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New trends in time-domain methods for plasmonic media

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In this chapter, we have focused on formulations of a TD-SIE solver and a TD -VIE solver for characterizing electromagnetic field interactions on plasmonic structures. The TD-SIE solver discretizes TD-PMCHWT-SIE using RWG basis and testing functions in space and polynomial basis functions and point testing in time. The resulting systems of equations are solved recursively using the MOT scheme. The TD -VIE solver discretizes TD-EFVIE using SWG basis and testing functions in space and polynomial basis functions and point testing in time. Similarly, the resulting systems of equations are solved recursively using the MOT scheme. Since the permittivity of a plasmonic structure is dispersive, both solvers call for discretization of temporal convolutions. This is carried out by projecting the result of the convolutions onto polynomial basis function space and testing the resulting equation at discrete times. The temporal samples of the time -domain Green function (for the TD-SIE solver) and the time -domain permittivity functions (for the TD-SIE and TD -VIE solvers), which are required by this discretization procedure (and also the MOT scheme), are obtained numerically from their frequency -domain samples. This is achieved by representing the frequency -domain Green function and permittivity in terms of summations of weighted rational functions. The weighting coefficients are found by applying the FRVF scheme to the frequency -domain samples. Time-domain functions are then obtained by analytically computing the inverse Fourier transform of the summation. Numerical results demonstrate the accuracy, stability, and applicability of both solvers.

Chapter Contents:

• 6.1 Introduction
• 6.2 Formulation
• 6.2.1 Problem description
• 6.2.2 TD-SIE solver
• 6.2.2.1 Time-domain surface integral equation
• 6.2.2.2 Discretization of TD-SIE
• 6.2.3 TD-VIE solver
• 6.2.3.1 Time-domain volume integral equation
• 6.2.3.2 Discretization of TD-VIE
• 6.2.4 MOT solution
• 6.3 Numerical results
• 6.3.1 Sphere
• 6.3.2 Rounded cube
• 6.3.3 Rounded prism
• 6.3.4 Dimer
• 6.4 Conclusions
• References

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