Stopping Light on a Defect

Details Stopping Light on a Defect Stopping Light on a Defect

2001-10-10

arxiv.org/abs/nlin/0110020v1

Nonlinear Sciences

Pattern Formation and Solitons

45 pages, Submitted to Journal of the Optical Society B

Scientific paper

10.1364/JOSAB.19.001635

Gap solitons are localized nonlinear coherent states which have been shown both theoretically and experimentally to propagate in periodic structures. Although theory allows for their propagation at any speed $v$, $0\le v\le c$, they have been observed in experiments at speeds of approximately 50% of $c$. It is of scientific and technological interest to trap gap solitons. We first introduce an explicit multiparameter family of periodic structures with localized defects, which support linear defect modes. These linear defect modes are shown to persist into the nonlinear regime, as {\it nonlinear defect modes}. Using mathematical analysis and numerical simulations we then investigate the capture of an incident gap soliton by these defects. The mechanism of capture of a gap soliton is resonant transfer of its energy to nonlinear defect modes. We introduce a useful bifurcation diagram from which information on the parameter regimes of gap soliton capture, reflection and transmission can be obtained by simple conservation of energy and resonant energy transfer principles.

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