On an application of a 2D transparent-influx boundary condition for photonic crystals

J.B. Nicolau, A. Sopaheluwakan, Embrecht W.C. van Groesen

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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Abstract

We present a hybrid analytic-numeric method to calculate the transmission and reflection of light that is fluxed into a bounded complicated optical structure surrounded by air. The solution is obtained by numerically calculations inside a square containing the structure and by analytical calculations outside the square. For solving the 2D Helmholtz equation we formulate Transparent-Influx Boundary Conditions (TIBC’s) on the boundaries of the square; these are incorporated into a variational formulation of the Helmholtz equation to obtain a FEM-implementation for the interior calculations. We illustrate the method for a two-dimensional finite photonic crystal formed by dielectric rods with a defect, and study the response of the structure for given influx.
Original languageEnglish
Title of host publicationProceedings of the 13th International Workshop on Optical Waveguide Theory and Numerical Modeling (OWTNM)
EditorsX. Letartre
Place of PublicationLyon
PublisherEcole Centrale de Lyon
Pages-
Number of pages1
ISBN (Print)not assigned
Publication statusPublished - Apr 2005
Event13th International Workshop on Optical Waveguide Theory and Numerical Modelling, OWTNM 2005 - Grenoble, France
Duration: 8 Apr 20059 Apr 2005
Conference number: 13
https://www.owtnm-workshop.org/

Conference

Conference13th International Workshop on Optical Waveguide Theory and Numerical Modelling, OWTNM 2005
Abbreviated titleOWTNM
CountryFrance
CityGrenoble
Period8/04/059/04/05
Internet address

Fingerprint

Helmholtz equations
photonics
boundary conditions
crystals
rods
formulations
air
defects

Keywords

  • Transparent-Influx Boundary Conditions
  • IR-65067
  • METIS-226040
  • Finite Element Method
  • Helmholtz problems
  • Dirichlet-to-Neumann operator
  • Photonic crystals
  • hybrid analytic-numeric method
  • EWI-13931

Cite this

Nicolau, J. B., Sopaheluwakan, A., & van Groesen, E. W. C. (2005). On an application of a 2D transparent-influx boundary condition for photonic crystals. In X. Letartre (Ed.), Proceedings of the 13th International Workshop on Optical Waveguide Theory and Numerical Modeling (OWTNM) (pp. -). Lyon: Ecole Centrale de Lyon.
Nicolau, J.B. ; Sopaheluwakan, A. ; van Groesen, Embrecht W.C. / On an application of a 2D transparent-influx boundary condition for photonic crystals. Proceedings of the 13th International Workshop on Optical Waveguide Theory and Numerical Modeling (OWTNM). editor / X. Letartre. Lyon : Ecole Centrale de Lyon, 2005. pp. -
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abstract = "We present a hybrid analytic-numeric method to calculate the transmission and reflection of light that is fluxed into a bounded complicated optical structure surrounded by air. The solution is obtained by numerically calculations inside a square containing the structure and by analytical calculations outside the square. For solving the 2D Helmholtz equation we formulate Transparent-Influx Boundary Conditions (TIBC’s) on the boundaries of the square; these are incorporated into a variational formulation of the Helmholtz equation to obtain a FEM-implementation for the interior calculations. We illustrate the method for a two-dimensional finite photonic crystal formed by dielectric rods with a defect, and study the response of the structure for given influx.",
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Nicolau, JB, Sopaheluwakan, A & van Groesen, EWC 2005, On an application of a 2D transparent-influx boundary condition for photonic crystals. in X Letartre (ed.), Proceedings of the 13th International Workshop on Optical Waveguide Theory and Numerical Modeling (OWTNM). Ecole Centrale de Lyon, Lyon, pp. -, 13th International Workshop on Optical Waveguide Theory and Numerical Modelling, OWTNM 2005, Grenoble, France, 8/04/05.

On an application of a 2D transparent-influx boundary condition for photonic crystals. / Nicolau, J.B.; Sopaheluwakan, A.; van Groesen, Embrecht W.C.

Proceedings of the 13th International Workshop on Optical Waveguide Theory and Numerical Modeling (OWTNM). ed. / X. Letartre. Lyon : Ecole Centrale de Lyon, 2005. p. -.

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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N2 - We present a hybrid analytic-numeric method to calculate the transmission and reflection of light that is fluxed into a bounded complicated optical structure surrounded by air. The solution is obtained by numerically calculations inside a square containing the structure and by analytical calculations outside the square. For solving the 2D Helmholtz equation we formulate Transparent-Influx Boundary Conditions (TIBC’s) on the boundaries of the square; these are incorporated into a variational formulation of the Helmholtz equation to obtain a FEM-implementation for the interior calculations. We illustrate the method for a two-dimensional finite photonic crystal formed by dielectric rods with a defect, and study the response of the structure for given influx.

AB - We present a hybrid analytic-numeric method to calculate the transmission and reflection of light that is fluxed into a bounded complicated optical structure surrounded by air. The solution is obtained by numerically calculations inside a square containing the structure and by analytical calculations outside the square. For solving the 2D Helmholtz equation we formulate Transparent-Influx Boundary Conditions (TIBC’s) on the boundaries of the square; these are incorporated into a variational formulation of the Helmholtz equation to obtain a FEM-implementation for the interior calculations. We illustrate the method for a two-dimensional finite photonic crystal formed by dielectric rods with a defect, and study the response of the structure for given influx.

KW - Transparent-Influx Boundary Conditions

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KW - METIS-226040

KW - Finite Element Method

KW - Helmholtz problems

KW - Dirichlet-to-Neumann operator

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KW - EWI-13931

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Nicolau JB, Sopaheluwakan A, van Groesen EWC. On an application of a 2D transparent-influx boundary condition for photonic crystals. In Letartre X, editor, Proceedings of the 13th International Workshop on Optical Waveguide Theory and Numerical Modeling (OWTNM). Lyon: Ecole Centrale de Lyon. 2005. p. -