Journal of the European Optical Society - Rapid publications, Vol 6 (2011)

A fast inversion method for highly conductive submicron wires on a substrate

M. Karamehmedovic, P.-E. Hansen, T. Wriedt


A numerical method is presented for sizing of highly conductive penetrable and perfectly electrically conducting (PEC) submicron wires on substrates. For efficiency, the Method of Auxiliary Sources is used in the forward model of the inverse Kirsch-Kress Method. The radius of the circular cross section of PEC and silver wires positioned on a semi-infinite silicon substrate is estimated based on numerically simulated scattered far field. The illumination is monochromatic, transverse electric (TE) polarised, and with fixed angle of incidence. Average relative errors smaller than 1% and 5% are achieved for PEC and penetrable wires, respectively, in the dynamic ranges 0.2–1.3 and 0.8–1.3 times the operating free-space wavelength, respectively. In all cases, the inversion time is less than 1 sec.

© The Authors. All rights reserved. [DOI: 10.2971/jeos.2011.11039]

Full Text: PDF

Citation Details

Cite this article


A. Kirsch, and R. Kress, "On an integral equation of the first kind in inverse acoustic scattering", Inverse Probl., Internat. Schriftenreihe Numer. Math. 77, 93-102 (1986).

David Colton, and Rainer Kress, Inverse Acoustic and Electromagnetic Scattering Theory (Springer, 1998).

L. B. Felsen, and N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, New Jersey, 1973).

Y. Rahmat-Samii, R. Mittra, and P. Parhami, "Evaluation of Sommerfeld integrals for lossy half-space problems", Electromagnetics 1, 1-28 (1981).

V. D. Kupradze, "On the approximate solution of problems of mathematical physics", Russ. Math. Surv.+ 22, 59-107 (1967).

G. Fairweather, A. Karageorghis, and P. A. Martin, "The method of fundamental solutions for scattering and radiation problems", Eng. Anal. Bound. Elem. 27, 759-769 (2003).

G. Fairweather, and A. Karageorghis, "The method of fundamental solutions for elliptic boundary value problems", Adv. Comput. Math. 9, 69-95 (1998).

A. Doicu, Y. A. Eremin, and T. Wriedt, Acoustic & Electromagnetic Scattering Analysis Using Discrete Sources (Academic Press, 2000).

D. I. Kaklamani, and H. T. Anastassiu, "Aspects of the method of auxiliary sources (MAS) in computational electromagnetics", IEEE Antennas Propag. Mag. 44, 48-64 (2002).

Y. Leviatan, and A. Boag, "Analysis of Electromagnetic Scattering from Dielectric Cylinders Using a Multifilament Current Model", IEEE Trans. Antennas Propag. 35, 1119-1127 (1987).

J. Tal, and Y. Leviatan, "Inverse scattering analysis for perfectly conducting cylinders using a multifilament current model", Inverse Probl. 6, 1065-1074 (1990).

C.-Y. Lin, and Y.-W. Kiang, "Inverse Scattering for Conductors by the Equivalent Source Method", IEEE Trans. Antennas Propag. 44, 310-316 (1996).

F. Obelleiro, L. Landesa, J. L. Rodrguez, and M. R. Pino, "Fast Two-Dimensional Reconstruction of Impenetrable Objects Using Multipolar Equivalent Sources", IEEE T. Magn. 35, 1570-1573 (1999).

C. J. S. Alves, and N. F. M. Martins, "The direct Method of Fundamental Solutions and the inverse Kirsch-Kress Method for the reconstruction of elastic inclusions or cavities", J. Integral Equations Appl. 21, 153-178 (2009).

M. Karamehmedovic, P.-E. Hansen, and T. Wriedt, "An efficient scattering model for PEC and penetrable nanowires on a dielectric substrate", J. Eur. Opt. Soc. Rapid Publ. 6, 11021 (2011).

Elena Eremina, Yuri Eremin, and Thomas Wriedt, "Discrete sources method for simulation of resonance spectra of nonspherical nanoparticles on a plane surface", Opt. Commun. 246, 405-413 (2005).

Elena Eremina, Yuri Eremin, and Thomas Wriedt, "Analysis of the light scattering properties of a gold nanorod on a plane surface via discrete sources method", Opt. Commun. 273, 278-285 (2007).

COMSOL Multiphysics demonstration CD-ROM can be requested at

W. B. J. Zimmerman, Multiphysics Modelling with Finite Element Methods (World Scientific, 2006).

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, Boston, 1985).

I. V. Lindell, and E. Alanen, "Exact Image Theory for the Sommerfeld Half-Space Problem, Part I: Vertical Magnetic Dipole", IEEE T. Antenn. Propag. AP-32, 126-133 (1984).

I. V. Lindell, and E. Alanen, "Exact Image Theory for the Sommerfeld Half-Space Problem, Part III: General Formulation", IEEE T. Antenn. Propag. AP-32, 1027-1032 (1984).

A. Wchter, and L. T. Biegler, "On the Implementation of a Primal-Dual Interior Point Filter Line Search Algorithm for Large-Scale Nonlinear Programming", Math. Program. 106, 25-57 (2006).