Journal of the European Optical Society - Rapid publications, Vol 2 (2007)

Numerical analysis of a slit-groove diffraction problem

P Lalanne, M. Besbes, J.P. Hugonin, S. van Haver, O.T.A. Janssen, A.M. Nugrowati, M. Xu, S.F. Pereira, HP Urbach, A.S. van de Nes, P. Bienstman, G. Granet, A Moreau, S. Helfert, M. Sukharev, T Seideman, F. Baida, B. Guizal, D. van Labeke

Abstract


We present a comparison among several fully-vectorial methods applied to a basic scattering problem governed by the physics of the electromagnetic interaction between subwavelength apertures in a metal film. The modelled structure represents a slit-groove scattering problem in a silver film deposited on a glass substrate. The benchmarked methods, all of which use in-house developed software, include a broad range of fully-vectorial approaches from finite-element methods, volume-integral methods, and finite-difference time domain methods, to various types of modal methods based on different expansion techniques.

© The Authors. All rights reserved. [DOI: 10.2971/jeos.2007.07022]

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References


S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha and H. A. Hatwater, "Plasmonics - A Route to Nanoscale Optical Devices" Adv. Mater. 13, 1501 (2001).

C. Genet and T. W. Ebbesen, "Light in tiny holes" Nature 445, 39-46 (2007).

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O'Dwyer, J. Weiner, H. J. Lezec, "The optical response of nanostructured surfaces and the composite diffracted evanescent wave model" Nat. Phys. 2, 262-267 (2006).

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, T. W. Ebbesen, "Beaming light from a subwavelength aperture" Science 297, 820-822 (2002).

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. 't Hooft, D. Lenstra and E. R. Eliel, "Plasmon-assisted two-slit transmission: Young's experiment revisited" Phys. Rev. Lett. 94, 053901 (2005).

N. Kuzmin, G. W. 't Hooft, E. R. Eliel, G. Gbur, H. F. Schouten, T. D. Visser, "Enhancement of spatial coherence by surface plasmons" Opt. Lett. 32, 445-447 (2007).

R. Gordon, "Near-field interference in a double slit in a perfect conductor" J. Opt. A: Pure Appl. Opt. 8, L1-L3 (2006).

P. Lalanne, J. P. Hugonin, "Interaction between optical nanoobjects at metallo-dielectric interfaces" Nat. Phys. 2, 551-556 (2006).

G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O'Dwyer, M. Sukharev and T. Seideman, "The response of nanostructured surfaces in the near field" Nat. Phys. 2, 792 (2006).

P. Lalanne, J. P. Hugonin, M. Besbes and P. Bienstman, "Reply: The response of nanostructured surfaces in the near field" Nat. Phys. 2, 792-793 (2006).

J. Van Bladel, Singular Electromagnetic Fields and Sources, (D.G. Dubley, ed., IEEE Press, New York, 1991).

M.G. Moharam, E. B. Grann, D. A. Pommet and T. K. Gaylord, "Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings" J. Opt. Soc. Am. A 12, 1068-1076 (1995).

P. Lalanne and G. M. Morris, "Highly improved convergence of the coupled-wave method for TM polarization" J. Opt. Soc. Am. A 13, 779-784 (1996).

G. Granet and B. Guizal, "Efficient implementation of the coupledwave method for metallic lamellar gratings in TM polarization" J. Opt. Soc. Am. A 13, 1019-1023 (1996).

L. Li, "Use of Fourier series in the analysis of discontinuous periodic structures" J. Opt. Soc. Am. A 13, 1870-1876 (1996).

E. Silberstein, P. Lalanne, J. P. Hugonin and Q. Cao, "On the use of grating theory in integrated optics" J. Opt. Soc. Am. A. 18, 2865- 2875 (2001).

J. P. Hugonin and P. Lalanne, "Perfectly-matched-layers as nonlinear coordinate transforms: a generalized formalization" J. Opt. Soc. Am. A. 22, 1844-1849 (2005).

R. Pregla and W. Pascher, "The Method of Lines", in Numerical Techniques for Microwave and Millimeter Wave Passive Structures, T. Itoh, ed., 381-446, (J. Wiley Publ., New York, USA, 1989).

R. Pregla, "MoL-BPM Method of Lines Based Beam Propagation Method", in Methods for Modeling and Simulation of Guided-Wave Optoelectronic Devices (PIER 11), Progress in Electromagnetic Research, W.P. Huang, ed., 51-102, (EMW Publishing, Cambridge, Massachusetts, USA, 1995).

R. Pregla and S. F. Helfert, "Modeling of Microwave devices with the method of lines", in Recent Research developments in Microwave Theory & Techniques, B. Beker and Y. Chen, eEds., 145- 196 (Research Signpost, Kerala, India, 2002).

S. F. Helfert and R. Pregla, "The method of lines: a versatile tool for the analysis of waveguide structures" Electromagnetics 22, 615-637 (2002).

P. Bienstman and R. Baets, "Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers" Optical and Quantum Electronics 33, 327-341 (2001). freely available from http://camfr.sourceforge.net.

W. C. Chew and W. H. Weedon, "A 3D perfectly matched medium from modified Maxwell's equations with stretched coordinates" Microw. Opt. Techn. Let. 7, 599-604 (1994).

K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media" IEEE T. Antenn. Propag. 14, 302-307 (1966).

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, (2nd edition, Artech House, Boston, MA, 2000).

J. P. Bérenger, "A perfectly matched layer for the absorption of electromagnetic waves", J. Comput. Phys. 114, 185-200 (1994).

Xiuhong Wei, "Three Dimensional Rigorous Model for Optical Scattering Problems" Ph.D. dissertation, Optics Research Group, Delft University of Technology, November 2006.

X. Wei, H. P. Urbach, A. J. H. Wachters, "Finite Element Model for Three-Dimensional Optical Scattering Problems" J. Opt. Soc. Am. A 24, 866-881 (2007).

A. Bossavit, "A rationale for edge-elements in 3D fields computations" IEEE T. Magn. 24, 74-79 (1988).

O. J. F. Martin, C. Girard and A. Dereux, "Generalized Field Propagator for Electromagnetic Scattering and Light Confinement" Phys. Rev. Lett. 74, 526-529 (1995).

O. J. F. Martin, A. Dereux and C. Girard, "Iterative scheme for computing exactly the total field propagating in dielectric structures of arbitrary shape" J. Opt. Soc. Am. A 11, 1073-1080 (1994).

A. S. van de Nes, J. J. M. Braat and S. F. Pereira, "High-density optical data storage" Rep. Prog. Phys. 69, 2323-2363 (2006).

M. Paulus, P. Gay-Balmaz and O. J. F. Martin, "Accurate and efficient computation of the Green's tensor for stratified media" Phys. Rev. E 62, 5797-5807 (2000).

C. Girard and A. Dereux, "Near-field optics theories" Rep. Prog. Phys. 59, 657-699 (1996).

A. S. van de Nes, "Rigorous Electromagnetic Field Calculations for Advanced Optical Systems" Delft University of Technology, PhD thesis (2005). Available at: http://www.library.tudelft.nl/dissertations.

E. Popov, M. Nevière, B. Gralak and G. Tayeb, "Staircase approximation validity for arbitrary-shaped gratings" J. Opt. Soc. Am. A. 19, 33-42 (2002).

P. Lalanne, J. P. Hugonin and J. C. Rodier, "Theory of surface plasmon generation at nanoslit aperture" Phys. Rev. Lett. 95, 263902 (2005).

L. Chen, J. T. Robinson and M. Lipson, "Role of radiation and surface plasmon polaritons in the optical interactions between a nano-slit and a nano-groove on a metal surface" Opt. Express 14, 12629-36 (2006).

L. Aigouy, P. Lalanne, J. P. Hugonin, G. Julié, V. Mathet and M. Mortier, "Near-field analysis of surface waves launched at nanoslit apertures" Phys. Rev. Lett. 98, 153902 (2007).

L. Li, "Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings" J. Opt. Soc. Am. A 13, 1024-1035 (1996).

G. Granet, "Reformulation of the lamellar grating problem through the concept of adaptive spatial resolution" J. Opt. Soc. Am. A 16, 2510-2516 (1999).

G. Granet and J. P. Plumey, "Parametric formulation of the Fourier Modal Method for crossed surface-relief gratings" J. Opt. A: Pure Appl. Opt. 4, S145-S149 (2002).

T. Vallius and M. Honkanen, "Reformulation of the Fourier modal method with adaptive spatial resolution: application to multilevel gratings" Opt. Express 10, 24-34 (2002).

P. Lalanne and M. P. Jurek, "Computation of the near-field pattern with the coupled-wave method for TM polarization" J. Mod. Optic. 45, 1357-1374 (1998).

P. Bienstman, S. Selleri, L. Rosa, H. P. Uranus, W. C. L. Hopman, R. Costa, A. Melloni, L. C. Andreani, J. P. Hugonin, P. Lalanne, D. Pinto, S. S. A. Obayya, M. Dems, K. Panajotov, "Modelling leaky photonic wires: a mode solver comparison" Opt. Quant. Electron. 38, 731-759 (2007).

J. A. Roden, S. D. Gedney, "Convolutional PML (CPML): An Efficient FDTD Implementation of the CFS-PML for Arbitrary Media" Microw. Opt. Techn. Let. 27, 334 (2000).

M. Fujii, M. Tahara, I. Sakagami, W. Freude, P. Russer, "Highorder FDTD and auxiliary differential equation formulation of optical pulse propagation in 2-D Kerr and Raman nonlinear dispersive media" IEEE J. Quantum Elect. 40, 175-182 (2004).

G. Parent, D. Van Labeke and F. I. Baida, "Theoretical Study of Transient Phenomena in Near-Field Optics" J. Microscopy 202, 296- 306 (2001).

F. I. Baida and D. Van Labeke, "Light transmission by subwavelength annular aperture arrays in metalic films" Opt. Commun. 209, 17-22 (2002).

M. Sukharev, T. Seideman, "Coherent control approaches to light guidance in the nanoscale" J. Chem. Phys. 124, 144707 (2006).

G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O'Dwyer, M. Sukharev, T. Seideman "Surface quality and surface waves on subwavelength-structured silver films" Phys. Rev. E 75, 016612 (2007).

Y. Saad, Iterative methods for sparse linear systems, (2nd ed., Society for Industrial and Applied Mathematics, 2003).

J. L. Volakis, A. Chatterjee and L. C. Kempel, "Review of the finiteelement method for three-dimensional electromagnetic scattering" J. Opt. Soc. Am. A 11, 1442-1454 (1994).