Anisotropic Light Scattering in Nanoporous Materials:  A Photon Density of States Effect

Abstract

Similar to spontaneous emission of photons and inelastic (Raman) scattering, elastic (Rayleigh) scattering of light is controlled by spectraland spatial distribution of photon density of states, DOS (density of electromagnetic modes). However, to date Rayleigh scattering in nanoporous media has not become the subject of discussion in the context of photon DOS effects. In this paper, we consider light scattering in porous materials in the context of spectral, spatial, and angular redistribution of photon DOS in materials with pores whose size and spacing are of the order of light wavelength. The DOS effect results in predictable and controllable modification of scattering and can be purposefully used in certain light harvesting and illumination systems. A possible role of the effect in the cornea of eye is outlined for seeing at grazing incidence of light beams with respect to an eye pupil.Photon density of states, DOS (density of electromagnetic modes) appears in a number of formulas describing emission of photons by matter. First of all, it appears in the Plank's formula for spectral density of equilibrium (thermal) electromagnetic radiation. The density of equilibrium electromagnetic radiation is the product of photon energy, BoseEinstein distribution function, and photon DOS value. Second, photon DOS is known to appear in the expression for the lifetime of excited atoms, molecules, and solids since spontaneous emission of photons is viewed as stimulated emission with stimulating photons coming from zero-point oscillations of electromagnetic field. 1 Third, photon DOS can be found as a factor in formulas describing inelastic (Raman) scattering of photons by molecules and solids. 2 Finally, photon DOS factor is in the expression for the probability of elastic (Rayleigh) scattering of photons. 3 Similar to inelastic scattering, elastic scattering in terms of quantum electrodynamics is considered as virtual excitation of matter with subsequent photon emission. Elementary photon emission is considered as a result of interaction of an excited (actually or virtually) quantum system with electromagnetic zero-field fluctuations. Accordingly, the spontaneous emission rate, the probability of inelastic and elastic scattering of photons, is proportional to photon DOS. In a homogeneous space, the scattering rate W for photons with frequency ω into elementary solid angle dΩ reads where I(ω) is the incident photon flux, V is the matrix element for photon emission, and D(ω) is photon DOS. In a continuous medium, photon DOS D(ω) is expressed by the formula where c is the speed of light in vacuum and n is the refractive index of a medium under consideration (see, e.g., refs 1 and 2 and refs therein for more detail on DOS in various media). Noteworthy, the well-known ω 4 dependence of scattering probability, which is responsible for the blue sky color and sunset/sunrise redness, occurs essentially from the contribution of D(ω) in the form of eq 2. In complex media such as dense sols, matrices with pores, cavities, or inclusions ...

Research Background and Motivation

“…They observed high reflection (*80 %) of incident visible light within the porous plane of anodic porous alumina, and also very high (*98 %) transmission of the light along the pore channel direction. These indicated strong redistribution of photon density of states in the porous plane with a decrease of density; and an increase of density for the pore channel direction [111]. Mammalian eye cornea has a similar porous structure as anodic porous alumina [112], and due to the same reasons above the porous structure removes reflection at the air/cornea interface and provides superior transmission of light into the eye [111].…”

“…Also, by infiltrating metals into the pore channels metallodielectric photonic crystals can be formed with unique optical properties compared with traditional dielectric photonic crystals [105,106,110]. Anisotropic light scattering in selfordered anodic porous alumina in the context of photon density-of-states effects has been experimentally investigated by Lutich et al [111]. They observed high reflection (*80 %) of incident visible light within the porous plane of anodic porous alumina, and also very high (*98 %) transmission of the light along the pore channel direction.…”

“…Mammalian eye cornea has a similar porous structure as anodic porous alumina [112], and due to the same reasons above the porous structure removes reflection at the air/cornea interface and provides superior transmission of light into the eye [111]. In this way, Lutich et al [111] proposed that porous materials like anodic porous alumina can be used in focusing and spatial concentration of waves based on the anisotropic scattering of incident light.…”

Luminescence of Lanthanides from Xerogels Embedded in Mesoporous Matrices

“…4a). This feature is considered regarding anisotropy of the photonic density of states (DOS) in mesoscopic structures with periodically modulated refractive index in 2 dimensions -2D photonic crystals [35]. Anisotropy of DOS in PAA is well refined from the scattering measurement (Fig.…”

“…High-transparency of anodic alumina oxide on the one hand and strong optical anisotropy on the other hand may be the reasons of growing interest to exploit this material as a cage for light-emitting species. Filling the channels of the pores of anodic alumina films with silica [36][37][38], titania [23,[39][40][41][42], alumina [43][44][45] xerogels doped with lanthanide ions Er [37][38][39], Tb [23,38,44] and Eu [35,[40][41][42]45], organic dyes [46], semiconductor nanocrystals [47,48], polymers [ 49,50], quantum dots [51,52], and biological samples [53] was investigated, and strong luminescence of optically active species incorporated in voids of anodic alumina or, probably, in its walls [54,55] was reported.…”