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We propose a novel finite-difference time-domain (FDTD) scheme for thesolution of the Maxwell's equations in which linear dispersive effects arepresent. The method uses high-order accurate approximations in space and timefor the dispersive Maxwell's equations written as a second-order vector waveequation with a time-history convolution term. The modified equation approachis combined with the recursive convolution (RC) method to develop high-orderapproximations accurate to any desired order in space and time.High-order-accurate centered approximations of the physical Maxwell interfaceconditions are derived for the dispersive setting in order to fully restoreaccuracy at discontinuous material interfaces. Second- and fourth-orderaccurate versions of the scheme are presented and implemented in two spatialdimensions for the case of the Drude linear dispersion model. The stability ofthese schemes is analyzed. Finally, our approach is also amenable tocurvilinear numerical grids if used with appropriate generalized Laplaceoperator.

High-Order Accurate FDTD Schemes for Dispersive Maxwell's Equations in Second-Order Form Using Recursive Convolutions