In this work, we report on the light focusing ability exploited by the microshell of a marine organism: the Coscinodiscus wailesii diatom. A 100 µm spot size of a red laser beam is narrowed up to less than 10 µm at a distance of 104 µm after the transmission through the regular geometry of the diatom structure, which thus acts as a microlens. Numerical simulations of the electromagnetic field propagation show a good qualitative agreement with the experimental results. The focusing effect is due to the superposition of the waves scattered by the holes present on the surface of the diatom valve. Very interesting applications in micro-optic devices are feasible due to the morphological and biological characteristic of these unicellular organisms.
© 2007 Optical Society of America
Integrated optical components often require materials with regularly repeating 2-D and 3-D structures with features below the micrometer size range which are difficult to fabricate by standard technologies1. On the other hand, biological organisms can exhibit ordered geometries and complex photonic structures which sometimes overcome the best available man-made products2–. Diatoms are microalgae with a peculiar cell wall made of amorphous hydrated silica valves, reciprocally interconnected like a Petri dish in a structure called “frustule”. The valve surfaces exhibit specie-specific patterns of regular arrays of holes, called “areolae”. The diameter of the areolae can range from a few hundreds of nanometers to a few microns and can be circular, polygonal or elongate4. The forming of the frustules and their patterns can be described by the self-organised phase separation model5–6. Despite of the high level of knowledge on the genesis and morphology of diatom frustules, their functions are not completely understood. Herewith we are showing that the silica frustule of a centric marine diatom, Coscinodiscus walesii, has unsuspected optical properties: we found that the diatom valve can focus an incoming laser light in a small spot of few microns. Our experimental results and numerical calculations indicate that this phenomenon is due to a coherent superposition of the light scattered by the areolae7.
When observed by scanning electron microscopy, the valves of the C. walesii strain we studied range between 150 µm and 200 µm (Fig. 1a) and have an average thickness of approx. 700 nm (Fig. 1b, down). The valve surface exhibit almost perfect hexagonal patterns of areolae, with a lattice constant (nearest neighbour center-to-center) of 2600–2700 nm, as it can be seen in Fig. 1b (top). Before scanning electron microscopy and optical characterisation, the diatoms have been cleaned by their organic matter by washing them in a strong acid solution, and then deposited on a glass slide. A detailed description of the cleaning process can be found in ref. 8. The areolae arrays of C. walesii are arranged on the diatom surface with a radial symmetry which is very similar to the one of some man-made optical devices, such as photonic crystal fibres or phase-locked arrays of optical fibres or lasers: the uncommon features of light propagation through these regular structures don’t only depend on the interaction with the matter but also on the spatial order of the periodic lattice7, 9. We have therefore investigated the light transmission characteristics of a single valve, by using the experimental set-up shown in Fig. 2. We have selected the central section of a diode laser beam (@λ=785 nm, elliptical spot size of approximately 2 mm) by a 100 µm pinhole placed at 1 cm from the glass slide to fit the valve dimension. The transmitted signal is collected by a 20x objective, with a numerical aperture of 0.49, and recorded by a CCD camera (Leica DFC300 FX).
We have verified that the optical setup (pin-hole, glass slide and objective) without the diatom does not change the features of the laser light: the beam profile divergence and its intensity change less than 5 % over a distance of 250 µm from the focal plane of the diatom. The measurement starts when the diatom surface is in the objective focal plane; then, we have registered the transmitted light spot image by moving the objective up to 200 µm by steps of 4 µm. We have found, quite surprisingly, that the valve acts as a microlens: the laser beam is highly focused at an output distance from the valve surface ranging from 100 µm to 110 µm; then the light beam diverges. The beam is confined in 8.1 µm (value of the full width at half maximum) in its narrowest point, resulting in a spot size about 12 times smaller than the pinhole diameter (see Fig. 3(a) and 3(b)). The light focusing occurs at the centre of the diatom valve in correspondence of the uniform zone, free of areolae, which is about 15 µm in size.
Even if it’s possible to demonstrate that the diatom valve could act as a guiding structure and hence support a guided mode in this defect10, we attribute this focusing effect to a coherent superposition of the unfocused wave fronts coming from the approx. 600 areolae of C. walesii valve which are quasi-regularly disposed on the diatom surface11: the light scattered by the holes on the diatom surface interferes constructively only at a fixed distance, which also depends on the holes spatial disposition, determining a well-defined spotlight. This lensing effect is in a manner similar to the Talbot effect that can be observed in periodic and quasi-periodic diffraction arrays12, 13. The difference between the two systems is that while there exists one degenerate Talbot distance (equal to 31/2 tx/λ2 for the perfect hexagonal arrays, where tx is the lattice constant) for periodic gratings, in the quasi-periodic case, such as for the diatoms, the self-imaging distance changes for different orders of diffraction and wavelengths. The result is that the reconstruction of a non perfectly regular arrays of holes is a complex process which is the sum of a large number of reconstructions at different heights from the array surface giving to the existence of a well defined focus at a well defined distance. In this view, it is also important to take into account the influence of the numerical aperture of the objective which corresponds to a gathering light angular semi-cone of 30°. In the Fraunhofer regime (N=a2/λz<<1, where a is the radius of the areola and z the focusing distance) only the first two orders of diffraction14 are captured by the objective, so that the spot intensity would probably change if the numerical aperture used is different.
Moreover, the focusing effect found gets also a contribute from the diffraction from a round obstacle, as in the well-known case of the Poisson-Arago spot15 but it cannot be completely ascribed to it. The intensity of this bright spot, which appears in the shadow behind a circular obscuration, can be exactly evaluated in the frame of the Fresnel-Kirchoff or the Rayleigh-Sommerfeld diffraction models16. The intensity value of the Poisson-Arago spot increases continuously with the distance and saturates at z/a≈4, where a is the radius of the obstacle. In the case of the diatom observed this would mean a focusing distance of about 300 µm, which is outside the range investigated. In Fig. 4 we report the intensity of the spot center, both experimental and numerical data, we observed as a function of the distance compared to the intensity of the Arago spot having the same radius of the diatom: the light converges with a complex modulation which cannot be simply fitted by the Rayleigh-Sommerfield diffraction theory. The numerical simulations based on our assumption qualitatively reproduce the behaviour of the experimental data. In order to calculate the optical properties and analyze the light propagation through a real sample of diatom and not just exploiting a model of this organism, we have digitalised the electron microscope image of the tested valve and used the measured geometrical parameters to simulate the optical transmission through it. The development of a full vectorial model, like the finite difference time domain method, of the electromagnetic field propagation through the 3-D structure of the diatom is far beyond the scope of this work since it requires a very strong calculus effort. To overcome these difficulties and have a quite reliable picture of the effect, the numerical calculations have been performed by a wide angle Beam Propagation Method, based on multi-steps Padè-wide angle technique17–18.
The calculations grid is composed by 2000×2000×50 points and a (1, 1) Padè coefficient has been adopted in order to investigate the beam propagation with a divergence of about 30°. The valve refractive index value, used in numerical simulations, has been estimated by reflectivity measurement to be 1.43, in accordance to the values elsewhere reported19. The inner structure of the diatom valve has been taken into account as a homogeneous layer of amorphous silica with proper thickness (400 nm), since the holes size (20–30nm this ultrastructure is well below the light wavelength. We have calculated the light intensity distribution on the diatom surface and reported the colour plot in Fig. 5: from this picture is well evident that the highest contribution to the transmitted intensity comes from the valve holes. The numerical results of the focusing simulation, plotted in Fig. 3(a) as black curves, are in a qualitative agreement with the experimental ones (red curves in Fig. 3(a)): even if the maximum focusing effect is found at the same distance by the focal plane, the full widths at half a maximum differ by a factor of three. This discrepancy can be attributed to some approximations we used in the geometrical model of the diatom: we have not take into account the slight curvature of the diatom frustule, so that the diffraction contribution of the areolae next to the valve edge could be not exactly estimated. Moreover, the inner structure of the diatom valve, which we have approximated as a homogeneous layer, can produce light losses that enhance the spreading of the focused beam. If the focusing effect really depends on the interference from the light scattered by the areolae, the focalisation distance would behave as the diffraction angle which is proportional to 1/λ. In Fig. 6 we have reported the calculated focusing distances, as function of the incoming light wavelength, which are perfectly fitted by a rationale curve (i.e. 1/λ curve) thus clearly suggesting that the diatom focusing is a holes diffraction-driven effect.
The discovery of the C. walesii focusing features really opens new opportunities in the field of microlenses and of diatom nanotechnology in general. Diatom based microlenses could be more flexible than those fabricated with usual technologies20, due to the intrinsic properties of their frustules: silica atoms can be substituted with other species without losing the structure21, and since diatoms decrease in size through the succeeding generations, in a short period they can scale to nano-dimensions preserving symmetries and other characteristics4.
Furthermore, the diatoms have a very high reproduction rate that means lot of samples with their precise and reproducible nanometre scale features at very low production cost. The valves are easy to handle by standard micro-needles or micro-tips since geometry and material properties can make diatom frustules mechanically very strong, hence resistant to large physical forces22. Single valves could fit the top of an optical fibre to make a lensed fibre without modifying the glass core or, similarly, they could match the output of a vertical cavity surface emitting laser23. Other photonic micro-components which could benefit of diatoms focusing ability could be semiconductors and organic light emitting devices and in general all other optical micro-arrays. The focusing ability of the diatom’s frustule could also have a biological function, which should of course be deepened in following researches. This mechanism could provide an effective way to concentrate the light with biologically useful wavelengths inside the diatom’s protoplasm; indeed it is known that light intensity causes a redistribution of the chloroplast away from the frustule to the centre of the cell19.
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