In order to understand guiding light ability, fundamental physical principles on the injection of light into materials structure and propagation of electromagnetic waves must be recalled. Light propagation over long distances is based on the total reflection phenomenon. When a light ray falls on a diopter that is a plan surface separating two different media of different refractive index n₁ and n₂, a part of this beam is reflected and leaves again in the medium of incidence at an angle θ_R equal to that of incidence θ_i, while the remaining part continues its path in the second medium at an angle θ_r different from the angle of incidence, so called refracted beam. The famous law of Snell-Descartes connects these different angles: (1){θi= θRn1sin (θi)= n2sin (θr)

After the diopter, the refracted ray deviates from the normal one with an angle that depends on the two indexes values difference (Figures 1A,B). When the incidence angle exceeds a critical θ_c value (calculated by dividing n₂ by n₁), the refracted light is tangential to the surface: there is no longer refraction and the light is totally reflected (Figure 1C). For this exact angle, it is said the wave is evanescent and propagates by damping rapidly along the surface.

Now for an optical fiber which consists of a core presenting an n_H index slightly higher than n_c the cladding index, when a light wave penetrates into the core at an angle >θ_c it propagates from one end to the other without any loss (Figure 1D). If the incidence angle at the fiber inlet is too high, part of the beam is transmitted through the cladding at each reflection, and the wave is quickly damped (Figure 1E). As is often the case for fibers in the air or immersed, the index of the external environment is lower than that of the cladding, the light can penetrate and spread in the cladding (Figure 1F), so called “cladding modes.” Optical fibers are characterized by their numerical aperture (N.A) that define light cone acceptance of the fiber, where the critical angle is related to the indexes of the core and the cladding by: (2)N.A=sin θc = nH2−nC2

If a ray of light penetrates the fiber by its cone, then it will be guided by internal total reflection, otherwise, it will not be guided.

We shall also briefly recall the fundamental principles of photonics and show how it differs from wave optics. As the name suggests, photonics is the art of manipulating photons. We therefore use the corpuscular model of light, established by Einstein and Planck in the early twentieth century. In this model light is a flux of particles called photons characterized by their energy E, spin S, and wave vector k. The wave vector is related to the momentum that contains all information on the direction of propagation. Well-known relations relate these quantities to the different characteristics of the electromagnetic field in the wave model: (3){E=hνk= 2πλ where ν is the frequency of the wave and λ its wavelength. The spin is connected to the circular polarization of the wave, but we will not use this quantity in these reminders.

In an interaction between light and matter, matter is characterized by its complex index (4)N=n−ikm where n is the refractive index of the material. The imaginary part k^m will be considered as negligible in our purpose. In periodically structured materials also called “photonic crystals” (Johnson et al., 1999; Johnson and Joannopoulos, 2001) a proper way to deal with, is to consider the periodic material as a particle of a lattice constant “a” and a wave vector |K_a| = 2π/a. In the same way, a wave of spatial period λ can be represented as a particle (photon) of wave vector |k| = 2π/λ. The interaction between these two particles is then treated as an elastic shock satisfying the conservation principles of energy, momentum, and angular momentum. Quantum mechanics shows that momentum exchanges are quantified and occur with K multiples. An incident photon of wave vector k will emerge from the structure with a wave vector k′ such that: (5)k−k′= ± nKa

In linear optics, k and k′ having the same modulus, this relation (5) allows an easy diffraction wave direction determination. Moreover, each time |k| is a multiple of |K_a| there is an exchange of momentum where light can no longer propagate in the structure and it is totally reflected. The consequence is the appearance of forbidden frequency bands whose width depends on the contrast of the index of the materials. This mechanical approach of the light-matter interaction allows the diffractive and interferential phenomenon explanation.

Among the entire diatom studied, material scientists have focused on Coscinodiscus species, probably because of their relatively large cell size in the range of 100–200 μm width. Coscinodiscus present a highly structured frustule not only in two dimensions but also in 3-D (Sumper, 2002; Sar et al., 2008; Romann et al., 2015a,b; Aitken et al., 2016; Xing et al., 2017). The valve consists of three overlapping silica layers; the external side named cribrum, it includes smaller porous silica connections called cribellum and finally a third internal layer named foramen. The cribrum is connected to the foramen by silica walls named areola (Figure 3). The areola shows a honeycomb-like structure whereas foramen displays a hexagonal array of circular pores. More, foramen holes are aligned at the same time with the hexagonal pattern of areola and cribrum pores. It is also believed that the formation of these patterns is the result of a self-organized phase separation process (Sumper, 2002). There is no doubt that such porous biosilica nano-structured patterns have been found to be very interesting for optics and photonics investigations.

From an optical point of view two features are important to consider: the physical dimension of the periodic structure (number of porous silica layers, thickness, and holes diameters) and the refractive index contrast made by the complementarity of silica (refractive index n ≈ 1.45) and air pores (n = 1) in the visible range. Indeed, most studies have been performed from purified materials and in air conditions, in order to ensure a relatively good refractive index contrast needed to enable and quantify some optical properties (i.e., light diffraction through silica/air patterns). The scale of holes, of specific layers should be in the order of light wavelengths, which then allow interaction with incoming wavelengths whether diffracting, scattering or guiding them. In addition, some diatom valves, such as the one from Coscinodiscus, present a periodic pattern of holes in one directional slab (alternation of slica/air holes) resembling to a slab waveguide photonic crystal. Periodicity and porosity in the structure enable light-frustule interaction and can be regarded as particle (photon)-particle (matter) interaction as described in the theoretical part before, so then incoming wavelengths can be diffracted, scattered, or guided.

The frustule of the diatom can be considered as a nano-structured biosilica shell that can act as a photonic crystal because of its hierarchical structure, which enable to envision several applications as for example micro-lenses, optical filters, and waveguides. Table 1 summarizes most of recent studies reported in literature on the optical properties of diatoms frustules.

Light concentration and focusing ability of centric frustules was first studied for Coscinodiscus wailesii by illuminating a single valve by a red laser beam. It was demonstrated that the initial beam diameter of 100 μm was reduced about 12 times (~ 10 μm diameter) at a distance around 104 μm from the valve position (De Stefano et al., 2007). This lens behavior was attributed to a coherent superposition of the transmitted unfocused wave fronts through the quasi-regular areolae of the valve. In 2010, it was further suggested that the light confinement could be attributed to the regular pore pattern and the superposition of diffracted wave fronts (De Tommasi et al., 2010). However, it was also shown for C. wailesii valve that the focusing distance from the reference's valve position (named z^*) is wavelength dependent, where by illuminating with laser beam of 532, 557, 582, and 633 nm wavelengths result in the focused distances at 130, 115, 110, and 105 μm, respectively (De Tommasi et al., 2010). Furthermore, similar focusing behavior was shown for the centric single valve of Arachnoidiscus sp. where a 633 nm laser beam was confined at 163 μm from the valve (Ferrara et al., 2014).

These results suggest that light propagation through the valve doesn't only depend on the interaction with the silica itself but likely on the spatial distribution of the pores in the periodic structure, therefore centric valve can be considered as multifocal lens. Multifocal lens and waveguide ability by confocal hyper-spectral imaging was investigated for two centric diatoms Cosinodiscus centralis and C. wailesii, it was shown, at several wavelengths (485, 535, 625, and 675 nm), that multiple light cones were transmitted through the centric valve (Romann et al., 2015a,b). These authors also shown that light convergence depends on the valve orientation, where the intensity of transmitted light decreases strongly when the incident light illuminate the internal side of the valve (i.e., the foramen side), whereas the light intensity increases upon illumination of external side (i.e., the cribrum side). Furthermore, tilting the incident light of 10° doesn't change the concentration behavior (Romann et al., 2015a,b). All of these reported strengthen the light focusing ability of valves from centric species.

A recent study by Chen et al. highlighted the light trapping effect of Cosinodiscus sp. species in photovoltaic application (Chen et al., 2015). For this purpose, Coscinodiscus sp. valves were deposited by floating assembly method on a 50 nm layer of low band-gap polymer PTB7:PC₇₁BM photovoltaic active material. Absorption spectra of polymer coated diatoms sample showed a broadband enhancement (between 400 and 700 nm) estimated to be about 28% comparing to diatoms free sample. Moreover, in the same study, RCWA and FDTD simulation methods were applied to evaluate transmitted light behavior over the active layer. Results suggested that placing diatoms internal plate faced to the top of the PV active layer enhances the absorption efficiency by a factor of 1.41 from 380 to 800 nm. In addition, it was shown that this enhancement effect is the combination of the enhancement contribution by each separated layer in the valve's structure (Chen et al., 2015).

The light focusing, guiding, and trapping ability of frustules described above highlight the photonic crystal behavior of silica shells. T. Fuhrmann et al. were the first to perform band diagram simulations for valve and girdle bands of a centric species Cosinodiscus granii (Fuhrmann et al., 2004). Generated crystal photonics modes depend on the periodicity of the structure (lattice constant of each silica grid) the slab thickness and the incident wavelength. For C. granii valve and girdle bands influence incident light by coupling it into waveguides with distinct photonic crystal modes, for example red light was shown to be coupled in the valve but not in the girdle. It is also believed that to be able to exhibit a complete 2-D photonic crystal band-gaps, a refractive index contrast in the material of about 2 is needed (Knight, 2003). Kieu et al. reported the optical properties of a C. wailesii valve fixed on the top of an optical fiber by the external valve's side, by irradiating with coherent supercontinuum broadband laser (400–1,700 nm) a region of ~20 μm (Kieu et al., 2014). Then they studied the diffracted and transmitted light through the valve as a function of the lattice constant in the periodic structure. When irradiated by wavelengths at different angles, the hexagonal pattern generated colorful transmitted patterns. As a consequence, a white spotlight was observed on the screen without the valve in the setup, while changing the irradiated spot area on the valve changed its color. In addition, it was shown that the hexagonal colorful patterns resulted from the interaction with the periodic structure (Kieu et al., 2014).

All the above-mentioned studies were performed with frustules from centric diatoms, therefore with radial symmetry, so what about cylindrical frustules? Recently, the photonic crystalline characteristics of the cylindrical frustule of the diatom Melosira variance were reported (Yoneda et al., 2016). Clean frustules were studied with a microfiber spectroscopic method. The frustule was put on a micromanipulator and illuminated by a 10 μm sophisticated fiber optic end connected to a 300 W Xe lamp (300–1,100 nm) and transmitted light was collected and analyzed with a spectrometer. This method showed a fine space resolution due to the deployed micro-scale, which make it suitable to study the photonic crystallinity. When a frustule was irradiated through its internal side a transmittance valley was observed between 400 and 500 nm, while when it was irradiated perpendicular to the silica side wall, no particular valleys was observed. The authors concluded that transmitted spectra observed were related to the periodicity of the refractive index in the structure, and that the photonic crystalline characteristics assist light absorption but depending on the orientation (Yoneda et al., 2016).

Frustules have also been investigated for their capability in protecting the cells against harmful wavelengths and excessive light intensities. In other word, acting as optical filters. It is known that diatoms use blue and red wavelengths for photosynthesis, so excess supply of blue light might generate active oxygen molecules that are dangerous for the living cell. It was proposed that the ordered porous silica shell might protect from dangerous UV and excessive wavelength intensities (Ellegaard et al., 2016).

Using Melosira varians frustules it was shown that the transmission of incident light was principally dependent in the wavelength, with enhanced transmission of red light and absorption in the blue range (Yamanaka et al., 2008). Such filtering behavior was also shown for circular valve from Arachnoidiscus sp. for which green and red wavelengths were shown to be more concentrated than blue light (Ferrara et al., 2014). In addition, in the case of UVB light it was shown that the light spot was very weak, and far away from the valve. These results were consistent with simulations (Ferrara et al., 2014).

A distinctive optical feature, photoluminescence (PL), was also observed with frustules. When porous biosilica was irradiated by UV wavelengths it emitted one or more PL peaks in the visible spectral region (Yoon and Goorsky, 1995; Cullis et al., 1997). Scientists investigated such features and their potential applications, for example in gas detection (Table 2). Photoluminescence responses of Thalassiosira rotula valves were examined when exposed to several gases and volatiles substances. Frustules irradiated by a He-Cd laser (325 nm) showed a multiband PL (between 450 and 690 nm) that was attributed to oxidized silicon nanocrystals (533 nm), porous silicon (609 nm), and hydrogenated amorphous silicon (661 nm). As a result, valves PL were quenched with electrophilic gases while they were enhanced for nucleophilic ones (De Stefano et al., 2005; Bismuto et al., 2008). Furthermore, PL of T. rotula frustules was quenched when exposed to NO_2(g) flux, showing a high sensitivity in the order of sub-ppm level that it is strongly dependent on the structure, porosity, and gas nature (Bismuto et al., 2008). PL properties of the frustules from other centric and pennate species (T. rotula, Cosinodiscus. Wailesii, and Cocconeis scutellum) were also demonstrated, and high gas detection sensitivity was shown at room temperature (Setaro et al., 2007).

Photoluminescence was also investigated for chemically modified diatoms frustules. Townley et al. report a study on nickel sulfate modified C. wailesii frustules. When irradiated with a He-Cd laser (442 nm), intact frustules exhibit a broad PL peak (500–650 nm) while those growing with NiSO₄ quenched the PL (Townley et al., 2007). Photoluminescence of chemically modified frustules have been investigated, for medical purposes, by fixing antibodies on the silica shells. Antibodies doped frustules were irradiated by 325 nm laser's wavelength, which show a high sensitivity in the order of 1.2 nm.μm⁻¹ and detection limit around 100 nmol.L⁻¹ (De Stefano et al., 2009). Recently, frustules from the pennate diatom Psammodictyon panduriforme were investigated under 325 nm laser excitation. Frustules showed two emission peaks at 417 and 534 nm that were considered as radiative luminescence generated by oxygen-vacancy defects in the structure (Camargo et al., 2016). However, under pulse laser excitation, a single narrow emission peak was observed near 475 nm. This result was interpreted as the consequence of a putative quantum confinement effect due to the mesoporous silica and the quasi-regular pores in frustules structure (Camargo et al., 2016).

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.