Spectral Width of Maximum Deposition Eigenchannels in Diffusive Media

TL;DR

This study explores how the spectral width of maximum power deposition eigenchannels in diffusive media varies with target depth, revealing a weak, non-monotonic dependence and the effects of absorption on spectral width.

Contribution

It provides a detailed numerical analysis of the spectral width behavior of deposition eigenchannels across different depths and conditions in diffusive systems, highlighting their sensitivity and underlying interference mechanisms.

Findings

Spectral width varies weakly and non-monotonically with target depth.

Narrower deposition width correlates with higher power enhancement.

Absorption increases spectral width but does not alter depth dependence qualitatively.

Abstract

The maximum deposition eigenchannel provides the largest possible power delivery to a target region inside a diffusive medium by optimizing the incident wavefront of a monochromatic beam. It originates from constructive interference of scattered waves, which is frequency sensitive. We investigate the spectral width of maximum deposition eigenchannels over a range of target depths using numerical simulations of a 2D diffusive system. Compared to tight focusing into the system, power deposition to an extended region is more sensitive to frequency detuning. The spectral width of enhanced delivery to a large target displays a rather weak, non-monotonic variation with target depth, in contrast to a sharp drop of focusing bandwidth with depth. While the maximum enhancement of power deposited within a diffusive system can exceed that of power transmitted through it, this comes at the cost of a narrower spectral width. We investigate the narrower deposition width in terms of the constructive interference of transmission eigenchannels within the target. We further observe that the spatial field distribution inside the target region decorrelates slower with spectral detuning than power decay of the maximum deposition eigenchannel. Additionally, absorption increases the spectral width of deposition eigenchannels, but the depth dependence remains qualitatively identical to that without absorption. These findings hold for any diffusive waves, including electromagnetic waves, acoustic waves, pressure waves, mesoscopic electrons, and cold atoms.