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Contour-path effective permittivities for the two-dimensional finite-difference time-domain method.

Ahmad Mohammadi, Hamid Nadgaran, Mario Agio

|June 9, 2009

Summary

This summary is machine-generated.

Accurate effective permittivities for the two-dimensional Finite-Difference Time-Domain (FDTD) method are derived using a contour path approach. This method improves accuracy and reduces errors, especially for resonance calculations.

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Area of Science:

Computational electromagnetics
Numerical methods for wave propagation

Background:

The Finite-Difference Time-Domain (FDTD) method is widely used for electromagnetic simulations.
Accurate modeling of dielectric interfaces is crucial for FDTD accuracy.
Existing approximations like staircase and volume-average methods have limitations.

Purpose of the Study:

To derive accurate effective permittivities for the 2D FDTD method.
To develop a simpler phenomenological formula for effective permittivities.
To validate the proposed methods against Mie theory and compare with existing approximations.

Main Methods:

Derivation of effective permittivities using a contour path approach.
Accounting for electromagnetic field boundary conditions at dielectric interfaces.
Development and application of a phenomenological formula for effective permittivities.

Main Results:

The contour path approach yields accurate effective permittivities.
The proposed phenomenological formula offers a simpler, effective alternative.
Significant improvements in accuracy and reduced error fluctuations were demonstrated compared to staircase and volume-average methods.
Validation against Mie theory confirmed the accuracy of the proposed schemes, particularly for resonance calculations.

Conclusions:

The contour path approach provides a robust method for calculating effective permittivities in 2D FDTD.
The phenomenological formula presents a practical and accurate alternative for FDTD simulations.
The developed methods enhance the accuracy of electromagnetic simulations, especially for resonant phenomena.