Computing Photonic Crystal Defect Modes by Dirichlet-to-Neumann Maps | Zendy

Shaojie Li | Zendy; Ya Yan Lu | Zendy

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Computing Photonic Crystal Defect Modes by Dirichlet-to-Neumann Maps

Author(s) -

Shaojie Li,

Ya Yan Lu

Publication year - 2007

Publication title -

optics express

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.394

H-Index - 271

ISSN - 1094-4087

DOI - 10.1364/oe.15.014454

Subject(s) - discretization , photonic crystal , neumann boundary condition , boundary (topology) , mathematical analysis , operator (biology) , boundary value problem , matrix (chemical analysis) , field (mathematics) , physics , domain (mathematical analysis) , optics , mathematics , materials science , pure mathematics , biochemistry , chemistry , repressor , transcription factor , composite material , gene

We develop an efficient numerical method for computing defect modes in two dimensional photonic crystals based on the Dirichletto- Neumann (DtN) maps of the defect and normal unit cells. The DtN map of a unit cell is an operator that maps the wave field on the boundary of the cell to its normal derivative. The frequencies of the defect modes are solved from a condition that a small matrix is singular. The size of the matrix is related to the number of points used to discretize the boundary of the defect cell. The matrix is obtained by solving a linear system involving only discrete points on the edges of the unit cells in a truncated domain.

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