Selectively exciting quasi-normal modes in open disordered systems

TL;DR

This paper demonstrates how the transmission matrix can be used to selectively excite quasi-normal modes in disordered systems, enhancing internal energy and controlling wave behavior, with implications for wave control in complex media.

Contribution

It introduces a method to analyze the transmission matrix into modal components, revealing limits to modal selectivity due to speckle pattern correlations and mode non-orthogonality.

Findings

Spectra of the transmission matrix can be decomposed into modal transmission matrices of rank one.

Energy within the sample can be enhanced by a factor equal to the number of channels.

Speckle pattern correlations increase with modal spectral overlap and non-Hermitian mode non-orthogonality.

Abstract

Transmission through disordered samples can be controlled by illuminating a sample with waveforms corresponding to the eigenchannels of the transmission matrix. But can the TM be exploited to selectively excite quasi-normal modes and so control the spatial profile and dwell time inside the medium? We show in microwave and numerical studies that spectra of the TM can be analyzed into modal transmission matrices of rank unity. This makes it possible to enhance the energy within a sample by a factor equal to the number of channels. Limits to modal selectivity arise, however, from correlation in the speckle patterns of neighboring modes. In accord with an effective Hamiltonian model, the degree of modal speckle correlation grows with increasing modal spectral overlap and non-orthogonality of the modes of non-Hermitian systems. This is observed when the coupling of a sample to its surroundings increases, as in the crossover from localized to diffusive waves.