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

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 7717, Issue , 2010, Pages

  Bouchon, P ^a,b   Pardo, F ^b   HaIdar R ^a   Pelouard, J L ^b  

^a ONERA   (France)

^b CNRS   (France)

Author keywords

B splines; Modal method; Sparse matrices; Subwavelength gratings

Indexed keywords

B SPLINES; B-SPLINE; DESIGN AND ANALYSIS; FAST COMPUTATION; MODAL METHOD; NANOOPTICS; NONUNIFORM B SPLINE; SPARSE MATRICES; SPEED-UPS; SUB-WAVE LENGTH GRATING; SUB-WAVELENGTH STRUCTURES;

DESIGN; MATRIX ALGEBRA; MAXWELL EQUATIONS; OPTICAL DEVICES; OPTICAL INSTRUMENTS; SHIP PROPELLERS;

SPLINES;

EID: 77954986083     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.854552     Document Type: Conference Paper

References (23)

1. Barnes, W., Dereux, A., and Ebbesen, T., "Surface plasmon subwavelength optics," Nature 424(6950), 824-830 (2003).
2. Schuller, J., Barnard, E., Cai, W., Jun, Y., White, J., and Brongersma, M., "Plasmonics for extreme light concentration and manipulation," Nature Materials 9(3), 193-204 (2010).
3. Lalanne, P. and Morris, G., "Highly improved convergence of the coupled-wave method for TM polarization," Journal of the Optical Society of America A 13(4), 779-784 (1996).
4. Yee, K., "Numerical solution of inital boundary value problems involving maxwell's equations in isotropic media," IEEE Transactions on antennas and propagation 14(3), 302-307 (1966).
5. Taflove, A. and Umashankar, K., "The finite-difference time-domain method for numerical modeling of electromagnetic wave interactions," Electromagnetics 10(1), 105-126 (1990).
6. Wei, X., Wachters, A., and Urbach, H., "Finite-element model for three-dimensional optical scattering problems," Journal of the Optical Society ofAmerica A 24(3), 866-881 (2007).
7. Bouchon, P., Pardo, F., Haïdar, R., and Pelouard, J., "Fast modal method for subwavelength gratings based on B-splines formulation," Journal of the Optical Society of America A 27(4), 696-702 (2010).
8. Schoenberg, I., "Contributions to the problem of approximation of equidistant data by analytic functions. Part A: On the problem of smoothing or graduation. A first class of analytic approximation formulae. Part B: On the problem of osculatory interpolation. A second class of analytic approximation formulae.," Quart. Appl. Math. 4, 45-99,112-141 (1946).
9. Cox, M., "The Numerical Evaluation of B-Splines*," IMA Journal of Applied Mathematics 10(2), 134-149 (1972).
10. De Boor, C., "On calculating with B-splines," J. Approx. Theory 6(1), 50-62 (1972).
11. Ko, D. and Sambles, J., "Scattering matrix method for propagation of radiation in stratified media: attenuated total reflection studies of liquid crystals," Journal of the Optical Society of America A 5(11), 1863-1866 (1988).
12. Pardo, F., Gottesman, Y., and Pelouard, J., "Strictly rigorous Maxwell and polynomial constitutive function approximation: a new powerful tool for electromagnetic computations," In preparation .
13. Lehoucq, R., Sorensen, D., and Yang, C., [ARPACK users' guide: solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods], Siam (1998).
14. Skigin, D. and Depine, R., "Transmission resonances of metallic compound gratings with subwavelength slits," Physical review letters 95(21), 217402 (2005).
15. Porto, J., Garcia-Vidal, F., and Pendry, J., "Transmission resonances on metallic gratings with very narrow slits," Physical Review Letters 83(14), 2845-2848 (1999).
16. Collin, S., Vincent, G., Haïdar, R., Bardou, N., Rommeluère, S., and Pelouard, J., "Nearly Perfect Fano Transmission Resonances through Nanoslits Drilled in a Metallic Membrane," Physical Review Letters 104(2), 027401 (2010).
17. Vincent, G., Collin, S., Bardou, N., Pelouard, J., and Haïdar, R., "Large-area dielectric and metallic freestanding gratings for midinfrared optical filtering applications," Journal of Vacuum Science © Technology B: Microelectronics and Nanometer Structures 26, 1852 (2008).
18. Palik, E. and Ghosh, G., [Handbook of optical constants of solids], Academic press (1985).
19. Haïdar, R., Vincent, G., Guérineau, N., Collin, S., Velghe, S., and Primot, J., "Wollaston prism-like devices based on blazed dielectric subwavelength gratings," Optics Express 13(25), 9941-9953 (2005).
20. Verslegers, L., Catrysse, P., Yu, Z., and Fan, S., "Planar metallic nanoscale slit lenses for angle compensation," Applied Physics Letters 95, 071112 (2009).
21. Verslegers, L., Catrysse, P., Yu, Z., White, J., Barnard, E., Brongersma, M., and Fan, S., "Planar lenses based on nanoscale slit arrays in a metallic film," Nano letters 9(1), 235-238 (2008).
22. Verslegers, L., Catrysse, P., Yu, Z., and Fan, S., "Deep- subwavelength focusing and steering of light in an aperiodic metallic waveguide array," Physical Review Letters 103(3), 033902 (2009).
23. Christodoulides, D., Lederer, F., and Silberberg, Y., "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424(6950), 817-823 (2003).