Simulations of nano-optics devices with a fast B-spline modal method

Here, we address the need for fast computation of subwavelength structures. It allows fast conception of optical devices. We present a modal method based on B-splines formulation which solves Maxwell equations. The two assets of this method are to use non uniform B-splines permitting to adapt the mesh to the structure, and to produce sparse matrices which permit to speed up the computation. As an illustration, we make use of this method for the design and analysis of variously shaped infrared optical devices.

[1]  Ricardo A Depine,et al.  Transmission resonances of metallic compound gratings with subwavelength slits. , 2005, Physical review letters.

[2]  C. D. Boor,et al.  On Calculating B-splines , 1972 .

[3]  Jean-Luc Pelouard,et al.  Nearly perfect Fano transmission resonances through nanoslits drilled in a metallic membrane. , 2010, Physical review letters.

[4]  K. Yee.  Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media , 1966 .

[5]  Zongfu Yu,et al.  Planar metallic nanoscale slit lenses for angle compensation , 2009 .

[6]  John Roy Sambles,et al.  Scattering matrix method for propagation of radiation in stratified media: attenuated total reflection studies of liquid crystals , 1988 .

[7]  Allen Taflove,et al.  The Finite-Difference Time-Domain Method for Numerical Modeling of Electromagnetic Wave Interactions , 1990 .

[8]  H Paul Urbach,et al.  Finite-element model for three-dimensional optical scattering problems. , 2007, Journal of the Optical Society of America. A, Optics, image science, and vision.

[9]  Yaron Silberberg,et al.  Discretizing light behaviour in linear and nonlinear waveguide lattices , 2003, Nature.

[10]  Zongfu Yu,et al.  Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array , 2009, OPTO.

[11]  L. Verslegers,et al.  Planar lenses based on nanoscale slit arrays in a metallic film , 2009, 2009 Conference on Lasers and Electro-Optics and 2009 Conference on Quantum electronics and Laser Science Conference.

[12]  W. Cai,et al.  Plasmonics for extreme light concentration and manipulation. , 2010, Nature materials.

[13]  Chao Yang,et al.  ARPACK users' guide - solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods , 1998, Software, environments, tools.

[14]  F. García-Vidal,et al.  Transmission Resonances on Metallic Gratings with Very Narrow Slits , 1999, cond-mat/9904365.

[15]  W. Barnes,et al.  Surface plasmon subwavelength optics , 2003, Nature.

[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]  Jean-Luc Pelouard,et al.  Large-area dielectric and metallic freestanding gratings for midinfrared optical filtering applications , 2008 .

[18]  I. J. Schoenberg.  Contributions to the problem of approximation of equidistant data by analytic functions. Part B. On the problem of osculatory interpolation. A second class of analytic approximation formulae , 1946 .

[19]  Jean-Luc Pelouard,et al.  Fast modal method for subwavelength gratings based on B-spline formulation. , 2010, Journal of the Optical Society of America. A, Optics, image science, and vision.

[20]  E. Palik.  Handbook of Optical Constants of Solids , 1997 .

[21]  M. Cox.  The Numerical Evaluation of B-Splines , 1972 .

[22]  Jérôme Primot,et al.  Wollaston prism-like devices based on blazed dielectric subwavelength gratings. , 2005, Optics express.