The reduced Rayleigh equation for the scattering of a surface plasmon polariton incident non-normally on a one-dimensional ridge or groove on an otherwise planar metal surface is solved by a purely numerical approach. The solution is used to calculate the transmission, reflection, and out-of-plane scattering coefficients of the surface plasmon polariton. The angular dependence of the out-of-plane scattering is found to have a conical nature.
This is a preview of subscription content, log in to check access.
Buy single article
Instant unlimited access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Sánchez-Gil JA (1998) Surface defect scattering of surface plasmon polaritons: mirrors and light emitters. Appl Phys Lett 73:3509–3511
Sánchez-Gil JA, Maradudin AA (1999) Near-field and far-field scattering of surface plasmon polaritons by one-dimensional surface defects. Phys Rev B 60:8359–8367
Sánchez-Gil JA, Maradudin AA (2003) Resonant scattering of surface plasmon polariton pulses by nanoscale metal defects. Opt Lett 28:2255–2257
Sánchez-Gil JA, Maradudin AA (2004) Dynamic near-field calculations of surface-plasmon polariton pulses resonantly scattered at sub-micron metal defects. Opt Express 12:883–894
Sánchez-Gil JA, Maradudin AA (2005) Surface plasmon polariton scattering from a finite array of nano grooves/ridges: efficient mirrors. Appl Phys Lett 86(1–3):251106
Maradudin AA (1994) An impedance boundary condition for a rough surface, pp. 33–45. Topics in Condensed Matter Physics, ed. M.P. Das. Nova Science Publishers, New York
Nikitin AY, López-Tejeira F, Martín-Moreno L (2007) Scattering of surface plasmon polaritons by one-dimensional inhomogeneities. Phys Rev B75(1–8):035–129
Leskova TA, Maradudin AAE, García-Guerrero E, Méndez ER (2010) The scattering of surface plasmon polaritons by nanoscale surface defects. Fiz Nizkh Temperatur 36:1022–1029
Chremmos I (2010) Magnetic field integral equation analysis of surface plasmon scattering by rectangular dielectric channel discontinuities. J Opt Soc Am A27:85–94
Brucoli G, Martín-Moreno L (2011) Comparative study of surface plasmon scattering by shallow ridges and grooves. Phys Rev B 83(1–11):045–422
Brucoli G, Martín-Moreno L (2011) Effect of defect depth on surface plasmon scattering by subwavelength surface defects. Phys Rev B 83(1–10):075–433
Kuttge MF, García de Abajo J, Polman A (2009) How grooves reflect and confine surface plasmon polaritons. Opt Express 17:10385–10392
Polanco J, Fitzgerald RM, Maradudin AA (2013) Scattering of surface plasmon polaritons by one-dimensional surface defects. Phys Rev B 87:155417–155430
Nikitin AY, Martín-Moreno L (2007) Scattering coefficients of surface plasmon polaritons impinging at oblique incidence onto one-dimensional surface relief defects. Phys Rev B 75(1–4):081–405
Petit R, Cadilhac M (1996) Sur la diffraction d’une onde plane par un réseau infiniment conducteur. C R Acad Sci B 262:468–471
Millar RF (1969) On the Rayleigh assumption in scattering by a periodic surface. Proc Camb Philos Soc 65:773–791
Hill NR, Celli V (1978) Limits of convergence of the Rayleigh method for surface scattering. Phys Rev B 17:2478–2481
Van den Berg PM, Fokkema JT (1979) The Rayleigh hypothesis in the theory of reflection by a grating. J Opt Soc Am 69:27–31
Van den Berg PM, Fokkema JT (1980) The Rayleigh hypothesis in the theory of diffraction by a perturbation in a plane surface. Radio Sci 15:723–732
Schlup WA (1984) On the convergence of the Rayleigh ansatz for hard-wall scattering on arbitrary periodic surface profiles. J Phys A: Math Gen 17:2607–2619
DeSanto JA (1981) Scattering from a perfectly reflecting arbitrary periodic surface: an exact theory. Radio Sci 16:1315–1326
Paulick TC (1990) Applicability of the Rayleigh hypothesis to real materials. Phys Rev B 42:2801–2824
Millar RF (1973) The Rayleigh hypothesis and a related least-squares solution to scattering problems for periodic surfaces and other scatterers. Radio Sci 8:785–796
Rayleigh L (1896) The theory of sound, vol II, 2nd. MacMillan, London, pp 89, 297–311
Brown GC, Celli V, Haller M, Marvin A (1984) Vector theory of light scattering from a rough surface: Unitary and reciprocal expansions. Surf Sci 136:381–397
Maradudin AA, Mills DL (1976) The attenuation of Rayleigh surface waves by surface roughness. Ann Phys (N. Y.) 100:262–309. Appendix D
Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes. Cambridge University Press, Cambridge, UK, pp 109–110
Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes, Cambridge University Press, Cambridge, UK. Chapter 2
About this article
Cite this article
Polanco, J., Fitzgerald, R.M. & Maradudin, A.A. Scattering of an Obliquely Incident Surface Plasmon Polariton from Sub-Micron Metal Grooves and Ridges. Plasmonics 10, 1173–1183 (2015). https://doi.org/10.1007/s11468-015-9913-6
- Surface plasmon