in the polarisation of a wave reflected by the surface of a sample. This change can be directly related to the optical and geometrical characteristics of a surface, making ellipsometry a powerful tool for the optical analysis of surfaces.

It has been shown that the reflection coefficients Rp and Rs of a linearly polarised wave depends in differing ways on the angle of incidence of light: Rs is a monotonically increasing function, whereas Rp passes through a minimum for a particular angle of incidence (the Brewster angle). However these two waves may not be in synchrony with each other, thus the ratio of their amplitudes may be expressed in the following complex form:

[3.10]

These are the angles Ψ and Δ, or more commonly tgΨ and cosΔ which are directly measured.

The most general state of polarisation in a monochromatic wave is elliptical, i.e. the trace of the extremity of the electric vector field E in the plane wave is an ellipse. This field may be written in matrix form:

[3.11]

The state of polarisation is entirely determined by its Jones vector which takes the form:

[3.12]

and thus by the two quantities Ψ and Δ. In the case of a semi-infinite media, the reflection coefficients Rp and Rs are expressed in terms of the complex refractive indices of the two media and their angles of incidence and refraction. These values may be obtained by inverting the equations and measuring the two angles. The same method may be applied to a thin layer deposited on a substrate and, as considered here, on a multilayer where the calculations are more complex. The multilayer is considered to be a composite medium and the characteristics of the component layers are determined. Analysis of the components can be made using models of actual environments and an effective theory of mediums such as the Maxwell Garnett theory (Cohen et al., 1973; Berthier, 1993).

All types of ellipsometer are based on the principle illustrated in Fig. 3.6. A polariser and a compensator located on one arm of the ellipsometer determine a defined state of polarisation of the incident light. An analyser and a detector located on the other arm detect the change in polarisation produced by reflection on the surface of the sample. More complex procedures of generalised ellipsometry (GE) are used in the study of anisotropic materials, such as the wings of many butterflies and coleopteran (see Fig. 3.7).

3.6 Schematic representation of an ellipsometer. (Sa: sample, S: source, D: detector, P: polariser, A: analyser)

3.7 Variations of the angles Ψ (a) and Δ (b) in the ultraviolet, visible and near infrared for three Morphos belonging to three different sub genus (M. menelaus: Grasseia, M. rhetenor: Megamede and M. sulkowskyi: Cytheritis).

3.3.2 Polarimetric imaging

As described in section 3.2.2, changes in the polarisation state of an incident wave induced by a given structure can be represented in a matrix form known as the Mueller matrix. New experimental devices allow the visualisation of the various elements of that matrix.

Monochromatic light from different lasers is passed through a rotating linear polariser or a polariser followed by a quarter wave plate (λ/4) which generates a circularly right or left polarised wave. The same device will be crossed by the light which is retro-diffused by the object before reaching a charge coupled device (CCD) camera measuring the intensity (Hielsher et al., 1997). Thus, any state of polarisation can be sent to the object and measured after reflection, regardless of the incident state. It can therefore measure not only the reflectance of the structure for a given polarisation, but also any changes in polarisation and depolarisation phenomena. The camera is inclined 15° to the optical axis in order to remove specular reflections.

The 16 elements of the Mueller matrix are obtained by 49 measurements of intensity (Fig. 3.8). The matrix element M11 is the total backscattered light when the incident beam is not polarised. It is used as a reference for all other elements of the matrix.

3.8 Schematic diagram of the polarimetric measurement installation.

Two modes of imaging are available: in real space or reciprocal space. It is obvious that each element of the matrix has more or less evident number of interpretations. See Plate II (see colour section between pages 96 and 97).

Plate II (a) Mueller matrix in Fourier space, measured on a scale of M. rhetenor (normal incidence, λ = 450 nm). Mueller matrix of the same area, image mode (b).

3.4 Polarisation structures in insects

In the following, details of polarisation structures in insects are given. Both linear and circular polarisation structures are included.

3.4.1 Linear polarisation

Polarisation at the Brewster angle

A one-dimensional structure composed of multi-layered films is considered here. In the natural world, this is found in the carapaces of many insects and in the scales of certain butterflies. Among these structures, which are generally of a plane or cylindrical form, some are constituted by concave, roughly hemispherical, multi-layered basin shapes. These concave structures are composed of a stack of thin films, which alternate solid (chitin embedded in proteins) with air, as for example, in the scales of butterflies of the genus Papilio (Vukusic and Samble, 2003), or solid films of various composition as in the elytrons of certain coleopteran of genus Cicindela (Berthier, 2007a, 2007b).

Papilio

The covering scales of most of the species of the genus Papilio present a unified bulk and surface structure. The upper membrane can be seen to consist of a multi-layered air/chitin film of about 5 to 10 layers having an undulating surface between the ridges which forms a regular set of concave basins (see Fig. 3.9). Depending upon the species, these basins are roughly spherical (Papilio blumei) or slightly elongated (Papilio peranthus) (see Plate V).

3.9 (a) The scales of the dorsal side of Papilio ulysses (SEM). (b) Detail of the surface of a cover scale (SEM). (c) TEM view of a section of a cover scale showing the multi-layered structure of the upper membrane.

Plate III (a) Surface of the elytrons of Cicindela hybrida showing the coloured basins and (b) an SEM view of a cross-section of a single basin.

Plate IV The scales of Suneve coronata under TM (a) and TE (b) polarisation light. TE and TM are relative to the direction of the rows. The blue component, which is strongly TM polarised, nearly disappears when the incident light is TE polarised.

Plate V Cover scales of two papilio. (a) Papilio blumei: the basins are roughly spherical. (b) They are slightly elongated for Papilio peranthus. (c) Schematic representation of the scales.tl

Cicindela

Similar structures can be found in the elytrons of the species Cicindela among others (Schultz and Rankin, 1985a, 1985b). They differ from the above by the solid/solid composition of the multi-layer and by the random disposition of basins on the surface (see Plate III).

Two different phenomena occur when light falls on such hemispherical structures at a given angle of incidence, according to the position in the basin. If the light falls on or near the centre, specular reflection and inter-ferential phenomena occur, giving rise to a coloured effect which depends on the thickness e and the equivalent refractive index n of the layers, according to:

[3.13]

The extinguish wavelengh is denoted by λmin and k an integer. At close-to-normal incidence, this reflected colour is either polarised or very slightly polarised. If the light falls at a distance from the centre, which causes the normal angles of incidence to the surface to intersect at right angles at this point, the light will emerge after a double reflection in the incident direction. The angle of incidence on the surface is exactly equal to n/4 which is not far from the polarising angle θB The wavelength which interferes is shifted towards lower values and the corresponding colour towards blue.

When observing the insect from above, a uniform colour is seen to be produced by the concentric combination of various colours, in a manner similar to the juxtaposed points which can be found in pointillist paintings. The particularity here is that the ‘blue’ component, at the periphery of the basins, is strongly polarised while the ‘red’ component at the centre, is not (see Plate VIII).

Plate VI Element Mxx of the Mueller matrix of Morpho rhetenor showing a great contrast in the polarisation of the diffraction orders.

Plate VIII (a) Polarisation effect on Papilio paris scales. On the left, the polarisation of the incident wave is parallel to striae. The high edges of the basin illuminated under high incidence, send back a blue polarised light in this direction. On the right, polarisation is perpendicular to striae, the small edges of the basin now reflect the polarised wave. Under non-polarised light, the elongated shape of basins leads to a reflected light that is slightly polarised in the direction of striae. (b) Polarisation effect resulting from reflection in the basins of Cincidela hybrida elytrons. On the left, the polarisation direction is vertical, while it is horizontal on the right. The yellow background is not polarised, contrary to the green edges of basins.

Depending upon the symmetry of the basin, if two opposite sides – for example right and left – are Transverse Electric (TE) polarised, the two others – up and down – are Transverse Magnetic (TM) polarised, thus no macroscopic polarisation effects can be observed unless the symmetry is broken. This is the case with (Papilio paris), whose basins are slightly elongated, in the scale axis direction.

If this phenomenon is to be used to produce macroscopic effects for anti-counterfeiting devices, the ratio between S and P must be as great as possible, the ideal situation being infinite multi-layered grooves. This structure exists on a larger scale in a recently studied butterfly (Z. Bàlint, 2005): Suneve coronata.

Multi-scaled polarisation: Suneve coronata

Suneve coronata is a neotropical lycaenid butterfly distributed from Meso-america to NE South America (Berthier et al., 2007b). In common with most butterflies, the lycaenid have two layers of scales on their wings. The inner ones which are directly in contact with the wing membrane are called ‘ground scales’ or ‘basal scales’ while the outer ones are the ‘cover scales’. The scales of both sides of the wings have classical Urania-like structures with structural convex cover scales and pigmentary plane ground scales (see Plate IX).

Plate IX (a) Suneve coronata. (b) SEM view of the dorsal scales. Cover scales are convex and intersect at right angle. The ground scales are plane. (c) Photonic microscope view of the wing under unpolarised light.

The apexes of the cover scales of a given row cover the base of the neighbouring row perpendicular to its surface. The wing appears to be covered by long lines of alternate green and blue (Plate IX), corresponding respectively to the crests of the convex scales. These are barely polarised while the space between neighbouring rows is strongly polarised. The blue component can be almost extinguished with a linear polariser, thus changing the colour of the butterfly from blue to emerald green (Plate IV). This should provide the optimal situation for maximum polarisation contrast. However, the macroscopic measurements and direct observation do not show this to be the case (Fig. 3.10). This is attributable to the presence of another structure which polarises the reflected light in a direction perpendicular to the previous one. This structure is formed by the ridges of the scales which form a very regular periodic structure (Fig. 3.11).

3.10 Hemispherical reflectivity of the wings of Suneve coronata for the two states of linear polarisation and for non-polarised light. The maximum reflectivity is slightly shifted by about 8 nm.

3.11 (a) SEM view of a cross-section of a cover scale of Suneve coronata, showing the multi-layered structure of the membrane and a front view of the scale showing the regular disposition of the right angles.

Again, the mean angle is equal to π/2 but the axis of the ridges is perpendicular to the direction of the rows, which minimises the macroscopic polarisation ratio. This is a rare case where two structures with very different scales – a cover scale is about 200 μm × 70 μm, and a distance between two ridges which is equal to 2 μm – produce the same polarisation effect but in opposite directions, so that the macroscopic effect almost disappears.

Polarisation by diffraction

The Morphinae have developed a particular structure on their ground scales (and sometimes also on their cover scales) which is known as the ‘Christmas tree’ structure (Berthier, 2010) (Fig. 3.12). This acts as a complex grating which produces a blue colour by interference and diffracts it laterally. This type of structure also produces a unique phenomenon in which the diffraction orders are differently polarised. It was first predicted by simulation (Berthier, 2006) and then confirmed by spectrometric measurement and polarimetric imaging (Plate VI).

3.12 SEM view of a cut of a ground scale of Morpho rhetenor cassica showing the ‘Christmas tree’ structure of the scales.

Spectral analysis

As human eyes are not sensitive to the polarisation of light, its effects on the wings of Morphos appear primarily colorimetric (Berthier, 2010). The reflection spectra are shifted as the incident wave is polarised as transverse electric or magnetic. This can easily be observed under a light microscope or even on the insect itself. The effect appears to be regular, but varies in intensity according to the species (Fig. 3.13). A butterfly lit by a Transverse Electric polarised wave (TE) is always more blue in colour than the same illuminated by a Transverse Magnetic (TM) wave which will tend towards green (Fig. 3.14).

3.13 Chromatic variations of the wings of Morpho zephyritis for two perpendicular linear polarisation states of the incident light: (a) Transverse Magnetic and (b) Transverse Electric.

3.14 Coefficient of reflection of the wing of Morpho menelaus for both the TE (a) and TM (b) polarisation. In the TM mode, the spectrum consists of two peaks and is shifted towards green.

This observation is consistent with the theoretical predictions, which also reveal further information. It is significant that this diffracting structure slightly polarises the light, especially under quasi-normal incidence (Siewert, 1981, 1982), i.e. the diffraction orders have a quite different polarisation state when the structure is illuminated by natural non-polarised light. The order R1 is predominantly Transverse Magnetic polarised while the opposite order R-1 is predominantly in the Transverse Electric state. The specular order R0, is only minimally polarised, but still of very low intensity. All the properties of an electromagnetic wave reflected by a surface can be represented by the ‘Bidirectional Reflectivity Distribution Function’ (BRDF). This function is generally too complex to be completely determined and can only be ascertained for a limited number of parameters (e.g. a given wavelength, or a given direction). The calculations and maps of BRDF present a different picture. Illuminated under a non-polarised light, the diffracted wave is TE polarised on one side and TM polarised on the other. Although two polarisation states can be distinguished in Morphos, the advantage of this to the species is not obvious. Although highly attenuated, the effect may be verified experimentally. A division along the axis Φ at an angle of about 45° clearly shows the imbalance of the polarisation states between the two diffraction orders. (Fig. 3.15).

3.15 Cup in Bidirectional Reflectivity Distribution Function (BRDF) of M. menelaus for ϕ = 45° and λ = 450 nm (a). The order R1 is predominantly TE polarised, the R-1 order TM polarised. The BRDF in intensity, and the axis of cut (b).

3.4.2 Circular polarisation

The Cetonia and Plusiotis genus are well known for the extraordinary bright metallic appearance of many species (Moron, 1990). The epicuticle shows a helicoidal structure which generates both interference and circular polarisation. It consists of an anisotropic solid/solid multi-layer structure with a direction rotating from one layer to the other, creating a periodic, though weak, gradient of index in the epicuticle (Bouligan, 1969; Neville 1969, 1975; Caveney 1971; Filshie 1988; Hadley 1982; Beireither-Hahn et al., 1984). The small difference in index is offset by the large number of layers which cause a bright appearance. It is important to note that there is no alternation of materials with low and high indices in the multi-layer. This is the result of the rotation of a layer composed of a single material having two different indices in the perpendicular direction. Interference occurs between layers which have the same direction.

The layers are parallel in the exocuticles of most coleoptera, whereas the chitin micro fibrils which constitute the elytra bend at a relatively constant angle which is called the rotator, resulting in a helicoidal structure similar to that of some liquid crystals in the cholesteric phase (Fig. 3.16).

3.16 In a cholesteric stage, the director orientation regularly varies along the axis. A period shows up when the elements undergo a 180° rotation, determining a lamella (a). A cross-section through the endocuticle points out arched structures characterising cholesteric-type arrangement. Lamellae are formed by a 180° rotation of sticks (b).

Determining the rotator is not an easy task. The classical method consists of making an oblique section of the elytra at a specific angle. A complex arrangement of arches then appears which allows the thickness of the lamella to be measured. The coefficient of rotation a is given by θ = αz. Another technique consists in polishing the surface of the elytra and to proceed by ion bonding of the surface which causes the micro fibrils to appear (Fig. 3.17).

3.17 (a) Analysis of the cholesteric structure of the elytra of Plusiotis chrysargirea. The top of the elytra is polished and attacked by an ion beam. (b) The ion etching reveals the orientation of the chitin fibrils in each layer.

When circular polarised light falls on such a structure, two different situations may arise according to the respective rotation. Under conditions in which the wave and the structure turn in the same direction, the electric field E will always remain parallel to the chitin fibrils. The wave therefore experiences a homogeneous medium in which the direction of dispersion is a straight line and travels freely within it. However, when the wave and the structure turn in opposing directions, E is alternatively parallel and perpendicular to the fibrils. The effect is then that of a stratified medium of alternatively high refractive index when E is perpendicular to the fibrils, and is of low index when it is parallel. Gaps open in the direction of dispersion and the wave is reflected (Fig 3.18).

3.18 The relations of dispersion in a cholesteric medium for two circular waves turning in opposite directions. When the wave and the structure turn in the same direction, and if the rotators are equal, the layered medium appears homogeneous (a). When they turn in opposite directions, the refractive index changes periodically: the relation of dispersion is broken (b).

This phenomenon is clearly visible in most of the genus Plusiotis and in certain Scarabaeidae (Cetonia aurata). Plate XIII shows the Mueller matrix of the elytra of Cetonia aurata. The strong circular polarisation effect is evidenced by the M14 and M41 elements.

Plate XII Changes in colouration with the polarisation of the two systems: plane/grooves and perpendicular grooves. In the first one, the colour change but not the luminosity, in contrast to the perpendicular grooves system.

Plate XIII Cetonia aurata in flying position (a). Optical microscopic view of the elytron (× 100) (b) and its Mueller matrix element 1 × 4 in image mode showing that the circular polarisation arises from very local part of the elytron (c). The complete Mueller matrix of the elytron in image mode (× 10) (d).

3.5 Bio-inspired applications: anti-counterfeiting patterns

These structures can be adapted to provide an original solution to the problem of protecting against the forging of bank notes. Each bank note consists of a certain number of elements which ensure protection at three different levels and correspond to three types of users. Level-1 protection requires any individual to be able to recognise the authenticity of a bank note without the use of equipment. This involves various motifs, colours, papers, watermarks and holograms. Level-2 requires simple equipment which may be used by shopkeepers and cashiers to detect concealed properties through using ultraviolet light or polarisation. Level-3 protection involves all the physico-chemical properties of bank notes which can only be determined in a laboratory by the use of cumbersome equipment.

Once their symmetry is broken, the effects produced by Papilio and Cicindeles structures can ensure the two first levels of protection. These generate bright and iridescent colours which fulfil the level-1 protection requirements and are also capable of creating chromatic effects dependent upon polarisation which meets the needs of level-2 protection (Berthier et al., 2007a, b).

3.5.1 Change of colour

Several different processes can be created which are based on two main effects. The one most closely resembling Papilios and Ciccindeles is a succession of grooves and alternated planes of the same width. This produces a compound colour, one of the components of which can be suppressed by using a polariser to modify the colour. The colour of a motif may thus be varied from green to yellow for example, either by suppressing or permitting the blue component reflected by the multi-layer grooves which reflect yellow under normal incidence (see Fig. 3.19).

3.19 A coloured effect linked to the polarisation of one of the components. By suppressing a large part of the blue component with a polariser, one can make the general green colour turn yellow.

The calculated spectra of these different elements are presented in Fig. 3.20. The system consists of a multi-layer of alternatively high (nh = 1.94) and low (n1 = 1.51) indices and thicknesses eh and e1 respectively which produce a green colour under normal incidence which is very similar to that of the butterfly Sunive coronata: eh = 185 nm and e1 = 117 nm (see Fig. 3.21).

3.20 (a) Calculated reflectivity of a plane multi-layer under normal incidence. (b) Reflectivity of the structured film for the two polarisation states (TE and TM are relative to the axes of the grooves).

3.21 Calculated reflectivity of a succession of multi-layered planes and grooves of the same width and for the two polarisation states.

The polarisation contrast is relatively important (P ~ 0.43) and leads to a significant change in colour. The luminosity remains almost constant (Tables 3.1 and 3.2). The coloured effects are presented on a CIE diagram in Plate XII.

Table 3.1

Chromaticity coordinates of a motif composed of multi-layered planes and grooves; the luminosity is nearly constant but the colour changes

CIE coordinates (x′, y′) Luminosity
TE 0.23, 0.52 16.9
TM 0.16, 0.36 6.5

Table 3.2

Chromaticity coordinates of a motif composed of multi-layered perpendicular grooves; the colour stays unchanged but the contrast of luminosity is important

CIE coordinates (x′, y′) Luminosity
TE 0.09, 0.23 13
TM 0.12, 0.24 33

3.5.2 Change of luminosity

Another method consists of using only grooved areas perpendicular to each other. Without a polariser, these appear to be exactly the same colour, but when perpendicularly polarised, only one will appear, thus causing concealed motifs to emerge (Table 3.2) (see Fig. 3.22).

3.22 When one uses ridged areas only, they present the same colour under natural light and it is impossible to distinguish any pattern. They can become apparent by using a polariser letting the reflected component penetrate. TE and TM are relative to the central motif structures.

3.6 Conclusion

Insects have long been known to be sensitive to the polarisation of light. It has been shown that polarised light increases the sensitivity of compound eyes by about 15–30% when compared to unpolarised light of the same intensity (Rossel, 1988). Exhibiting a polarising structure could therefore be advantageous for the insect as it enhances its visibility. Many insects, including most of the Morphinae and many coleoptera (Cetonia, Plusiotis) reflect a fairly strong polarised light, in either a linear or circular manner. Many others have developed surface structures that depolarise reflected light. This is the case in many butterflies of the genus Papilio (Papilionidae) and certain coleoptera (Cicindelidae). Except under normal incidence, the light reflected by a given surface is always polarised to some degree. To avoid this phenomenon, the surface has to present facets perpendicular to each other in the same proportions. This is generally achieved by concave structures on the wing scales of butterflies or on the surface of the elytra. In some rare cases, as for example, in some Lycaenidae, the depolarising structure is multi-scaled. One polarising structure is formed by the scales themselves, while the other is formed by the grooves of these scales. The exposed surfaces are roughly equivalent and as they reflect light polarised in perpendicular directions, they appear unpolarised from the macroscopic point of observation.

Significant local changes in colour or luminosity may be made to appear by the use of a polariser and these effects can be used for the first two levels of protection for banknotes and credit cards. By combining multi-layered planes and grooves, an infinite number of devices may be posited that will produce coloured effects linked to polarisation. Two examples are presented, one producing a change in colouration, the other giving a variation of intensity. Circular polarisation may also be envisaged.

Plate VII (top) Image of the patterned, undoped silk film illuminated at grazing angle under white light illumination. Different colours appear because of the pitch of the individual patterns. The scheme of the experimental layout is illustrated in the figure as well, whereas the bottom image shows the nanopatterned doped silk film. The enhancement in emission corresponds to specific lattice constants that are matched to the fluorescence spectrum from different pitch nanopatterns. Shown underneath the fluorescent image are images collected at λ = 550 nm and λ = 630 nm, illustrating the specific nanopatterned squares that give rise to enhancement at those wavelengths.

3.7 References

Abeles, F. Optics of thin films. In: Advanced Optical Techniques. Amsterdam: North Holland Publishing; 1967:145–187.

Beireither-Hahn, J., Matoltsy, A. G., Richards, K. S., Biology of the integumentInvertebrates. Berlin: Springer-Verlag, 1984. [vol. 1].

Berthier, S. Omtique des milieux composites. Paris: Polytechnica; 1993.

Berthier, S. Structure and optical properties of the wings of Morphidae. Insect Sciences. 2006; 13:145. [ISBN 2-84054-015-0].

Berthier, S., IridescenceThe Physical Colors of Insects. Springer Science + Business Media, 2007.

Berthier, S., Boulenguez, J., Balint, Z. Multiscaled polarization effects in Suneve coronata (Lepidoptera) and other insects: application to anti-counterfeiting of banknotes. Appl. Phys. 2007; A86:123–130.

Berthier, S. Photonique des Morphos. Paris: Springer France; 2010.

Bouligand, Y. Sur l’existence de pseudomorphoses cholesteriques chez divers organismes vivants. J. de Physique. 1969; 30(C4-90):103.

Caveney, S. Cuticule reflectivity and optical activity in scarab beetles: the role of uric acid. Proc. R. Soc. London B. 1971; 178:205–225.

Cohen, R. W., Cody, G. D., Couts, M. D., Abeles, B. Phys. Rev, 1973. [B8, 3689. ].

Filshie, B. K. Fine structure of the cuticule of insects and other arthropods. Insect Ultrastructure. 1988; 1:281–312.

Fox, M. Optical Properties of Solids. New York: Oxford University Press, 2001.

Gabor, H., Dezso, V. Polarized Light in Animal Vision. Springer Verlag Berlin: Heidelberg, 2004.

Gel’fand, I. M., Shapiro, Z. Y. Representation of the group of rotations of dimensional space and their application. Amer. Math. Soc. Translation. 1956; 2:207.

Hadley, N. F. Cuticule ultrastructure with respect of the lipid waterproofing barrier. J. Exp. Zoology. 1982; 222–223:239–248.

Hielsher, A. H., Eick, A. A., Mourant, J. R. Diffuse backscattering Mueller matrices of highly scattering media. Optics Express. 1997; 1:441.

Huard, S. Polarisation de la Lumière. Paris: Masson; 1994.

Hutley, M. C. Diffraction Gratings. London: Academic Press; 1982.

Kusceri, I., Rubaric, M. Matrix formalism in the theory of diffusion of light. Optica Acta. 1959; 6:42.

Jackson, J. D. Classical Electrodynamics. New York: Wiley; 1975.

Lipson, S. G., Lipson, H., Tannhauser, D. S. Optical Physics. Cambridge: Cambridge University Press; 1995.

Michelson, A. A. On the metallic colouring in birds and insects. Phil. Mag. 21, 1911.

Moron, M. A. The Beetles of the World. Sciences Nat: France; 1990. [10].

Neville, A. C., Caveney, S. Scarabaeide beetle exocuticule as an optical analogue of the cholesteric liquid crystals. Biol. Rev. 1969; 44:531–562.

Neville, A. C. Biology of the Arthropod cuticule. Berlin: Springer-Verlag; 1975.

Rossel, S. Polarization sensitivity in compound eyes. In: Stavenga D. G., Hardie R. C., eds. Facets of the Vision. Berlin: Springer-Verlag, 1988.

Schultz, T. D., Rankin, M. A. The ultrastructure of the epicular interference reflectors of tiger beetles (Cicindela). J. Exp. Biol. 1985; 117:111–117.

Schultz, T. D., Rankin, M. A. Developmental changes in the interference reflectors and colorations of tiger beetles (Cicindela). J. Exp. Biol. 1985; 117:87–110.

Schulz, F. M., Stammes, K., Weng, F. VIDISORT: an improved and generalized discrete ordinate method for polarized radiative vector. J. Quant. Spectrosc. Radiat. Transfer. 1999; 61:1005.

Siewert, C. E. On the equation of transfer relevant to the scattering of polarized light. The Astrophys Journal. 1981; 245:1080.

Siewert, C. E. On the phase matrix relevant to the scattering of polarized light. The Astrophys Journal. 1982; 109:195.

Vukusic, P., Samble, J. Nature. 2003; 424:852.

Ziman, J. M. Principle of the Theory of Solids, 2, Cambridge: Cambridge University Press, 1979. [ISBN 978–0521297332].