Ben Payne

Position-dependent diffusion of light in disordered waveguides

Summary form only given. Diffusion is a statistical description of random walk of a classical particle, and the diffusion constant D0 is the only parameter in the diffusion equation. For light as well as for other kinds of waves, this is an approximation, because the interference of partial waves is ignored [1]. Such interference is essential to Anderson localization. Proper account of the interference effects in random samples of finite size [2] and/or with absorption [3] results in spatial variation of the diffusion coefficient D(r) in the self consistent theory (SCT) of localization.To observe position-dependent diffusion, disordered waveguide structures were fabricated with the silicon on insulator wafer (see Fig. 1a). The patterns were written by electron beam lithography and etched in an inductive coupled reactive ion etcher. The waveguides contained 2D random arrays of air holes that scattered light, and the scattering length was varied by the hole size and filling fraction. The waveguide walls were made of photonic crystals that had complete bandgap in 2D, so that light could not escape laterally. However, light will leak out of the plane while being scattered by the air holes. This vertical leakage can be described by an effective absorption or dissipation. The relevant parameters are the diffusive absorption length ȟa0 and the transport mean free path . The localization length ȟ is determined by and the waveguide width W. Light from a CW laser source was injected into the waveguide from one end, and transported through the random medium. Spatial distribution of light intensity on the sample surface was imaged onto a camera by an objective lens. After entering the random medium, light is attenuated due to competing effects of backscattering and dissipation. I(y, z) was integrated along the transverse y-direction to determine the variation of intensity along the axial z-direction (parallel to the waveguide axis).Fig. lb shows the measured light intensity I(z) inside the ensembles of random waveguides of different width W (blue). The values of ξ and ξασ are obtained by fitting the most diffusive sample (W = 60 μm, longest ξ) with SCT (red dashed line) [2,3]. Using these values, SCT successfully predicts I(z) for all other samples. D(z) corresponding to red curves in Fig. lb are plotted in Fig. lc, showing a suppression of diffusion in the middle of the sample with increase ξασ/ξ (decrease of W) as predicted by SCT.

Anderson localization as position-dependent diffusion in disordered waveguides

We show that the recently developed self-consistent theory of Anderson localization with a positiondependent diffusion coefficient is in quantitative agreement with the supersymmetry approach up to terms of the order of 1 /g 0 with g0 the dimensionless conductance in the absence of interference effects and with large-scale ab initio simulations of the classical wave transport in disordered waveguides, at least for g0 0.5. In the latter case, agreement is found even in the presence of absorption. Our numerical results confirm that in open disordered media, the onset of Anderson localization can be viewed as position-dependent diffusion.

Interplay between localization and absorption in disordered waveguides.

This work presents results of ab-initio simulations of continuous wave transport in disordered absorbing waveguides. Wave interference effects cause deviations from diffusive picture of wave transport and make the diffusion coefficient position- and absorption-dependent. As a consequence, the true limit of a zero diffusion coefficient is never reached in an absorbing random medium of infinite size, instead, the diffusion coefficient saturates at some finite constant value. Transition to this absorption-limited diffusion exhibits a universality which can be captured within the framework of the self-consistent theory (SCT) of localization. The results of this work (i) justify use of SCT in analyses of experiments in localized regime, provided that absorption is not weak; (ii) open the possibility of diffusive description of wave transport in the saturation regime even when localization effects are strong.

Classification of Regimes of Wave Transport in Quasi-One-Dimensional Non-Conservative Random Media

Passive quasi-one-dimensional random media are known to exhibit one of the three regimes of transport – ballistic, diffusive or localized – depending on the system size. In contrast, in non-conservative systems, the physical parameter space also includes the gain/absorption length scale. Here, by studying the relationships between the transport mean free path, the localization length, and the gain/absorption length, we enumerate 15 regimes of wave propagation through quasi-one-dimensional random media with gain or absorption. The results are presented graphically in the form of a phase diagram. Of particular experimental importance in an absorbing random medium, we identify three different regimes that bear the signatures of the localized regime of the passive counterpart. We also review the literature and, when possible, assign experimental systems to a particular regime on the diagram.

Effect of evanescent channels on position-dependent diffusion in disordered waveguides

Abstract We employ ab initio simulations of wave transport in disordered waveguides to demonstrate explicitly that although accounting for evanescent channels manifests itself in the renormalization of the transport mean free path, the position-dependent diffusion coefficient, as well as distributions of angular transmission, total transmission and conductance, all remain universal.

Position-dependent Diffusion Coefficient as Localization Criterion in Non-Conservative Random Media

Position-dependent diffusion coefficient is used to distinguish different regimes in wave transport in random media with absorption or gain.

Effect of Evanescent Modes on Conductance Distribution in Disordered Waveguides

We demonstrate that proper account of evanescent modes in wave propagation results in a reduction of transport mean free path whilst preserving the universality of the conductance distribution and its single parameter scaling.

Classification of Regimes of Wave in Non-Conservative Random Media

In search of a criterion of Anderson localization applicable in random media with absorption or gain, we explore the parameter space of the system and identify different regimes in wave transport.