Advances in Radio Science www.adv-radio-sci.net 1684-9965 1684-9973 7 Kleinheubacher Berichte 2008 2009 10.5194/ars-7-23-2009 http://www.adv-radio-sci.net/7/23/2009/ http://www.adv-radio-sci.net/7/23/2009/ars-7-23-2009.html http://www.adv-radio-sci.net/7/23/2009/ars-7-23-2009.pdf 23 27 2009-05-18 3-D eigenmode calculation of metallic nano-structures B. Bandlow bandlow@tet.upb.de R. Schuhmann University Paderborn, EIM-E, FG Theoretische Elektrotechnik, Warburger Straße 100, 33098 Paderborn, Germany In the calculation of eigenfrequencies of 3-D metallic nanostructures occurs the challenge that the material parameters depend on the desired eigenfrequency. We propose a formulation where this leads to a polynomial eigenvalue problem which can be tackled by different solving strategies. A comparison between a Newton-type method and a Jacobi-Davidson algorithm is given. Bai, Z., Demmel, J., Dongarra, J., Ruhe, A., and van~der Vorst, H.: Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide, SIAM, Philadelphia, 2000. Berenger, J.-P.: A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., 114, 185–200, 1994. Computer Simulation Technology AG (CST): CST Studio Suite 2008, http://www.cst.com, 2008. Guo, H., Meyrath, T P., Zentgraf, T., Liu, N., Fu, L., Schweizer, H., and Giessen, H.: Optical resonances of bowtie slot antennas and their geometry and material dependence, Opt. Express, 16, 7756–7766, prefixhttp://www.opticsexpress.org/abstract.cfm?URI=oe-16-11-7756, 2008. Hochstenbach, M E. and Sleijpen, G. L G.: Harmonic and refined Rayleigh-Ritz for the polynomial eigenvalue problem, Numerical Linear Algebra with Applications, 15, 35–54, 2008. Johnson, P B. and Christy, R W.: Optical Constants of the Noble Metals, Phys. Rev. B., 6, 4370–4379, 1972. Ordal, M A., Long, L L., Bell, R J., Bell, S E., Bell, R R., R W Alexander, J., and Ward, C A.: Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared, Appl. Opt., 22, 1099–1119, prefixhttp://ao.osa.org/abstract.cfm?URI=ao-22-7-1099, 1983. Palik, E D.: Handbook of Optical Constants of Solids , 1997. Rakic, A D., Djurišic, A B., Elazar, J M., and Majewski, M L.: Optical Properties of Metallic Films for Vertical-Cavity Optoelectronic Devices, Appl. Opt., 37, 5271–5283, prefixhttp://ao.osa.org/abstract.cfm?URI=ao-37-22-5271, 1998. Schreiber, K.: Nonlinear Eigenvalue Problems: Newton-type Methods and Nonlinear Rayleigh Functionals, Ph.D. thesis, TU Berlin, prefixhttp://nbn-resolving.de/urn:nbn:de:kobv:83-opus-18754, 2008. Sleijpen, G. L G. and Fokkema, D R.: Bi-CGSTAB(l) for linear equations involving unsymmetric matrices with complex spectrum, Elec. Trans. Numer. Anal., 1, 11–32, 1993. Sleijpen, G. L G., Booten, A. G L., Fokkema, D R., and der Vorst, H. A V.: Jacobi-Davidson type methods for generalized and polynomial eigenproblems, BIT, 36, 595–633, 1996. Weiland, T.: Eine Methode zur Lösung der Maxwellschen Gleichungen für sechskomponentige Felder auf diskreter Basis, Archiv für Elektronik und Übertragungstechnik, 31, 116–120, 1977. Weiland, T.: Time Domain Electromagnetic Field Computation with Finite Difference Methods, International Journal of Numerical Modelling, 9, 295–319, 1996.