Multiple light scattering in porous gallium phosphide

Abstract

where E i and I i are respectively the field and intensity of light propagating only along the path i. The sum of intensities along all the paths leads to the diffusion result, as in Eq. 1.3. The interference term can not in practice be calculated for a single configuration of the distribution of scatterers, but statistical properties (intensity distributions or spatial correlations for example) can be derived [12-15]. where the ensemble-average of fields from path j i, i * is 0 for independent scatterers. The fields from the time-reversed paths i and i * are equal, provided the time-reversal symmetry is not broken [17]. Time-reversed paths always interfere constructively, and therefore double the intensity of light returning to the origin A, compared to the case when no interference is present. If the point A is not inside the multiple-scattering medium, but is outside, in the far field, the factor 2 increase in intensity of I A→A compared to I A→B leads to the so-called coherent or enhanced backscattering (EBS). In the exact backscattered direction, where the incident and outgoing wave vectors are opposite, the interference of the time-reversed paths is fully constructive and the intensity is twice the diffusion expectation. In practice, the EBS is a cone of light, on top of the diffuse background, as showed in Fig. 1.3b. At exact backscattering (in the center of Fig. 1.3b), a multiple-scattering sample reflects up to twice as much intensity as outside the EBS cone. The EBS cone is characteristic of the multiple scattering of waves, and its width is related to the two length scales involved, and λ respectively, as λ/. The EBS cone is fully derived and described in section 2.6. 1.2.3 Anderson localization The constructive interference of time-reversed paths leads to a more dramatic effect than the EBS. The higher intensity I A→A compared to I A→B means that the probability of a photon

Experimental observation of second-harmonic generation and diffusion inside random media

“…We used eight samples with different values of mean free path. These samples were previously fabricated for other optical experiments [21,22,23].…”

Interplay between multiple scattering, emission, and absorption of light in the phosphor of a white light-emitting diode

“…Multiple light scattering in diffusive photonic media is often studied by total transmission T -also known as diffuse transmission -which is the transmission integrated over all outgoing angles at which light exits from a medium. In general the total transmission contains information on the transport mean free path tr , a crucial parameter that describes multiple scattering of light [9][10][11][12][13][14]. The transport mean free path is the distance it takes for the direction of light to become randomized while light performs a random walk in a scattering medium.…”

“…An improved description of multiple light scattering can be obtained by analytical theories originating from nanophotonics, wherein multiple scattering of light is described from first principles [9][10][11][12]. The advantage of such ab initio models over ray tracing is that one obtains fundamental physical insight, starting from the detailed nanostructure of a sample.…”

“…We present the mean free paths of scattering and absorption, a set of characteristic diffusion parameters that encapsulates the underlying mechanisms from first principles. We compare their values to the thickness of the LEDs' phosphor plate, which is an essential parameter in multiple light scattering [9][10][11]. This represents the first time white LEDs have been studied with a combined experimental and analytical approach from first principles based on diffusion theory.…”

Light transport in anisotropically scattering and absorbing media

“…The blue color of the sky is a popular Scattering of light example of Rayleigh scattering, where blue light is scattered more strongly than other visible wavelengths by atmospheric molecules and aerosols. The scattering cross-section in Rayleigh scattering depends on the inverse fourth power of the wavelength of light σ scat ∝ 1 λ 4 [11]. Geometrical scattering describes the converse case, in which the size of the scatterer is much larger than λ (r ≫ λ), as with macroscopic objects like a windowpane or a bottle.…”