Anderson Localization of Light in the Presence of Non-linear Effects

Abstract

The goal of the thesis presented here, was to further investigate the findings of Dr. Störzer in order to prove the wave nature of Anderson Localization. For this, two different approaches and setups were used.The first was a single photon counting Time-of-Flight setup, but with increased laser power and less noise in the detection part, where band pass filters were used as a crude spectrometer for analysing the spectral distribution of the photons travelling through highly turbid random media consisting of TiO2 particles. A spectral broadening of the light travelling through such samples could be measured, caused by the non-linear response of TiO2. The amount of wave-length shifted photons could be determined as being dependent on the turbidity kl*. Given, that the energy density is high in interference loops causing Anderson localization, which is a common picture for explaining the effect, one can show using the non-linearity of TiO2, that these interference loops become more and more populated when the turbidity of the sample is increased (i.e. kl* is lowered). We varied the turbidity with samples of different TiO2 particles as well as with the same sample, but varying the wavelength of the incident light. Both of these approaches yield the same changes in dependence of kl*. This excludes sample-intrinsic properties (apart from the non-linearity) as being the cause for different responses.Secondly, a new setup with an ultrafast gatable high rate image intensifier and a 16bit-CCD camera was built, which made it possible to directly observe the time evolution of the exiting photon cloud emerging from a highly scattering sample. As theoretical predictions suggest, Anderson localization should be detectable in the time evolution of the lateral confinement of the exiting photonic cloud. We could demonstrate that this is generally correct using a purely diffusive and several non-diffusive samples. Furthermore, we could show that the predicted time evolution of the lateral width sigma^2 proportional to the squareroot of t of the photonic cloud is not observed but rather, that the width behaves linearly, as one would intuitively expect from diffusion theory. Again, by variation of the incident wavelength we could show, that the localizing behaviour is not sample intrinsic but kl*-dependent, as expected for the Anderson transition.