Simulation and optimisation methods for non-periodic subwavelength structures

The use of nano-structured elements in the fabrication of micro-optical subwavelength components requires a fully vectorial solution to Maxwell's curl equations. In this paper, we compare the results generated by two of the main methods used in the solution of the curl equations, the Fourier Modal Method (FMM) and the Finite Difference Time Domain (FDTD) method. We address the computational issues surrounding the accurate modelling of nano-structured elements (with features in the 10nm-100nm range) for a range of micro-optical elements, e.g. cylindrical lenses, photonic bandgap reflectors and polarisation dependent beamsplitters. Finally, we show the experimental verification of the nano-structured designs using microwave radiation.

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

[2]  Philippe Lalanne,et al.  Perfectly matched layers as nonlinear coordinate transforms: a generalized formalization. , 2005, Journal of the Optical Society of America. A, Optics, image science, and vision.

[3]  E Popov,et al.  Maxwell equations in Fourier space: fast-converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media. , 2001, Journal of the Optical Society of America. A, Optics, image science, and vision.

[4]  Dorothea Heiss-Czedik,et al.  An Introduction to Genetic Algorithms. , 1997, Artificial Life.

[5]  Emile H. L. Aarts,et al.  Simulated Annealing: Theory and Applications , 1987, Mathematics and Its Applications.

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

[7]  Jin-Fa Lee,et al.  A perfectly matched anisotropic absorber for use as an absorbing boundary condition , 1995 .

[8]  Ehl Emile Aarts,et al.  Simulated annealing and Boltzmann machines , 2003 .

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

[10]  C. Burckhardt.  Diffraction of a Plane Wave at a Sinusoidally Stratified Dielectric Grating , 1966 .

[11]  Andrew J. Waddie,et al.  Diffractive optical element design techniques for high-fidelity optical interconnections and beam-shaping applications , 2004, SPIE Photonics Europe.

[12]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[13]  Jari Turunen,et al.  Eigenmode method for electromagnetic synthesis of diffractive elements with three-dimensional profiles , 1994 .

[14]  Allen Taflove,et al.  Computational Electrodynamics the Finite-Difference Time-Domain Method , 1995 .

[15]  M R Taghizadeh,et al.  Analysis of gratings with large periods and small feature sizes by stitching of the electromagnetic field. , 1996, Optics letters.

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

[17]  Melinda Piket-May,et al.  9 – Computational Electromagnetics: The Finite-Difference Time-Domain Method , 2005 .

[18]  Lifeng Li,et al.  Reformulation of the fourier modal method for surface-relief gratings made with anisotropic materials , 1998 .

[19]  V. Cerný.  Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm , 1985 .

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

[21]  S.,et al.  Numerical Solution of Initial Boundary Value Problems Involving Maxwell’s Equations in Isotropic Media , 1966 .

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

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