Unified perfectly matched layer for finite-difference time-domain modeling of dispersive optical materials
Finite-difference time-domain (FDTD) simulations of any electromagnetic problem require truncation of an often-unbounded physical region by an electromagnetically bounded region by deploying an artificial construct known as the perfectly matched layer (PML). As it is not possible to construct a universal PML that is non-reflective for different materials, PMLs that are tailored to a specific problem are required. For example, depending on the number of dispersive materials being truncated at
... ing truncated at the boundaries of a simulation region, an FDTD code may contain multiple sets of update equations for PML implementations. However, such an approach is prone to introducing coding errors. It also makes it extremely difficult to maintain and upgrade an existing FDTD code. In this paper, we solve this problem by developing a new, unified PML algorithm that can effectively truncate all types of linearly dispersive materials. The unification of the algorithm is achieved by employing a general form of the medium permittivity that includes three types of dielectric response functions, known as the Debye, Lorentz, and Drude response functions, as particular cases. We demonstrate the versatility and flexibility of the new formulation by implementing a single FDTD code to simulate absorption of electromagnetic pulse inside a medium that is adjacent to dispersive materials described by different dispersion models. The proposed algorithm can also be used for simulations of optical phenomena in metamaterials and materials exhibiting negative refractive indices. A frequency-dependent finite-difference time-domain formulation for general dispersive media," IEEE Trans. Microwave Theory Tech. 41, 658-665 (1993). 27. W. D. Hurt, "Multiterm Debye dispersion relations for permittivity of muscle," IEEE Trans. Bio. Eng. 32, 60-64 (1985). 28. K. E. Oughstun, "Computational methods in ultrafast time-domain optics," Comput. Sci. Eng. 5, 22-32 (2003). 29. J. Xi and M. Premaratne, "Analysis of the optical force dependency on beam polarization: Dielectric/metallic spherical shell in a Gaussian beam," J. Opt. Soc. Am. B 26, 973-980 (2009). 30. A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, and M. L. Chapelle, "Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method," Phys. Rev. B 71, 085416(1-7) (2005).