Effect of absorption on the wave transport in the strong localization regime

Nonunitary Scaling Theory of Non-Hermitian Localization

Non-Hermiticity can destroy Anderson localization and lead to delocalization even in one dimension. However, a unified understanding of non-Hermitian delocalization has yet to be established. Here, we develop a scaling theory of localization in non-Hermitian systems. We reveal that non-Hermiticity introduces a new scale and breaks down the one-parameter scaling, which is the central assumption of the conventional scaling theory of localization. Instead, we identify the origin of unconventional non-Hermitian delocalization as the two-parameter scaling. Furthermore, we establish the threefold universality of non-Hermitian localization based on reciprocity; reciprocity forbids delocalization without internal degrees of freedom, whereas symplectic reciprocity results in a new type of symmetry-protected delocalization.

Maximal absorption regime in random media

Efficient optical energy transfer is key to many technologies, ranging from biosensing to photovoltaics. Here, for the first time we show that by introducing a random medium with appropriate filling factor, absorption in a specific volume can be maximized. Using both numerical simulations and an analytical diffusion model, we identify design rules to maximize absorption in the system with different geometrical and scattering properties. By combining a random medium with an open photonic cavity, we numerically demonstrate a 23-fold enhancement of the absorbed energy. We also show how absorption as high as 99% can be reached in a device as thin as 500 μm for normal incidence illumination. Finally, our data indicate that introducing a non-absorbing random medium into a light trapping system for thin solar cells can enhance absorption of energy by a factor of 2.2. This absorption enhancement, caused by the random medium, is broadband and wide-angle and can help design efficient solar cells, light trapping devices, biosensors and random lasers.

Giant fluctuations of local magnetoresistance of organic spin valves and the non-Hermitian 1D Anderson model

Motivated by recent experiments, where the tunnel magnetoresitance (TMR) of a spin valve was measured locally, we theoretically study the distribution of TMR along the surface of magnetized electrodes. We show that, even in the absence of interfacial effects (like hybridization due to donor and acceptor molecules), this distribution is very broad, and the portion of area with negative TMR is appreciable even if on average the TMR is positive. The origin of the local sign reversal is quantum interference of subsequent spin-rotation amplitudes in the course of incoherent transport of carriers between the source and the drain. We find the distribution of local TMR exactly by drawing upon formal similarity between evolution of spinors in time and of the reflection coefficient along a 1D chain in the Anderson model. The results obtained are confirmed by the numerical simulations.

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.

Effect of size disorder on the optical transport in chains of coupled microspherical resonators

We investigate statistical properties of collective optical excitations in disordered chains of microspheres using transfer-matrix method based on nearest-neighbors approximation. Radiative losses together with transmission and reflection coefficients of optical excitations are studied numerically. We found that for the macroscopically long chain, the transmission coefficient demonstrates properties typical for a one dimensional strongly localized system: log-normal distribution with parameters obeying standard scaling relation. At the same time, we show that the distribution function of the radiative losses behaves very differently from other lossy optical systems. We also studied statistical properties of the optical transport in short chains of resonators and demonstrated that even small disorder results in significant drop of transmission coefficient acompanied by strong enhancement of the radiative losses.

Asymptotically exact probability distribution for the Sinai model with finite drift

We obtain the exact asymptotic result for the disorder-averaged probability distribution function for a random walk in a biased Sinai model and show that it is characterized by a creeping behavior of the displacement moments with time, <x(n)>∼t(μn), where μ<1 is dimensionless mean drift. We employ a method originated in quantum diffusion which is based on the exact mapping of the problem to an imaginary-time Schrödinger equation. For nonzero drift such an equation has an isolated lowest eigenvalue separated by a gap from quasicontinuous excited states, and the eigenstate corresponding to the former governs the long-time asymptotic behavior.

Suppression of Anderson localization in disordered metamaterials

We study wave propagation in mixed, 1D disordered stacks of alternating right- and left-handed layers and reveal that the introduction of metamaterials substantially suppresses Anderson localization. At long wavelengths, the localization length in mixed stacks is orders of magnitude larger than for normal structures, proportional to the sixth power of the wavelength, in contrast to the usual quadratic wavelength dependence of normal systems. Suppression of localization is also exemplified in long-wavelength resonances which largely disappear when left-handed materials are introduced.

Localization-delocalization transition in non-hermitian disordered systems

Using the supersymmetry technique, we study the localization-delocalization transition in quasi-one-dimensional non-Hermitian systems with a direction. In contrast to chains, our model captures the diffusive character of carriers' motion at short distances. We calculate the joint probability of complex eigenvalues and some other correlation functions. We find that the transition is abrupt and it is due to an interplay between two saddle points in the free energy functional.

High-frequency dynamics of wave localization

We study the effect of localization on the propagation of a pulse through a multimode disordered waveguide. The correlator <u(omega(1))u(*)(omega(2))> of the transmitted wave amplitude u at two frequencies differing by delta omega has for large delta omega the stretched exponential tail proportional to (- square root[tau(D)delta omega/2]). The time constant tau(D)=L(2)/D is given by the diffusion coefficient D, even if the length L of the waveguide is much greater than the localization length xi. Localization has the effect of multiplying the correlator by a frequency-independent factor exp(-L/2 xi), which disappears upon breaking time-reversal symmetry.