Optimal transmission through a randomly perturbed waveguide in the localization regime

Josselin Garnier

doi:10.3934/dcdsb.2011.15.597

Article Contents

2011, Volume 15, Issue 3: 597-621. Doi: 10.3934/dcdsb.2011.15.597

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Optimal transmission through a randomly perturbed waveguide in the localization regime

Josselin Garnier^1,

1.
Laboratoire de Probabilités et Modèles Aléatoires & Laboratoire Jacques-Louis Lions, Université Paris VII, site Chevaleret, case 7012, 75205 Paris Cedex 13

Received: December 31, 2009

Revised: June 30, 2010

Published: September 2011

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Abstract

We demonstrate that increased power transmission through a random single-mode or multi-mode channel can be obtained in the localization regime by optimizing the spatial wave front or the time pulse profile of the source. The idea is to select and excite the few modes or the few frequencies whose transmission coefficients are anomalously large compared to the typical exponentially small value. We prove that time reversal is optimal for maximizing the transmitted intensity at a given time or space, while iterated time reversal is optimal for maximizing the total transmitted energy. The statistical stability of the optimal transmitted intensity and energy is also obtained.

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Mathematics Subject Classification: Primary: 35L05, 35R60; Secondary: 60F05.

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