Scales of the Papilio nireus combine fluorophores confined in a natural photonic structure. By means of numerical simulations based on the scattering-matrix formalism, we reveal the bi-functional optical role of this peculiar architecture. Two aspects are considered: the absorption of an incident light flux and the emission of another luminous flux. First, results highlight a light trapping effect and a light absorption increase in the ultraviolet, visible and near infrared ranges. Then, results highlight an enhanced fluorescence occurring in the spatial as well as in the frequency domain. This observation could be of great interest to design new optical devices.
©2012 Optical Society of America
In devices such as solar cells, lasers, light emitting diodes, etc., the control of the distribution of light intensities is overwhelmingly important. Photonic crystals (PC), with their periodic modulation of the refractive index, are suitable materials to be employed for this purpose. The resulting photonic band gaps inhibit light propagation, both in the frequency domain and in the spatial domain [1, 2]. Using such a structure to confine fluorescent molecules offers new possibilities. Indeed, it allows to control the fluorescence at each of its two stages: the absorption of an incident light flux and the emission of another luminous flux. A good understanding of these causal mechanisms could impact interesting applications such as biosensors , DNA microarrays , new generations of solar cells , photonic crystal fibers [6, 7], etc.
In order to improve these devices, it is crucial to well understand their underlying physics and in particular the way they distribute light intensities. In this work, we propose a bio-inspired approach of this problem. We investigate the optical response of the colored scales of the Papilio nireus butterfly, these scales containing highly fluorescent molecules confined in a natural photonic structure . We describe the bi-functional optical role of this peculiar architecture, i.e., its influence on both aspects of the fluorescence process: the absorption of an incident light flux and the emission of a luminous flux. We approach this problem by performing refined and rigorous numerical simulations based on the scattering-matrix formalism.
The paper is organized as follows: Section 2 presents the state of knowledge acquired from morphological investigations of the Papilio nireus and the study of the fluorescence properties of this butterfly. Section 3 develops the scattering-matrix formalism and brings various numerical considerations. Sections 4 and 5 report the two functions of the photonic structure: its influence on the absorption and emission properties, respectively.
2. State of the art
The Papilio nireus, also called “Narrow Green Banded Swallowtail”, is a member of the large Papilionidae family. Three subspecies coexist: the Papilio nireus lyaeus (Doubleday , 1845), the Papilio nireus pseudonireus (Felder , 1865) and the Papilio nireus wilsoni (Rothschild , 1926). Found in the Afrotropic ecozone, this butterfly was first described in 1758 by Linnaeus . Its distribution extends from Senegal through Somalia and South Africa, excluding Madagascar and the Comoros. Adult moths are most common along logging road or in the secondary forest, where they seek flowers such as Tridax or Eupatorium plants. But it is also possible to see this butterfly into the savannah. Caterpillars are very sensitive to their living environment because they feed on very specific plants such as Calodendrum capense, Clausena anisata, Fagara macrophylla, Oricia bachmanii, Toddalia asiatica, Zanthoxylum spp., Teclea spp., Vepris spp. and Citrus spp. (spp. meaning species).
With a wingspan of about 10 – 12 centimeters, the dorsal side of the wings is principally black, decorated with colored bands. Small colored spots are also present at the apex of the forewings and at the outer edge of the hindwings. According to subspecies, this coloration varies from turquoise to metallic green. By contrast, the ventral side of the wings is similar for the three subspecies: the coloration is primarily dark – brown, patterned by black veins and golden spots at the outer edge of the hindwings. The body is black. The sexual dimorphism is very weak, the female having larger colored spots on the upperside and no golden spots on the underside.
The ultrastructure of the colored scales of the Papilio nireus was revealed in the pioneering work of Vukusic and Hooper . They investigated the morphology of an individual scale by means of scanning and transmission electron microscope images (Fig. 1 ) and described the architecture of the scales. It can be viewed as a small flattened bag filled with air. The lower lamina, having no significant rumpling, consists in a distributed Bragg reflector (DBR) composed of three layers. The thickness of each layer is respectively close to 75, 35 and 75 nanometers. The upper lamina contains a structured medium defined as a two-dimensional photonic crystal (2D PC) by the authors. It consists in a set of hollow air cylinders distributed according to an hexagonal lattice in a host medium of solid cuticle. The thickness of the 2D PC is close to 1300 nm, the mean diameter of the cylinders is close to 240 nm and the mean spacing between two cylinders is close to 340 nm. Above the 2D PC is found a set of parallel ridges running from the base to the apex of the scale. With a 745 nm height, they are periodically distributed with a lattice parameter close to 1800 nm. Both sides of these ridges support lamellae. Upper and lower lamina are maintained at 1500 nm from each other with trabeculae. A schematic representation is given Fig. 2 .
In their paper, Vukusic and Hooper showed the presence of highly fluorescent molecules infused throughout the photonic structure of the scales. Their measurements revealed a broad emission band with a peak emission wavelength close to 505 nm, the peak excitation wavelength being close to 420 nm. In parallel, the authors calculated the photonic band diagram for the idealized 2D PC and found a pseudo-gap region defined by a significantly depleted density of accessible optical states. This pseudo-gap, ranging from 455 nm to 545 nm, encompasses the peak emission wavelength. The consequence was an inhibition of the emitted light in the plane of the 2D PC and an enhancement in directions parallel to the cylinders axis. Besides, they calculated that the spectral band gap of the DBR matched with the peak emission wavelength. They proposed that the downward emitted light interacting with the DBR was reflected upward, towards the outside environment. The combination of the DBR and the 2D PC allowed to exalt the light extraction from the photonic structure. It corresponded to the manifestation of an enhanced fluorescence in the scales of the Papilio nireus.
Vukusic and Hooper investigated one aspect of a fluorescence process: the influence of the photonic structure on the emission properties. But another aspect must not be neglected: the absorption of the incident light flux. In this present work, we propose to confirm the assumptions of Vukusic and Hooper by means of refined and rigorous numerical simulations based on the scattering-matrix formalism. We also propose to extend this study to the first aspect of the fluorescent process, i.e., the absorption of an incident light flux. In this way, we highlight the bi-functional optical role of the photonic structure in the scales of the Papilio nireus.
3. Numerical photonic computational aspects
In 1999, Whittaker and Culshaw  presented a scattering-matrix formalism providing a numerical solution of Maxwell’s equations for a stratified medium with lateral periodicity. The “stratified medium with lateral periodicity” concept was presented elsewhere [13, 14]. It consists in a stack of planar layers. An individual layer, characterized by an homogeneous refractive index along the direction perpendicular to the interface, is formed by the periodic repetition of a unit cell in the lateral directions (parallel to the interface). This elementary cell is composed by a host medium, incorporating one or more distinct inclusions. The scattering-matrix formalism introduces a scattering-matrix relating the amplitudes of ingoing and outgoing propagating waves in a layer and the following. This matrix is obtained by solving the boundary conditions at the interface. Iteratively, the total scattering-matrix for the whole system is then built up. This method allows access to reflectivity or transmission spectra for light incident from the outside, or emission spectra from an internal dipole source. In 2008, Liscidini et al.  extended this treatment to asymmetric unit cells and/or birefringent materials. Two years later, Zhao et al.  considered the emission from an internal planar source. Inspired from these three articles, a 3D scattering-matrix FORTRAN code was developed at the University of Namur, Belgium.
In the present work, this code was devoted to theoretically predict the optical response of the ultrastructure constituting the colored scale of the Papilio nireus. From this perspective, we considered a perfect ideal system, neglecting the statistical variation of all parameters such as the cylinder radius, the inter-cylinders spacing, the 2D PC thickness, etc. Moreover, in our numerical simulations, we solely consider the distributed Bragg reflector and the two-dimensional photonic crystal. Although the trabeculae, the lamellae and the ridges can, to some extent, influence the optical properties of the scales in some parts of the electromagnetic spectrum, we neglected their presence for three reasons. Firstly, in their paper, Vukusic and Hooper suggested that the enhanced fluorescence was induced by the DBR and the 2D PC. They did not taken into account the trabeculae, the lamellae and the ridges. In order to be as close as possible of their considerations and to confirm their assumptions by means of numerical simulations, we also neglected these elements. Secondly, the purpose of these numerical simulations is not to integrate the natural structure in its entirety but to highlight the contribution of dominant elements (in this case, the DBR and the 2D PC) on the optical properties of the system. We think that adding the other elements would have given too many details to the results that could shortchange the message. Thirdly, in the present bio-inspired approach, the scope of this paper is to observe the optical properties of a natural sample in order to understand the underlying physics and then to try to apply the observations in the current technology. In this approach, the exact reproduction of the natural structure in its entirety is not necessary. We selected some parts of the structure that we believe playing a key role in the optical properties of the sample and that can be easily reproduced for technology applications (photovoltaic devices, diodes, sensors, etc.). Current industrial techniques allow to easily synthesize structures such as the DBR (for instance by physical vapor deposition  or thermal deposition ) or such as the 2D PC (for instance by electron beam lithography-based methods [19, 20]). On the other hand, the artificial reproduction of the natural structure in its entirety requires more complex experimental setup [21–24]. In the present realizations, we assumed that the biological material constituting the scale of the butterfly is chitin. Its refractive index n was chosen equal to 1.56 + i 0.06, an average value commonly accepted [25, 26]. A complex refractive index allows to account for the absorbent character of the scale.
In order to interpret the results, an axis system was defined. From a macroscopic point of view (Fig. 3(a) ), the wing was placed in the xy plane, the y-axis pointing from the termen to the base of the wing. The z-axis was normal to the wing. From a microscopic point of view (Fig. 3(b)), the x- and y-axis correspond to the directions parallel to the interface, while the z-axis corresponds to the direction perpendicular to the interface. The light propagation direction is defined by two angles: θx, named polar angle, is the angle between the normal to the sample and the light propagation direction while φx is the azimuth angle, counted counterclockwise from the x-axis. The index “x” is either “i” in the case of the incidence or “d” in the case of the detection.
4. First function of the photonic structure: impact on the absorption properties
At first, we investigated the impact of the natural photonic structure of the Papilio nireus on the absorption properties. With the 3D scattering-matrix computational code mentioned above, we calculated the reflectivity and transmission spectra, respectively R(λ) and T(λ), of the system composed by the DBR and the 2D PC. The incident light direction was considered normal to the sample. By subtracting both spectra from the unit spectrum, we obtained the absorbance spectra Asyst(λ) of a such system. This latter was compared with that of an equivalent homogeneous layer presenting the same refractive index and the same volume of absorbent material, indicated Ahom(λ). The gain Q was defined by the relative error between Asyst(λ) and Ahom(λ). This value allowed us to quantify the contribution of the material structuring (relative to a non-patterned system) on the absorption of an incident light flux.
The curve of the gain Q according to the wavelength λ is represented in Fig. 4 . We considered the ultraviolet, visible and near infrared range, i.e., between 200 and 1200 nm. Whatever the wavelength, the gain is positive, its value varying from 2% to 20%. This observation means that the geometry proposed in the scales of the Papilio nireus allows to induce a light trapping effect and to significantly increase its absorption, by comparison to a non-patterned system. Two aspects can be distinguished. First, the absorption of the incident ultraviolet light is favored. Hence, the fluorescent molecules infused throughout the photonic structure of the scales are more excited and the resulting fluorescence is enhanced. Second, the absorption of the incident infrared light is favored. Butterflies being cold-blooded, i.e., their body temperature being not regulated on their own, this parameter is greatly affected by the surroundings temperature. By practicing behavioral tactics such as a shivering of their wings or basking in the sun, they regulate their body temperature and keep it warm. In the case of the Papilio nireus, the numerical predictions show that the peculiar geometry of its scales helps this goal. Its increases the absorption of the infrared light, leading to an increase of the scale temperature and contributing to the heating of the butterfly.
5. Second function of the structure: impact on the emission properties
In a second time, we calculated with the 3D scattering-matrix computational code mentioned above the impact of the natural photonic structure of the Papilio nireus on the emission properties. As previously, we solely considered the system composed by the DBR and the 2D PC. Until now, no study has successfully determined with a great precision the location of the fluorophores and their distribution within the natural structure of the Papilio nireus. This determination requires a deeper biological investigation that is out of the context of this paper. Therefore, the problem was simplified by choosing a basic configuration: an internal planar emitting source placed at mid-height of the 2D PC (as illustrated in Fig. 5(b) ). Another configuration, a point oscillating dipole placed in the host medium, at mid-height of the 2D PC, in the middle of the triangle formed by three cylinders, was also studied. The results are qualitatively similar for both configurations. For the clarity of this discussion, only the results for the first configuration will be presented. It would be more realistic to consider other kinds of sources such as sources distributed in volume or patterned sources. However, at this stage, our computational code does not allow to take into account such sources. The present numerical simulations, realized with an internal planar source inserted in the structure, are a very good first approximation. We set the emission wavelength to 505 nm, the peak emission wavelength of the emission band, as indicated by Vukusic and Hooper. The current density vector was set to (1,0,0). The orientation of this vector is of importance. A deeper discussion will be done in the following of this paper. We calculated the diagram of the emitted flux J according to the light collection direction (defined by the θd and φd angles). This diagram is normalized by a similar calculation performed for an equivalent homogeneous layer, being not-structured. A logarithmic representation is preferred in order to emphasize the contrasts.
The azimuth and polar angular distribution of coupling emission is shown in Fig. 5(a). The red areas are likely associated with the imposed strong ordering of our model. The diagram is not uniform: a high intensity circular spot is perceptible in a normal direction to the sample (θd = 0°, φd = 0°), as well as six oval spots distributed on the periphery of the diagram (θd = 70° to 80°) according to an hexagonal lattice (φd = 30°, 90°, 150°, 210°, 270° and 330°, respectively). The sixfold symmetry of this pattern reflects the hexagonal disposition of the air cylinders in the chitin host medium. In order to demonstrate this point, we performed similar numerical simulations by considering a square disposition of the air cylinders in the chitin medium instead of an hexagonal disposition, all the emission and collection conditions remaining identical. For this configuration, the diagram had a fourfold symmetry pattern (results not shown), with a high intensity spot in a normal direction to the sample and four spots distributed on the periphery of the diagram according to a square lattice. These results indicate that the geometry proposed in the scales of the Papilio nireus allows to induce an enhanced fluorescence process. Enhanced fluorescence means, in this context, angular redistribution by the photonic structure of the light emitted in the external space. The pattern of the photonic structure impacts directly the pattern of the emission diagram.
We performed numerical simulations for various orientations of the current density vector in order to highlight its influence on the optical properties of the system. For the clarity of the paper, we only present the results for two extreme configurations: a (1,0,0) current density vector and a (0,0,1) current density vector, i.e., a vector oriented in the xy-plane of the structure or a vector oriented according to the z-axis, perpendicularly to the plane of the structure, respectively. Figure 6 gives the related azimuth and polar angular distribution of normalized emission (log. scale). For the (1,0,0) configuration, a sixfold symmetry of the pattern was detected. By cons, the pattern obtained for the (0,0,1) configuration is different. In the particular spatial directions where, in the previous configuration, a high intensity spot was perceptible, we have in this configuration a low intensity spot. These peculiar directions are highlighted in the figure by dotted circles. These results highlight the importance of the orientation of the current density vector in the emission properties of the sample. By considering that the current density vector can take any orientation in space, an in-plane orientation (the (1,0,0) configuration, for instance) is statistically more likely than an orientation perpendicular to the plane (the (0,0,1) configuration, for instance). For this reason, we chose the first mentioned configuration. In order to determine with a great accuracy this vector, a deeper biological investigation of the fluorophore would be needed. The knowledge of the fluorophore identity, its fluorescence quantum yield, its intrinsic properties, etc. would be required. This investigation is, at this time, out of our possibilities.
As shown by Vukusic and Hooper, the emission band of the fluorescent molecules in the Papilio nireus is quite broad, extending from 450 nm to 650 nm. We performed numerical simulations as above for various wavelengths in this range, each one giving a diagram comparable to the Fig. 5(a). For each diagram, we integrated the external emitted flux on all collection directions (on all pairs of angles (θd, φd)). A sin θd correction was applicable as the spherical coordinates were used. Figure 7(a) represents the spectral variation of this value. A peak is perceptible between 460 nm and 545 nm, extended on either side by low intensity trays. By comparing this curve with the photonic band structure of the Papilio nireus, we see that this peak lies in the band gap (represented in light grey in the Fig. 7(a)). Hence, the geometry proposed in the scales of the Papilio nireus allows to induce an enhanced fluorescence process, the enhanced fluorescence being not only happen in the spatial domain, but also in the frequency domain. When an emitted ray has a wavelength lying in the band gap, the 2D PC inhibits its propagation in the crystal plane and favors the out-of-plane emission. Figure 7(c) is a related schematic representation. On the contrary, when an emitted ray has another wavelength, its propagation can be in the crystal as in an external direction, out of the crystal plane. Figure 7(d) is a related schematic representation. It is comprehensible that the integrated external emitted flux represented in the Fig. 7(a) is higher in the first configuration (wavelength in the band gap) than in the second one (wavelength out of the band gap). The present results confirm by means of refined and rigorous theoretical predictions the purposes of Vukusic and Hooper. Besides, the geometric parameters of the natural photonic structure seems adapted to the kind of fluorescent molecules present in the Papilio nireus, the band gap overlapping the emission band of the fluorophores (Fig. 7(b)). However, the structure can be compared to a bandpass filter: it enhances the fluorescence, but only for a fraction of the emission band of the fluorophores, excluding the wavelengths below 455 nm and above 545 nm.
Papilio nireus combines two features in its scales: fluorescent molecules and a natural photonic structure composed by a two-dimensional photonic crystal and a distributed Bragg reflector. The 2D PC is formed by an hexagonal arrangement of air cylinders in a solid host medium. The theoretical investigations presented in this paper reveal the bi-functional optical role of this photonic structure. Numerical simulations are based on the scattering-matrix formalism. The results clearly highlight the impact of this peculiar geometry on two aspects. The first aspect to be considered is the absorption of an incident light flux. Indeed, a light-trapping effect was detected in this butterfly for the ultraviolet, visible and near infrared range; increasing significantly the light absorption relative to a non-patterned system. The enhanced ultraviolet absorption allows for enhanced fluorescence because more energy is available for the excitation of involved molecules. The enhanced near infrared absorption allows for butterfly heating. The second aspect is the emission of a luminous flux. Indeed, an enhanced fluorescence process was detected, the enhancing occurring in the spatial domain as well as in the frequency domain. The pattern of the photonic structure directly impacts the angular redistribution of the light emitted in the external space. Moreover, the photonic structure acts as a bandpass filter, increasing the fluorescence only for a fraction of the emission band. This structure seems adapted to the environment in which the butterfly lives.
This bi-functional “biomimetic structure” would have a potential value in optical engineering. For instance, light-trapping properties and enhanced emission properties could be interesting for photovoltaic devices, diodes or sensors.
The authors acknowledge the use of Namur Interuniversity Scientific Computing Facility “Namur-iSCF”, a common project between the Belgian Fund for Scientific Research (F.R.S. – FNRS) and the University of Namur (FUNDP, Belgium). E. Van Hooijdonk is supported as research fellow by the F.R.S. – FNRS. The project was partly funded by the “Actions Concertées” (ARC), Grant No 10/15-033 from the French community of Belgium.
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