Generation of adaptive coordinates and their use in the Fourier Modal Method.

We present an improvement of the standard Fourier Modal Method (FMM) for the analysis of lamellar gratings that is based on the use of automatically generated adaptive coordinates for arbitrarily shaped material profiles in the lateral plane of periodicity. This allows for an accurate resolution of small geometric features and/or large material contrasts within the unit. For dielectric gratings, we obtain considerable convergence accelerations. Similarly, for metallic gratings, our approach allows efficient and accurate computations of transmittance and reflectance coefficients into various Bragg orders, the spectral positions of Rayleigh anomalies, and field enhancement values within the grating structures.

[1]  Lifeng Li,et al.  Note on the S-matrix propagation algorithm. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[2]  T. Gaylord,et al.  Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings , 1995 .

[3]  Lifeng Li,et al.  New formulation of the Fourier modal method for crossed surface-relief gratings , 1997 .

[4]  B. Bai,et al.  Group-theoretic approach to enhancing the Fourier modal method for crossed gratings with C4 symmetry , 2005 .

[5]  Daniel Maystre,et al.  Multicoated gratings: a differential formalism applicable in the entire optical region , 1982 .

[6]  Lifeng Li,et al.  Use of Fourier series in the analysis of discontinuous periodic structures , 1996 .

[7]  Evgeny Popov,et al.  Light Propagation in Periodic Media , 2002 .

[8]  M. Wegener,et al.  Periodic nanostructures for photonics , 2007 .

[9]  John A Rogers,et al.  Nanostructured plasmonic sensors. , 2008, Chemical reviews.

[10]  Luke P. Lee,et al.  Shadow overlap ion-beam lithography for nanoarchitectures. , 2009, Nano letters (Print).

[11]  Marc Lamy de la Chapelle,et al.  Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method , 2005 .

[12]  U. Leonhardt,et al.  General relativity in electrical engineering , 2006, SPIE Optics + Optoelectronics.

[13]  Jennifer S. Shumaker-Parry,et al.  Fabrication of Crescent‐Shaped Optical Antennas , 2005 .

[14]  Lifeng Li.  Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings , 1996 .

[15]  Lifeng Li,et al.  Fourier modal method for crossed anisotropic gratings with arbitrary permittivity and permeability tensors , 2003 .

[16]  P. Lalanne,et al.  Highly improved convergence of the coupled-wave method for TM polarization and conical mountings , 1996, Diffractive Optics and Micro-Optics.

[17]  F. G. D. Abajo.  Colloquium: Light scattering by particle and hole arrays , 2007, 0903.1671.

[18]  Wolfgang Osten,et al.  Normal vector method for convergence improvement using the RCWA for crossed gratings. , 2007, Journal of the Optical Society of America. A, Optics, image science, and vision.

[19]  Gérard Granet,et al.  Reformulation of the lamellar grating problem through the concept of adaptive spatial resolution , 1999 .

[20]  Brahim Guizal,et al.  Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization , 1996 .

[21]  Brahim Guizal,et al.  Analysis of strip gratings using a parametric modal method by Fourier expansions , 2005 .

[22]  Gygi.  Electronic-structure calculations in adaptive coordinates. , 1993, Physical review. B, Condensed matter.

[23]  D. Bird,et al.  Adaptive curvilinear coordinates in a plane-wave solution of Maxwell’s equations in photonic crystals , 2005 .

[24]  Matti Lassas,et al.  Cloaking Devices, Electromagnetic Wormholes, and Transformation Optics , 2009, SIAM Rev..

[25]  Wolfgang Osten,et al.  Normal vector method for the RCWA with automated vector field generation. , 2008, Optics express.

[26]  Tuomas Vallius,et al.  Reformulation of the Fourier modal method with adaptive spatial resolution: application to multilevel profiles. , 2002, Optics express.

[27]  Harald Giessen,et al.  Matched coordinates and adaptive spatial resolution in the Fourier modal method. , 2009, Optics express.

[28]  T. Gaylord,et al.  Diffraction analysis of dielectric surface-relief gratings , 1982 .

[29]  Gérard Granet,et al.  Parametric formulation of the Fourier modal method for crossed surface-relief gratings , 2002 .

[30]  M. Kreiter,et al.  Tuning resonances on crescent-shaped noble-metal nanoparticles , 2007 .