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On Guided Waves Created by Line Defects

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Abstract

The propagation of guided waves in photonic crystal fibers (PCFs) is studied. A photonic crystal fiber can be regarded as a perfect two-dimensional photonic crystal (PC) with a line defect along the axial direction. Under the assumption that the background spectrum has gaps, we give a simple condition on the parameters of the medium and of the line defect, which ensures the rise of eigenvalues in a specified subinterval of the given gap of the photonic crystal fiber. Using the modified Combes-Thomas estimates, we prove that the eigenfunctions corresponding to the eigenvalues decay exponentially away from the line defect.

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Authors and Affiliations

  1. Institute of Mathematics, Jilin University, Changchun, 130012, China

    Dong Miao & Fuming Ma

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  1. Dong Miao
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  2. Fuming Ma
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Correspondence to Dong Miao.

Additional information

The work was supported by the NSFC (10431030) of China.

D. Miao is currently visiting Department of Mathematics, Michigan State University, USA.

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Miao, D., Ma, F. On Guided Waves Created by Line Defects. J Stat Phys 130, 1197–1215 (2008). https://doi.org/10.1007/s10955-008-9480-8

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  • DOI: https://doi.org/10.1007/s10955-008-9480-8

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