We describe a procedure for designing metal-metal boundaries for the strong attenuation of surface plasmon-polaritons without the introduction of reflections or scattering effects. Solutions associated with different sets of matching materials are found. To illustrate the results and the consequences of adopting different solutions, we present calculations based on an integral equation formulation for the scattering problem and the use of a nonlocal impedance boundary condition. 1. Introduction In the numerical solution of spatially unbounded electromagnetic problems it is often necessary to truncate the computational domain. The use of a region of finite spatial size can introduce reflections and other spurious effects in the calculations. Several techniques have been proposed to overcome this problem. An established one, used commonly in finite-difference time-domain (FDTD) calculations [1], is the perfectly matched layer (PML) technique proposed by Berenger [2]. Such a layer can absorb electromagnetic waves without reflections at the vacuum-PML interfaces. Methods of calculation based on Green’s theorem (see, e.g., [3]) do not present such complications with volume waves, but the truncation of the interfaces can produce spurious effects in the presence of surface waves, like surface plasmon-polaritons (SPPs). The basic properties of SPPs have been known for some time, but their importance for nanophotonic applications has produced a renewed interest on the subject [4, 5]. In studies of the interactions of SPPs with objects or surface structures, the computational problem grows as a function of the physical size of the sample and, thus, it is desirable to reduce the computational domain as much as possible. The PML techniques known to us were not designed to handle truncation effects involving SPPs, and are not well-adapted for situations involving metallic structures and evanescent waves [6]. In this paper, we present a procedure for determining the optical constants of absorbing materials for the attenuation of SPPs without introducing, or minimizing at least, spurious reflections and/or radiative scattering effects. Although SPPs are already lossy traveling waves, a reduction of their propagation length in the matched medium permits an important reduction in the dimensions of the region over which the computational domain extends. Although our approach is related in spirit to the usual PML techniques, we point out that it addresses a different problem, namely, the termination of surfaces over which surface waves propagate without the introduction
References
[1]
A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method, Artech House, Boston, Mass, USA, 1995.
[2]
J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” Journal of Computational Physics, vol. 114, no. 2, pp. 185–200, 1994.
[3]
A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Méndez, “Enhanced backscattering of light from a random grating,” Annals of Physics, vol. 203, no. 2, pp. 255–307, 1990.
[4]
A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Physics Reports, vol. 408, no. 3-4, pp. 131–314, 2005.
[5]
S. A. Maier, Plasmonics: Fundamentals and Applications, Springer, New York, NY, USA, 2007.
[6]
C. C. Chao, S. H. Tu, C. M. Wang, H. I. Huang, C. C. Chen, and J. Y. Chang, “Impedance-matching surface plasmon absorber for FDTD simulations,” Plasmonics, vol. 5, no. 1, pp. 51–55, 2010.
[7]
R. F. Oulton, D. F. P. Pile, Y. Liu, and X. Zhang, “Scattering of surface plasmon polaritons at abrupt surface interfaces: implications for nanoscale cavities,” Physical Review B, vol. 76, no. 3, Article ID 035408, 12 pages, 2007.
[8]
J. Elser and V. A. Podolskiy, “Scattering-free plasmonic optics with anisotropic metamaterials,” Physical Review Letters, vol. 100, no. 6, Article ID 066402, 4 pages, 2008.
[9]
N. Zavareian and R. Massudi, “Study on scattering coefficient of surface plasmon polariton waves at interface of two metal-dielectric waveguides by using G-GFSIEM method,” Optics Express, vol. 18, no. 8, pp. 8574–8586, 2010.
[10]
P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Physical Review B, vol. 6, no. 12, pp. 4370–4379, 1972.
[11]
V. A. Markel, “Can the imaginary part of permeability be negative?” Physical Review E, vol. 78, no. 2, Article ID 026608, 5 pages, 2008.
[12]
R. A. Depine and J. M. Simon, “Surface impedance boundary condition for metallic diffraction gratings in the optical and infrared range,” Optica Acta, vol. 30, no. 3, pp. 313–322, 1983.
[13]
R. García-Molina, A. A. Maradudin, and T. A. Leskova, “The impedance boundary condition for a curved surface,” Physics Report, vol. 194, no. 5-6, pp. 351–359, 1990.
[14]
A. A. Maradudin and E. R. Méndez, “Theoretical studies of the enhanced backscattering of light from one-dimensional randomly rough metal surfaces by the use of a nonlocal impedance boundary condition,” Physica A, vol. 207, no. 1–3, pp. 302–314, 1994.
[15]
M. E. Knotts, T. R. Michel, and K. A. O'Donnell, “Comparisons of theory and experiment in light scattering from a randomly rough surface,” Journal of the Optical Society of America A, vol. 10, no. 5, pp. 928–941, 1993.
[16]
S. de la Cruz, E. R. Méndez, D. Macías, R. Salas-Montiel, and P. M. Adam, “Compact surface structures for the efficient excitation of surface plasmon-polaritons,” Physica Status Solidi B, vol. 249, no. 6, pp. 1178–1187, 2012.
