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

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

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 proceeding › Conference contribution › Academic › peer-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 language	English
Title of host publication	Proceedings of the 13th International Workshop on Optical Waveguide Theory and Numerical Modeling (OWTNM)
Editors	X. Letartre
Place of Publication	Lyon
Publisher	Ecole Centrale de Lyon
Pages	-
Number of pages	1
ISBN (Print)	not assigned
Publication status	Published - Apr 2005
Event	13th International Workshop on Optical Waveguide Theory and Numerical Modelling, OWTNM 2005 - Grenoble, France Duration: 8 Apr 2005 → 9 Apr 2005 Conference number: 13 https://www.owtnm-workshop.org/

Conference

Conference	13th International Workshop on Optical Waveguide Theory and Numerical Modelling, OWTNM 2005
Abbreviated title	OWTNM
Country	France
City	Grenoble
Period	8/04/05 → 9/04/05
Internet address	https://www.owtnm-workshop.org/

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

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@inproceedings{5184adce37ab45a7abb81db59fdecac0,

title = "On an application of a 2D transparent-influx boundary condition for photonic crystals",

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{\textquoteright}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.",

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",

author = "J.B. Nicolau and A. Sopaheluwakan and {van Groesen}, {Embrecht W.C.}",

year = "2005",

month = apr,

language = "English",

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booktitle = "Proceedings of the 13th International Workshop on Optical Waveguide Theory and Numerical Modeling (OWTNM)",

publisher = "Ecole Centrale de Lyon",

note = "13th International Workshop on Optical Waveguide Theory and Numerical Modelling, OWTNM 2005, OWTNM ; Conference date: 08-04-2005 Through 09-04-2005",

url = "https://www.owtnm-workshop.org/",

}

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 proceeding › Conference contribution › Academic › peer-review

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T1 - On an application of a 2D transparent-influx boundary condition for photonic crystals

AU - Nicolau, J.B.

AU - Sopaheluwakan, A.

AU - van Groesen, Embrecht W.C.

N1 - Conference code: 13

PY - 2005/4

Y1 - 2005/4

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

KW - IR-65067

KW - METIS-226040

KW - Finite Element Method

KW - Helmholtz problems

KW - Dirichlet-to-Neumann operator

KW - Photonic crystals

KW - hybrid analytic-numeric method

KW - EWI-13931

M3 - Conference contribution

SN - not assigned

SP - -

BT - Proceedings of the 13th International Workshop on Optical Waveguide Theory and Numerical Modeling (OWTNM)

A2 - Letartre, X.

PB - Ecole Centrale de Lyon

CY - Lyon

T2 - 13th International Workshop on Optical Waveguide Theory and Numerical Modelling, OWTNM 2005

Y2 - 8 April 2005 through 9 April 2005

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