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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 5, Iss. 10 — Jul. 19, 2010
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Multi-wavelength study of light transmitted through a single marine centric diatom

E. De Tommasi, I. Rea, V. Mocella, L. Moretti, M. De Stefano, I. Rendina, and L. De Stefano  »View Author Affiliations


Optics Express, Vol. 18, Issue 12, pp. 12203-12212 (2010)
http://dx.doi.org/10.1364/OE.18.012203


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Abstract

The characterization of partially coherent light transmission by micrometer sized valves of marine diatoms is an interesting optical challenge and, from the biological point of view, is of outmost relevance in order to understand evolution mechanisms of such organisms. In the present work, we have studied the transmission of light coming from a monochromator through single valves of Coscinodiscus wailesii diatoms. Incoming light is confined by the regular pore pattern of the diatom surface into a spot of few microns, its dimensions depending on wavelength. The effect is ascribed to the superposition of wavefronts diffracted by the pores’ edges. Numerical simulations help to demonstrate how this effect is not present in the ultraviolet region of the light spectrum, showing one of the possible evolutionary advantages represented by the regular pores patterns of the valves.

© 2010 Optical Society of America

1. Introduction

Evolution has provided, through eras, several animal and vegetal species with very efficient photonic structures [1

1. P. Vukusic and J. R. Sambles, “Photonic structures in biology,” Nature 424, 852–855 (2003). [CrossRef] [PubMed]

]. These micro- and nano-metric architectures appeared mainly in the shape of one-dimensional, two-dimensional or three-dimensional photonic crystals, leading to wavelength-dependent reflection or anti-reflection effects [1

1. P. Vukusic and J. R. Sambles, “Photonic structures in biology,” Nature 424, 852–855 (2003). [CrossRef] [PubMed]

, 2

2. A. R. Parker and H. E. Townley, “Biomimetics of photonic nanostructures,” Nature Nanotech. 2, 347–353 (2007). [CrossRef]

]. Insects, birds, flora and algae, owing to these optical structures, have been able to exploit light and its selection pressure, e.g. in enhancing the efficiency of photosynthetic processes or in evolving non-pigmentary, predator-prey co-developed colouration [3

3. P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, “Quantified interference and diffraction in single Morpho butterfly scales,” Proc. R. Soc. Lond. B 266, 1403–1411 (1999). [CrossRef]

]. The attempts to imitate these structures in opto-electronics and, in general, in fabrication of micro-opto-electromechanical systems (MOEMS), constitute an example of the so-called biomimetics. Nevertheless bio-inspired technology is often frustrated by the limitations of current engineering techniques and by the infeasibility of large-scale production. It is thus becoming clear that there is an advantage in employing the ability of the organisms themselves to manufacture micro- and nano- optical devices [2

2. A. R. Parker and H. E. Townley, “Biomimetics of photonic nanostructures,” Nature Nanotech. 2, 347–353 (2007). [CrossRef]

], in a bottom-up fabrication approach.

Among the organisms which developed complex photonic architectures, particular interest has been recently focused on diatoms. Diatoms are eukaryotic, monocellular microalgae provided with a distinctive shell wall consisting of two hydrated silica valves, interconnected in a structure called the frustule. Frustules present patterns of regular arrays of holes, the areolae, characterized by sub-micrometric dimensions [4

4. E. G. Vrieling, T. P. M. Beelen, R. A. van Santen, and W. W. C. Gieskes, “Nanoscale uniformity of pore architecture in diatomaceous silica: a combined small and wide angle X-ray scattering study,” J. Phycol. 36, 146–159 (2000). [CrossRef]

, 5

5. S. A. Crawford, M. J. Higgins, P. Mulvaney, and R. Wetherbee, “Nanostructure of the diatom frustule as revealed by atomic force and scanning electron microscopy,” J. Phycol. 37, 543–554 (2001). [CrossRef]

]. There are about 105 species of diatoms, whose frustules differ in shape, morphology and size. Traditionally, two main orders have been distinguished within this huge variety of species, namely Centrales (also known as centric diatoms), with a radial symmetry of the valves, and Pennates, with generally bilaterally symmetric valves [6

6. M. De Stefano and L. De Stefano, “Nanostructures in diatom frustules: functional morphology of valvocopulae in cocconeidacean monoraphid Taxa,” J. of Nanosc. and Nanotech. 5, 1–10 (2005).

]. In centric diatoms the radial simmetry is significantly extended to the spatial distribution of areolae throughout the frustule.

In the present work we measured transmission of partially coherent collimated light through a single frustule of a C. wailesii diatom. Variations in the spatial distribution of transmitted light with wavelength have been observed. Furthermore, numerical simulations computed on a digital model of the frustule confirmed these variations and allowed us to study the effect also in the ultraviolet and near infrared spectral regions.

2. Materials and Methods

2.1. Sample details and preparation

In Fig.1 some details of a single valve of C. wailesii frustule are shown. Organic matter has been removed by means of strong acid solutions (see Ref.[6

6. M. De Stefano and L. De Stefano, “Nanostructures in diatom frustules: functional morphology of valvocopulae in cocconeidacean monoraphid Taxa,” J. of Nanosc. and Nanotech. 5, 1–10 (2005).

] for more details). The diameter of the valves can range from 200 to 350 µm in their own environment, but the range becomes much wider (50–550 µm) in culture [15

15. A. M. Schmid, “Intraclonal variation in the valve structure of Coscinodiscus wailesii Gran et Angst,” Beih. Nova Hedw. , 100, 101–119 (1990).

]. In our strain, diameters ranged between 100 and 200 µm, while the average thickness of the wall was of about 1 µm. Every single valve is formed by two co-joined plates. The external plate comprises a complex hexagonal arrangement of hollow pores whose diameter (≃200 nm) is below the visible wavelengths. On the other side, the internal plate of the valve is characterized by hexagonally spaced pores whose diameter range between 1.5 and 1.7 µm and by a lattice constant of about 2.5 µm.

2.2. Experimental Set-Up

The optical set-up used to study the spatial properties of light transmitted by a single frustule of C. wailesii is shown in Fig.2. The light source is the tungsten lamp of a TRIAX 180 monochromator (Jobin Yvon Horiba). The selected wavelengths were, from green to red, 532, 557, 582, and 633 nm. Sparse frustules were deposited on a glass slide, which was mounted on an xyz micrometric translation stage in order to match the position of a single frustule along the optical axis. The transmitted light was collected by a 20× microscope objective (d in figure; NA: 0.3; focal length: 10 mm; working distance: 17 mm; focal depth: 3 µm) and recorded by a CCD camera (e in figure; Leica model DFC300 FX). Also the objective was mounted on a micrometric translational stage; the spatial resolution along the z axis was of 1 µm.

3. Results and Discussion

Figure 1. Scan electron microscope (SEM) images of the outer (a) and inner (b) plates of a single valve of C. wailesii and corresponding details (c and d, respectively). Scale bars are reported.
Figure 2. Experimental set-up for measurements with partially coherent light; a: TRIAX 180 monochromator equipped with a tungsten lamp; b: optical multimode fiber; c: collimating system; d: single diatom frustule on a glass slide; e: 20× microscope objective (NA: 0.3; focal length: 10 mm) f: CCD camera; g: PC for data acquisition and image analysis. The glass slide and the microscope objective are mounted on xyz micrometric translational stages.
Figure 3. Image of a single valve on the focal plane of the microscope objective and corresponding intensity distribution (a); image of the same valve at a distance z = 105 µm from the focal plane of the microscope objective and corresponding intensity distribution (b). Light source: tungsten lamp coupled with a TRIAX-180 monochromator; incident wavelength: 633 nm (see also Fig.4).

In Fig. 4, a strong dependence of z* on the wavelength of the incoming light beam can be noticed. This dependence has already been predicted elsewhere [12

12. L. De Stefano, I. Rea, I. Rendina, M. De Stefano, and L. Moretti, “Lensless light focusing with the centric marine diatom Coscinodiscus wailesii,” Opt. Express 15, 18082 (2007). [CrossRef] [PubMed]

] by means of numerical simulations based on wide-angle Beam Propagation Method (BPM) and represents evidence of the diffractive origin of the phenomenon. What has been defined as the “focusing effect” of the frustule is in fact due to the coherent superposition of the diffracted beams arising from the areolae of the frustule itself. Since every areola gives rise to a diffraction pattern characterized by an angular aperture of the central maximum proportional to λ/d [16

16. M. Born and E. Wolf, Principles of Optics, 6th (corrected) ed. (Pergamon Press, Oxford, 1993).

], where λ is the wavelength of the incoming light and d the diameter of the areola, one can expect that, increasing λ, the divergence of the diffracted beams increases and the zone where they interfere constructively giving rise to light confinement comes closer to the frustule, i.e. z* decreases.

As long as the transversal dimensions of the transmitted spot are concerned (see Fig. 5), a general decrease in the Full Width at Half Maximum (FWHM) of the intensity distribution for z = z* can be observed towards longer wavelengths. In general, the light is confined in a spot whose dimensions are about 18 to 25 times lower respect to the frustule diameter, depending on the incoming wavelength.

Figure 4. Distance z* of maximum intensity of the transmitted spot as a function of the wavelength of the incoming light beam.

4. Numerical simulations

Propagation of light through a single valve of C. wailesii has been studied by means of a wide angle BPM, based on multi-steps Padé-wide angle technique [12

12. L. De Stefano, I. Rea, I. Rendina, M. De Stefano, and L. Moretti, “Lensless light focusing with the centric marine diatom Coscinodiscus wailesii,” Opt. Express 15, 18082 (2007). [CrossRef] [PubMed]

, 17

17. G. R. Hadley, “Wide-angle beam propagation using Padé approximant operators,” Opt. Lett. 17, 1426–1428 (1992). [CrossRef] [PubMed]

]. Calculations have been performed by the BeamPROP Computer-Aided Design (CAD) tool within the RSoft Photonics Suite from RSoft Design Group, (http://www.rsoftdesign.com/).

The geometrical model for the valve represents an evolution respect to the model described in Ref. [12

12. L. De Stefano, I. Rea, I. Rendina, M. De Stefano, and L. Moretti, “Lensless light focusing with the centric marine diatom Coscinodiscus wailesii,” Opt. Express 15, 18082 (2007). [CrossRef] [PubMed]

] since it comprises also the outer plate of the valve, characterized by a more intricate pattern of areolae. The model has been obtained starting from the SEM image of Fig.1: the original greyscale image has been turned into a binary image, after the introduction of a proper threshold, and inserted as input refractive index profile in the CAD ; in particular, the “0” (black) pixels have been associated to the refractive index of air (nair = 1), while the “1” (white) pixels have been associated to the refractive index of silica in the spectral range considered for the simulations ( nSiO2=1.49 for λ = 280 nm, nSiO2=1.46 in the visible range and nSiO2=1.45 for λ = 1 µm [18

18. E. D. Palik, Handbook of optical constants of solids, (Academic Press, 1998).

]). Details of the CAD model used for the calculations are reported in Fig. 6. The valve is regarded as a “sandwich” where the inner and outer plates are divided by a layer of air (see also, for more details, Fig. 4 in Ref.[6

6. M. De Stefano and L. De Stefano, “Nanostructures in diatom frustules: functional morphology of valvocopulae in cocconeidacean monoraphid Taxa,” J. of Nanosc. and Nanotech. 5, 1–10 (2005).

]). The overall thickness of the valve is of 1 µm, while the diameter is of about 100 µm. The calculation grid size was set to 100 nm along all the directions, in order to resolve the details of the structures both in the xy plane and along the z direction. A rectangular distribution for the incoming field has been chosen, in order to better simulate the far-field conditions in which diatoms interact with natural light coming from the sun, but light-confinement effects have been obtained also working with gaussian or fiber-mode field distributions. The use of a rectangular distribution for incoming field is allowed because the coherence length of sunlight incident on the Earth’s surface is of the order of tens of microns [16

16. M. Born and E. Wolf, Principles of Optics, 6th (corrected) ed. (Pergamon Press, Oxford, 1993).

, 19

19. G. S. Agarwal, G. Gbur, and E. Wolf, “Coherence properties of sunlight,” Opt. Lett. 29, 459–461 (2004). [CrossRef] [PubMed]

], i.e. comparable with the frustule diameter. The incoming wavefront encounters the outer plate of the valve first, then the inner, as in an actual diatom in its normal environment.

Figure 5. Transversal dimension of the transmitted spot (expressed as Full Width at Half Maximum (FWHM) of the intensity distribution over a diameter of the frustule for z = z*) as a function of the wavelength of the incoming beam.

In Fig. 7 the spatial distribution of the calculated transmitted power at different wavelengths is reported. It can be noticed how, for λ = 280 nm, and, in general, in the entire UV spectral range (data not shown), there is no significant confinement of light, which is meaningful in terms of the evolutive advantage represented by the areolae patterns since UV radiation is harmful for living organisms and not useful for photosynthesis.

On the other side, in the visible and near-infrared spectral regions (see Fig.7 b-d), light is confined along the z axis and accumulates in a series of spots which are comprised in a divergent cone. These spots are not distinguishable in measurements since we did not make use of a confocal system. Thus contributions from out-of-focus planes are convolved and merge in a cone of light along the optical axis.

It can be noticed how the divergence of the diffracted beams increase passing from ultraviolet to infrared, thus causing the train of pulses to come closer to the diatom frustule (centered at z = 0 µm).

In Fig. 8 the calculated transmitted power distribution over the xy plane at z = z* = 180.5 µm, showing a closer similarity with experimental images, is reported in the case of λ = 633 nm and in correspondance to the first confined light spot which reaches its maximum in intensity. Power distribution over the x direction is also shown. The FWHM (which gives information about the entity of light confinement) equals 1 µm and is lower than the diffraction limit for a lens of the same dimensions of the frustule, expressed as dl = 1.22 · λ · z*/D; in our case λ = 633 nm, z* = 180.5 µm and D = 100 µm is the frustule diameter, giving as a result dl≃1.4 µm. Similar results are obtained also for the other considered wavelengths (see Tab. 1). Experimentally we observed a much wider confinement of light, due to a partial lack of resolution in xy plane.

Figure 6. Geometrical model of a frustule valve used in numerical simulations. The valve lies in the xy plane and the incoming rectangular wavefront travels along the z direction. The outer and inner plates have thicknesses t 1 and t 3 of 360 nm, and are separated by a layer of air 280 nm thick. At the center of the figure, the transverse refractive index profiles lieing in the xy plane for the outer and inner plates and for λ = 1 µm are reported. On the right, details for each plate are reported.

Table 1. Power distribution FWHMs and corresponding diffraction limits for different values of incoming wavelength.

table-icon
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It is fundemental to verify if the light confinement properties of the valve are preserved when it is immersed in its natural environment. In fig. 9 the calculated spatial distribution of transmitted power for a valve immersed in water (n = 1.33) and in cytoplasm (n = 1.35 [20

20. J. Y. Lee, C. W. Lee, E. H. Lin, and P. K. Wei, “Single live cell refractometer using nanoparticle coated fiber tip,” App. Phys. Lett. 93, 173110 (2008). [CrossRef]

]) is shown, at λ = 633 nm. A sketch of the whole frustule, formed by two valves linked by a girdle, is superimposed as dashed line: as it can be seen, light is confined inside the frustule in both cases. As a matter of fact, even if in water and in cytoplasm the indexes contrast is lowered, the “focusing” effect is still present due to its diffractive nature. Furthermore it has to be noticed that, in its environment, the frustule is invested by light in different directions, so that the whole axis of it is most likely involved in light confinement.

Figure 7. Spatial distribution of transmitted power for λ = 280 nm (a), λ = 532 nm (b), λ = 633 nm (c) and λ = 1 µm (d). Valve extends from z = −0.6 µm to z = 0.4 µm. Red arrow points at the direction of propagation of the incoming light. Power associated to the incoming field is set to 0.08 (a.u.).

5. Conclusions

The light-confining properties of frustules from C. wailesii diatoms, already demonstrated elsewhere making use of coherent light coming from a laser source, have been deeply investigated as a function of wavelength in case of partially coherent light, in order to better simulate the interaction between frustules and light in environmental conditions. Numerical simulations allowed to study in detail the power distribution transmitted by a single diatom valve and to predict the possibility to obtain confinement effects under the diffraction limit of a lens with the same dimensions of the considered frustule. Simulations also revealed how this effect does not take place in the UV spectral region, contributing to explain one of the possible evolutive advantages of the photonic properties of diatom frustules. The preservation of light confinement both in water and in cytoplasm has been also verified.

Figure 8. xy power distribution for λ = 633 nm and for z = z* = 180.5 µm (a) and corresponding detail (b); c: power distribution over x direction: the FWHM is lower than the diffraction limit of a lens with the same dimensions of the frustule.
Figure 9. Calculated spatial distribution of transmitted power for a valve immersed in water (a) and in cytoplasm (b), at λ = 633 nm. Dashed line shows the contour of the whole frustule.

References

1.

P. Vukusic and J. R. Sambles, “Photonic structures in biology,” Nature 424, 852–855 (2003). [CrossRef] [PubMed]

2.

A. R. Parker and H. E. Townley, “Biomimetics of photonic nanostructures,” Nature Nanotech. 2, 347–353 (2007). [CrossRef]

3.

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, “Quantified interference and diffraction in single Morpho butterfly scales,” Proc. R. Soc. Lond. B 266, 1403–1411 (1999). [CrossRef]

4.

E. G. Vrieling, T. P. M. Beelen, R. A. van Santen, and W. W. C. Gieskes, “Nanoscale uniformity of pore architecture in diatomaceous silica: a combined small and wide angle X-ray scattering study,” J. Phycol. 36, 146–159 (2000). [CrossRef]

5.

S. A. Crawford, M. J. Higgins, P. Mulvaney, and R. Wetherbee, “Nanostructure of the diatom frustule as revealed by atomic force and scanning electron microscopy,” J. Phycol. 37, 543–554 (2001). [CrossRef]

6.

M. De Stefano and L. De Stefano, “Nanostructures in diatom frustules: functional morphology of valvocopulae in cocconeidacean monoraphid Taxa,” J. of Nanosc. and Nanotech. 5, 1–10 (2005).

7.

T. Fuhrmann, S. Landwehr, M. El Rharbi-Kucki, and M. Sumper, “Diatoms as living photonic crystals,” Appl. Phys. B 78, 257–260 (2004). [CrossRef]

8.

L. De Stefano, I. Rendina, M. De Stefano, A. Bismuto, and P. Maddalena, “Marine diatoms as optical chemical sensors,” Appl. Phys. Lett. 87, 233902 (2005). [CrossRef]

9.

S. Lettieri, A. Setaro, L. De Stefano, M. De Stefano, and P. Maddalena, “The gas-detection properties of lightemitting diatoms,” Adv. Func. Mat. 18, 1257–1264 (2008). [CrossRef]

10.

L. De Stefano, A. Lamberti, L. Rotiroti, and M. De Stefano, “Interfacing the nanostructured biosilica microshells of the marine diatom Coscinodiscus wailesii with biological matter,” Acta Biomat. 4, 126–130 (2008). [CrossRef]

11.

D. K. Gale, T. Gutu, J. Jiao, C.H. Chang, and G. L. Rorrer, “Photoluminescence detection of biomolecules by antibody-functionalized diatom biosilica,” Adv. Func. Mat. , 19, 926–933 (2009). [CrossRef]

12.

L. De Stefano, I. Rea, I. Rendina, M. De Stefano, and L. Moretti, “Lensless light focusing with the centric marine diatom Coscinodiscus wailesii,” Opt. Express 15, 18082 (2007). [CrossRef] [PubMed]

13.

J. Noyes, M. Sumper, and P. Vukusic, “Light manipulation in a marine diatom,” J. Mater. Res. 23, 3229–3235 (2008). [CrossRef]

14.

S. Yamanaka, R. Yano, H. Usami, N. Hayashida, M. Ohguchi, H. Takeda, and K. Yoshino, “Optical properties of diatom silica frustule with special reference to blue light,” J. Appl. Phys. 103, 074701 (2008). [CrossRef]

15.

A. M. Schmid, “Intraclonal variation in the valve structure of Coscinodiscus wailesii Gran et Angst,” Beih. Nova Hedw. , 100, 101–119 (1990).

16.

M. Born and E. Wolf, Principles of Optics, 6th (corrected) ed. (Pergamon Press, Oxford, 1993).

17.

G. R. Hadley, “Wide-angle beam propagation using Padé approximant operators,” Opt. Lett. 17, 1426–1428 (1992). [CrossRef] [PubMed]

18.

E. D. Palik, Handbook of optical constants of solids, (Academic Press, 1998).

19.

G. S. Agarwal, G. Gbur, and E. Wolf, “Coherence properties of sunlight,” Opt. Lett. 29, 459–461 (2004). [CrossRef] [PubMed]

20.

J. Y. Lee, C. W. Lee, E. H. Lin, and P. K. Wei, “Single live cell refractometer using nanoparticle coated fiber tip,” App. Phys. Lett. 93, 173110 (2008). [CrossRef]

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(350.3950) Other areas of optics : Micro-optics
(160.1435) Materials : Biomaterials

ToC Category:
Diffraction and Gratings

History
Original Manuscript: February 19, 2010
Revised Manuscript: April 15, 2010
Manuscript Accepted: April 15, 2010
Published: May 25, 2010

Virtual Issues
Vol. 5, Iss. 10 Virtual Journal for Biomedical Optics

Citation
E. De Tommasi, I. Rea, V. Mocella, L. Moretti, M. De Stefano, I. Rendina, and L. De Stefano, "Multi-wavelength study of light transmitted through a single marine centric diatom," Opt. Express 18, 12203-12212 (2010)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-18-12-12203


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References

  1. P. Vukusic and J. R. Sambles, "Photonic structures in biology," Nature 424, 852-855 (2003). [CrossRef] [PubMed]
  2. A. R. Parker and H. E. Townley, "Biomimetics of photonic nanostructures," Nature Nanotech. 2, 347-353 (2007). [CrossRef]
  3. P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, "Quantified interference and diffraction in single Morpho butterfly scales," Proc. R. Soc. Lond. B 266, 1403-1411 (1999). [CrossRef]
  4. E. G. Vrieling, T. P. M. Beelen, R. A. van Santen, and W. W. C. Gieskes, "Nanoscale uniformity of pore architecture in diatomaceous silica: a combined small and wide angle X-ray scattering study," J. Phycol. 36, 146-159 (2000). [CrossRef]
  5. S. A. Crawford, M. J. Higgins, P. Mulvaney, and R. Wetherbee, "Nanostructure of the diatom frustule as revealed by atomic force and scanning electron microscopy," J. Phycol. 37, 543-554 (2001). [CrossRef]
  6. M. De Stefano and L. De Stefano, "Nanostructures in diatom frustules: functional morphology of valvocopulae in cocconeidacean monoraphid Taxa," J. Nanosc. Nanotech. 5, 1-10 (2005).
  7. T. Fuhrmann, S. Landwehr, M. El Rharbi-Kucki, and M. Sumper, "Diatoms as living photonic crystals," Appl. Phys. B 78, 257-260 (2004). [CrossRef]
  8. L. De Stefano, I. Rendina, M. De Stefano, A. Bismuto, and P. Maddalena, "Marine diatoms as optical chemical sensors," Appl. Phys. Lett. 87, 233902 (2005). [CrossRef]
  9. S. Lettieri, A. Setaro, L. De Stefano, M. De Stefano, and P. Maddalena, "The gas-detection properties of lightemitting diatoms," Adv. Func. Mat. 18, 1257-1264 (2008). [CrossRef]
  10. L. De Stefano, A. Lamberti, L. Rotiroti, and M. De Stefano, "Interfacing the nanostructured biosilica microshells of the marine diatom Coscinodiscus wailesii with biological matter," Acta Biomat. 4, 126-130 (2008). [CrossRef]
  11. D. K. Gale, T. Gutu, J. Jiao, C.H. Chang, and G. L. Rorrer, "Photoluminescence detection of biomolecules by antibody-functionalized diatom biosilica," Adv. Func. Mat.,  19, 926-933 (2009). [CrossRef]
  12. L. De Stefano, I. Rea, I. Rendina,M. De Stefano, and L. Moretti, "Lensless light focusing with the centric marine diatom Coscinodiscus wailesii," Opt. Express 15, 18082 (2007). [CrossRef] [PubMed]
  13. J. Noyes, M. Sumper, and P. Vukusic, "Light manipulation in a marine diatom," J. Mater. Res. 23, 3229-3235 (2008). [CrossRef]
  14. S. Yamanaka, R. Yano, H. Usami, N. Hayashida, M. Ohguchi, H. Takeda, and K. Yoshino, "Optical properties of diatom silica frustule with special reference to blue light," J. Appl. Phys. 103, 074701 (2008). [CrossRef]
  15. A. M. Schmid, "Intraclonal variation in the valve structure of Coscinodiscus wailesii Gran et Angst," Beih. Nova Hedw. 100, 101-119 (1990).
  16. M. Born and E. Wolf, Principles of Optics, 6th (corrected) ed., (Pergamon Press, Oxford, 1993).
  17. G. R. Hadley, "Wide-angle beam propagation using Pad’e approximant operators," Opt. Lett. 17, 1426-1428 (1992). [CrossRef] [PubMed]
  18. E. D. Palik, Handbook of optical constants of solids, (Academic Press, 1998).
  19. G. S. Agarwal, G. Gbur, E. Wolf, "Coherence properties of sunlight," Opt. Lett. 29, 459-461 (2004). [CrossRef] [PubMed]
  20. J. Y. Lee, C.W. Lee, E. H. Lin, and P. K. Wei, "Single live cell refractometer using nanoparticle coated fiber tip," App. Phys. Lett. 93, 173110 (2008). [CrossRef]

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