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Coherent Backscattering of Light by an Anisotropic Biological Network

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Coherent Backscattering of Light by an Anisotropic Biological Network Coherent backscattering of light by an anisotropic biological network ∗ Gianni Jacucci1, , Olimpia D. Onelli 1, Antonio De Luca 2,3, Jacopo Bertolotti 4, ∗ Riccardo Sapienza 5, , and Silvia Vignolini 1 Abstract The scattering strength of a random medium relies on the geometry and spatial distribution of its com- ponents as well as on their refractive index. Anisotropy can therefore play a major role in the optimisation of the scattering efficiency both in biological and synthetic materials. In this work, we show that by ex- ploiting the coherent backscattering phenomenon it is possible to characterise the optical anisotropy in the Cyphochilus beetle scales without the need of changing their orientation or their thickness. For this reason, such a static and easily accessible experimental approach is particularly suitable for the study of biologi- cal specimens. Moreover, the estimation of the anisotropy in the Cyphochilus beetle scales might provide inspiration for improving the scattering strength of artificial white materials. I. Introduction Nature, however, provides a different ap- proach that can serve as an inspiration for An object is opaque white when the light the manufacturing of polymeric, thin but still incident on it undergoes multiple scattering opaque white materials. [6, 7, 8] In partic- events before exiting the medium, i.e. when ular, the brilliant whiteness shown by the the object is optically thick. [1] The opti- Cyphochilus beetle is known to be generated cal thickness is defined as the ratio between by multiple scattering of light inside the ex- the physical thickness of an object and the tremely thin scales (' 7 µm thick) that cover transport mean free path (`t), namely the dis- its exoskeleton (Figure 1a-b). [9, 10, 11, 4, 12] tance that light travels before losing informa- The beetle intra-scale structure is composed of tion about its starting propagation direction a nanostructured network of chitin filaments [2, 3]. Commonly, `t is of the order of tens with a filling fraction of around 45%.[13] The of microns in low-refractive index white mate- chitin fibers inside the beetle scales are organ- rials. [4, 5] Therefore, opacity is only achieved ised anisotropically, i.e. mainly oriented par- for relatively large thicknesses (of the order allel to the surface of the scales (Figure 1c). of hundreds of microns) to allow a sufficient This structural anisotropy increases the scat- number of scattering events. tering strength in the orthogonal direction to the scale surface, at expense of the in-plane Gianni0 Jacucci, Dr. Olimpia Onelli, Dr. Silvia Vi- gnolini, Department of Chemistry, University of Cam- scattering, which is not as relevant for the to- bridge, Lensfield Road, Cambridge CB2 1EW, UK; ∗e-mail: tal reflectance of the insect. [12] With such [email protected] morphology and geometry, the beetle achieves Antonio De Luca, Department of Physics, University of a high total reflectance (about 70% over the Calabria, Rende (CS), via Pietro Bucci, 87036, Italy whole visible range) with a thin, lightweight, Jacopo Bertolotti, Department of Physics and Astronomy, and anisotropic network made of low refrac- University of Exeter, Stocker Road, Exeter EX4 4QL, UK tive index material. [4, 13, 12] Riccardo Sapienza, The Blackett Laboratory, Department of Physics, Imperial College London, London SW7 2BW, In the recent years a number of different United Kingdom; ∗ e-mail: [email protected] techniques have been used to characterise 1 Coherent backscattering of light by an anisotropic biological network a b c II. Results and Discussion To characterise light propagation in the Cyphochilus scales, we performed a coherent backscattering (CBS) experiment. We mea- sured the angular resolved light scattered by the sample around the backscattering direc- tion, which shows a characteristic peak pro- Figure 1: Images of the white beetle at different magni- file. [23] The CBS is the Fourier transform fications: a) photograph of the Cyphochilus of the spatial distribution of light exiting the beetle; b) micrograph of the scales organisa- tion; c) SEM image of the cross-section of a sample in the backscattering direction. [3] Cyphochilus scale showing the interconnected This phenomenon is often understood as an network of chitin filaments which is respon- interference effect that originates from the su- sible for the white appearance of the insect. perposition of a large number of two-wave Scale bar: 1 cm for a, 200 µm for b, 1 µm interference patterns from reciprocal waves. for c. [23, 24, 25, 26, 27] These waves have trav- eled the same optical path inside the medium but in opposite directions (Figure 2a) and are therefore phase-related. The resulting CBS in- anisotropic media, for example, spatially re- tensity distribution has a conical shape whose solved reflectance, [14, 15] imaging diffuse width provides a direct measurement of the transmission, [16, 17, 12] spatio-temporal vi- light transport mean free path of a material. sualisation of transmitted light, [18] and co- [3] herent backscattering. [19, 20, 21, 22] As The experimental setup is shown in Fig- of yet, the accuracy in the determination of ure 2b. A collimated laser diode (peak wave- the in-plane and out-of-plane components of length at 635 nm, spot-size of 2.5 mm, and the light transport mean free math in the output power of 1.2 mW) was used as light Cyphochilus beetle scales has been limited by source. The scattered signal was focused, us- the strong thickness dependency of the exper- ing a parabolic mirror, on a 100 µm core fiber imental techniques used. [4, 12] connected to a spectrometer. The angular res- ' In this work, we show that the coherent olution of our setup was 0.25 mrad. To ac- backscattering technique is well suited for quire the CBS line shape, the speckle pattern, studying the scattering properties of biological which occurs due to the high spatial coherence samples, allowing to estimate the anisotropy of the light source, needs to be averaged out. of a system without the need of changing its [26] This was done by placing the sample on orientation and its thickness. Moreover, the a motorised rotation mount whose axis was CBS provides a precise evaluation of the in- the same of the propagation direction of the plane transport mean free path without requir- incoming laser beam. This averaging proce- ing samples with different thicknesses, in con- dure precludes the possibility to investigate a trast with other static and easily accesible tech- potential in-plane, xy, anisotropy. However, it niques. Our experimental results contribute to has been recently shown that the Cyphochilus the understanding of scattering optimisation scales are characterised by an isotropic spec- in the Cyphochilus beetle scales, providing a tral density in the xy plane. [13] For this rea- valuable guide for the development of novel son, our work focused only on the study of an sustainable materials by showing how to ob- out-plane anisotropy. tain a strong optical response whilst using a The enhancement factor of the coherent sig- low-refractive index biopolymer as building nal, i.e. the ratio between the intensity at exact block. backscattering angle and the incoherent back- 2 Coherent backscattering of light by an anisotropic biological network ground, strongly depends on the polarisation. uration, as discussed in Ref. [28]. This is maximised when the single-scattered The measured CBS signal is reported in Fig- photons, which do not have a reciprocal coun- ure 3. The experimental data show a maxi- terpart and therefore contribute only to the in- mum lower than the theoretical value for semi- coherent background, are filtered out. This infinite media of 1 and a rounded top. This de- can be done by acquiring the CBS in the he- viation is a consequence of the small thickness licity conserving channel (HC) (Figure 2). The of the Cyphochilus scales and can be described HC signal was then normalised to the one ac- by the isotropic theory for finite media: [29] quired in a linear non conserving (LNC) config- [ [( ) ( )] − n (n − (n − a) cosh(2z a) (n − (n + a) cosh(2z a) g = e b (bu) e + e + c 3 cos n − a 2 2 a n 2 2 ( ( ) + u ) ( + ) + u u u + sin(bu) − sinh(2z a)+ (a + n)2 + u2 (n − a)2 + u2 e (1) (n − a) cosh((n − a)b − 2z a) − n cosh((n − a)b) + e + (n − a)2 + 2 u ] (n + a) cosh((n + a)b − 2z a) − n cosh((n + a)b) + e (a + n)2 + u2 m q n 1 1 where = cos( ), = 2 (1 + m ), u = dex (ne) of the chitin network, which was es- k`t(1 − m), a = k`t sin(q), B = b + 2ze. The timated by the Maxwell-Garnett’s theory. [34] parameters k, `t, and b are the wave vector, the The expression of ze used in this work, and isotropic transport mean free path, and the op- in the related literature regarding the study of tical thickness, respectively. For semi-infinite the Cyphochilus beetle, is the one derived for media, i.e. b ! ¥, section II reduces to: [29] isotropic systems. This approximation is justi- [ ( )] − a fied by the absence of an analytical formula of 3 a + n 1 − e 2z g = (2) the extrapolation length in anisotropic media. c,semi amn [(a + n)2 + 2] 2 u [35] The reduction of the theoretical maximum in Using a filling fraction of (45 6)%,[13] we finite media is caused by the suppression of calculated that n = (1.22 0.03), R = (0.32 long light paths, which are responsible for the e 0.04), and z = (1.29 0.11). Finally, using formation of the cusp of the CBS profile for e the extrapolation length found from the ex- semi-infinite media.
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