High order FDTD methods for transverse magnetic modes with dispersive interfaces

Duc Duy Nguyen; Shan Zhao

doi:10.1016/j.amc.2013.10.092

High order FDTD methods for transverse magnetic modes with dispersive interfaces

Duc Duy Nguyen, Shan Zhao

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

A new finite-difference time-domain (FDTD) algorithm is introduced to solve two dimensional (2D) transverse magnetic (TM) modes with a straight dispersive interface. Driven by the consideration of simplifying interface jump conditions, the auxiliary differential equation of the Debye constitution model is rewritten to form a new Debye-Maxwell TM system. Interface auxiliary differential equations are utilized to describe the transient changes in the regularities of electromagnetic fields across a dispersive interface. The resulting time dependent jump conditions are rigorously enforced in the FDTD discretization by means of a matched interface and boundary scheme. Higher order convergences are numerically achieved for the first time in the literature in 2D FDTD simulations of dispersive inhomogeneous media.

Original language	English
Pages (from-to)	699-707
Number of pages	9
Journal	Applied Mathematics and Computation
Volume	226
DOIs	https://doi.org/10.1016/j.amc.2013.10.092
State	Published - 2014

Bibliographical note

Funding Information:
This work is supported in part by the NSF Grants DMS-1016579 and DMS-1318898 .

Keywords

Auxiliary differential equation
Debye dispersive medium
Finite-difference time-domain (FDTD)
High order interface treatments
Matched interface and boundary (MIB)
Maxwell's equations

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2013.10.092

Cite this

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title = "High order FDTD methods for transverse magnetic modes with dispersive interfaces",

abstract = "A new finite-difference time-domain (FDTD) algorithm is introduced to solve two dimensional (2D) transverse magnetic (TM) modes with a straight dispersive interface. Driven by the consideration of simplifying interface jump conditions, the auxiliary differential equation of the Debye constitution model is rewritten to form a new Debye-Maxwell TM system. Interface auxiliary differential equations are utilized to describe the transient changes in the regularities of electromagnetic fields across a dispersive interface. The resulting time dependent jump conditions are rigorously enforced in the FDTD discretization by means of a matched interface and boundary scheme. Higher order convergences are numerically achieved for the first time in the literature in 2D FDTD simulations of dispersive inhomogeneous media.",

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author = "Nguyen, {Duc Duy} and Shan Zhao",

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doi = "10.1016/j.amc.2013.10.092",

language = "English",

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pages = "699--707",

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T1 - High order FDTD methods for transverse magnetic modes with dispersive interfaces

AU - Nguyen, Duc Duy

AU - Zhao, Shan

N1 - Funding Information: This work is supported in part by the NSF Grants DMS-1016579 and DMS-1318898 .

PY - 2014

Y1 - 2014

N2 - A new finite-difference time-domain (FDTD) algorithm is introduced to solve two dimensional (2D) transverse magnetic (TM) modes with a straight dispersive interface. Driven by the consideration of simplifying interface jump conditions, the auxiliary differential equation of the Debye constitution model is rewritten to form a new Debye-Maxwell TM system. Interface auxiliary differential equations are utilized to describe the transient changes in the regularities of electromagnetic fields across a dispersive interface. The resulting time dependent jump conditions are rigorously enforced in the FDTD discretization by means of a matched interface and boundary scheme. Higher order convergences are numerically achieved for the first time in the literature in 2D FDTD simulations of dispersive inhomogeneous media.

AB - A new finite-difference time-domain (FDTD) algorithm is introduced to solve two dimensional (2D) transverse magnetic (TM) modes with a straight dispersive interface. Driven by the consideration of simplifying interface jump conditions, the auxiliary differential equation of the Debye constitution model is rewritten to form a new Debye-Maxwell TM system. Interface auxiliary differential equations are utilized to describe the transient changes in the regularities of electromagnetic fields across a dispersive interface. The resulting time dependent jump conditions are rigorously enforced in the FDTD discretization by means of a matched interface and boundary scheme. Higher order convergences are numerically achieved for the first time in the literature in 2D FDTD simulations of dispersive inhomogeneous media.

KW - Auxiliary differential equation

KW - Debye dispersive medium

KW - Finite-difference time-domain (FDTD)

KW - High order interface treatments

KW - Matched interface and boundary (MIB)

KW - Maxwell's equations

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JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

High order FDTD methods for transverse magnetic modes with dispersive interfaces

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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