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Transmission eigenchannels are building blocks of coherent wave transport in diffusive media, and selective excitation of individual eigenchannels can lead to diverse transport behavior. An essential yet poorly understood property is the transverse spatial profile of each eigenchannel, which is critical for coupling into and out of it. Here, we discover that the transmission eigenchannels of a disordered slab possess localized incident and outgoing profiles, even in the diffusive regime far from Anderson localization. Such transverse localization arises from a combination of reciprocity, local coupling of spatial modes, and nonlocal correlations of scattered waves. Experimentally, we observe signatures of such localization despite finite illumination area. Our results reveal the intrinsic characteristics of transmission eigenchannels in the open slab geometry, commonly used for applications in imaging and energy transfer through turbid media.
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The optical memory effect has emerged as a powerful tool for imaging through multiple-scattering media; however, the finite angular range of the memory effect limits the field of view. Here, we demonstrate experimentally that selective coupling of incident light into a high-transmission channel increases the angular memory-effect range. This enhancement is attributed to the robustness of the high-transmission channels against perturbations such as sample tilt or wavefront tilt. Our work shows that the high-transmission channels provide an enhanced field of view for memory effect-based imaging through diffusive media.
Transmission eigenchannels and associated eigenvalues, that give a full account of wave propagation in random media, have recently emerged as a major theme in theoretical and applied optics. Here we demonstrate, both analytically and numerically, that in quasi one-dimensional ($1$D) diffusive samples, their behavior is governed mostly by the asymmetry in the reflections of the sample edges rather than by the absolute values of the reflection coefficients themselves. We show that there exists a threshold value of the asymmetry parameter, below which high transmission eigenchannels exist, giving rise to a singularity in the distribution of the transmission eigenvalues, $rho({cal T}rightarrow 1)sim(1-{cal T})^{-frac{1}{2}}$. At the threshold, $rho({cal T})$ exhibits critical statistics with a distinct singularity $sim(1-{cal T})^{-frac{1}{3}}$; above it the high transmission eigenchannels disappear and $rho({cal T})$ vanishes for ${cal T}$ exceeding a maximal transmission eigenvalue. We show that such statistical behavior of the transmission eigenvalues can be explained in terms of effective cavities (resonators), analogous to those in which the states are trapped in $1$D strong Anderson localization. In particular, the $rho ( mathcal{T}) $-transition can be mapped onto the shuffling of the resonator with perfect transmittance from the sample center to the edge with stronger reflection. We also find a similar transition in the distribution of resonant transmittances in $1$D layered samples. These results reveal a physical connection between high transmission eigenchannels in diffusive systems and $1$D strong Anderson localization. They open up a fresh opportunity for practically useful application: controlling the transparency of opaque media by tuning their coupling to the environment.
Selective excitation of a diffusive systems transmission eigenchannels enables manipulation of its internal energy distribution. The fluctuations and correlations of the eigenchannels spatial profiles, however, remain unexplored so far. Here we show that the depth profiles of high-transmission eigenchannels exhibit low realization-to-realization fluctuations. Furthermore, our experimental and numerical studies reveal the existence of inter-channel correlations, which are significant for low-transmission eigenchannels. Because high-transmission eigenchannels are robust and independent from other eigenchannels, they can reliably deliver energy deep inside turbid media.
Angstrom precision localization of a single nanoantenna is a crucial step towards advanced nanometrology, medicine and biophysics. Here, we show that single nanoantenna displacements down to few Angstroms can be resolved with sub-Angstrom precision using an all-optical method. We utilize the tranverse Kerker scattering scheme where a carefully structured light beam excites a combination of multipolar modes inside a dielectric nanoantenna, which then upon interference, scatters directionally into the far-field. We spectrally tune our scheme such that it is most sensitive to the change in directional scattering per nanoantenna displacement. Finally, we experimentally show that antenna displacement down to 3 Angstrom is resolvable with a localization precision of 0.6 Angstrom.
We investigate numerically the effect of long-range interaction on the transverse localization of light. To this end, nonlinear zigzag optical waveguide lattices are applied, which allows precise tuning of the second-order coupling. We find that localization is hindered by coupling between next-nearest lattice sites. Additionally, (focusing) nonlinearity facilitates localization with increasing disorder, as long as the nonlinearity is sufficiently weak. However, for strong nonlinearities, increasing disorder results in weaker localization. The threshold nonlinearity, above which this anomalous result is observed grows with increasing second-order coupling.
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