JMP  Vol.3 No.1 , January 2012
Optical Near Field Study of Ag Nanowires by the Differential Method
ABSTRACT
The optical response of subwavelength silver nanowires arranged periodically on silica has been analyzed numerically by the differential method improved by the S matrix algorithm. Our results improve the capacity of this rigorous method to give a description of various phenomena occurring in near and far field around the periodic grating. This renders pos- sible to determine the positions of plasmon’s resonance according to the choice of materials used and the geometrical properties. We study the behavior of the diffracted light by the nano-structure in both single nanowire case and grating nanowires case. The influence of the exact grating period and the induced modification of the spacer nanowire depend- ence are then discussed. Moreover, we present mappings of the electromagnetic field located at 50 nm above the nanowires.

Cite this paper
M. Chekroun, G. Bassou, L. Salomon, A. Zenati, A. Taalbi, H. Bendaoud and M. Ameri, "Optical Near Field Study of Ag Nanowires by the Differential Method," Journal of Modern Physics, Vol. 3 No. 1, 2012, pp. 102-109. doi: 10.4236/jmp.2012.31014.
References
[1]   A. L. Lereu, A. Passian, J.-P. Goudonnet, T. Thundat and T. L. Ferrell, “Thermo-Optical Processes in Thin Films Based on Surface Plasmons,” Applied Physics Letters, Vol. 86, No. 15, 2005, p. 154101. doi:10.1063/1.1900311

[2]   A. Passian, A. L. Lereu, E. T. Arakawa, A. Wig, T. Thundat and T. L. Ferrell, “Modulation of Multiple Photon Energies by Use of Surface Plasmons,” Optics Letters, Vol. 30, No. 1, 2005, pp. 41-43. doi:10.1364/OL.30.000041

[3]   A. Passian, S. Zahrai, A. L. Lereu, R. H. Farahi, T. L. Ferrell and T. Thundat, “Nonradiative Surface Plasmon Assisted Microscale Marangoni Forces,” Physical Review E, Vol. 73, No. 6, 2006, p. 066311. doi:10.1103/PhysRevE.73.066311

[4]   D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the Diffraction Limit,” Nature Photonics, Vol. 4, 2010, pp. 83-91. doi:10.1038/nphoton.2009.282

[5]   L. Cao and M. L. Brongersma, “Active Plasmonics: Ultrafast Developments,” Nature Photonics, Vol. 3, 2009, pp. 12-13. doi:10.1038/nphoton.2008.259

[6]   A. Christ, et al., “Controlling the Interaction between Localized and Delocalized Surface Plasmon Modes: Experiment and Numerical Calculations,” Physical Review B, Vol. 74, 2006, pp. 155435.

[7]   S. Maier, et al., “Plasmonics: Localization and Guiding of Electromagnetic Energy in Metal/Dielectric Structure JAP 98,” Vol. 1, 2005, p. 01110.

[8]   R. H. Ritchie, “Plasma Losses by Fast Electrons in Thin Films,” Physical Review, Vol. 106, No. 5, 1957, pp. 874- 881. doi:10.1103/PhysRev.106.874

[9]   S. C. Kitson, W. L. Barnes and J. R. Sambles, “Full Photonic Band Gap for Surface Modes in the Visible,” Physical Review Letters, Vol. 77, No. 13, 1996, pp. 2670- 2673. doi:10.1103/PhysRevLett.77.2670

[10]   S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard and J. M. Hvam, “Waveguiding in Surface Plasmon Polariton Band Gap Structures,” Physical Review Letters, Vol. 86, No. 14, 2001, pp. 3008-3011. doi:10.1103/PhysRevLett.86.3008

[11]   S. Linden, J. Kuhl and H. Giessen, “Controlling the Interaction between Light and Gold Nanoparticles: Selective Suppression of Extinction,” Physical Review Letters, Vol. 86, No. 20, 2001, pp. 4688-4691. doi:10.1103/PhysRevLett.86.4688

[12]   H. Raether, “Surface Plasmons on Smooth and Rough Surfaces and on Gratings,” Tracts in Modern Physics, Springer, 1988, p. 111.

[13]   U. Kreibig and M. Vollmer, “Optical Properties of Metal Clusters,” Springer-Verlag, Berlin, 1995.

[14]   C. Sonnichsen, S. Geier, N. E. Hecker, G. von Plessen, J. Feldmann, H. Ditlbacher, B. Lamprecht, J. R. Krenn, F. R. Aussenegg, V. Z. H. Chan, J. P. Spatz and M. Moller, “Spectroscopy of Single Metallic Nanoparticles Using Total Internal Reflection Microscopy,” Applied Physics Letters, Vol. 77, No. 19, 2000, pp. 2949-2951. doi:10.1063/1.1323553

[15]   A. Curry, G. Nusz, A. Chilkoti and A. Wax, “Substrate Effect on Refractive Index Dependence of Plasmon Resonance for Individual Silver Nanoparticles Observed Using Darkfield Microspectroscopy,” Optics Express, Vol. 13, No. 7, 2005, pp. 2668-2677. doi:10.1364/OPEX.13.002668

[16]   M. Quinten, “Local Fields Close to the Surface of Nano- particles and Aggregates of Nanoparticles,” Applied Physics B, Vol. 73, 2001, pp. 245-255.

[17]   N. Felidj, J. Aubard, G. Levi, J. R. Krenn, G. Schider, A. Leitner and F. R. Aussenegg, “Enhanced Substrate-Induced Coupling in Two-Dimensional Gold Nanoparticle Arrays” Physical Review B, Vol. 66, No. 24, 2002, p. 245407. doi:10.1103/PhysRevB.66.245407

[18]   B. Khlebtsov, V. Zharov, A. Melnikov, V. Tuchin and N. Khlebtsov, “Optical Amplification of Photothermal Therapy with Gold Nanoparticles and Nanoclusters,” Nanotechnology, Vol. 17, No. 20, 2006, p. 5167. doi:10.1088/0957-4484/17/20/022

[19]   J. R. Lakovicz, “Radiative Decay Engineering: Biophysical and Biomedical Applications,” Analytical Biochemistry, Vol. 298, No. 1, 2001, pp. 1-24. doi:10.1006/abio.2001.5377

[20]   A. L. Lereu, G. Sanchez-Mosteiro, P. Ghenuche, R. Quidant and N. F. van Hulst, “Individual Gold Dimers Investigated by Far and Near Field Imaging,” Journal of Microscopy, Vol. 229, No. 2, 2008, pp. 254-258. doi:10.1111/j.1365-2818.2008.01895.x

[21]   A. L. Lereu, G. Sanchez-Mosteiro, P. Ghenuche, A. Passian, R. Quidant and N. F. van Hulst, “Probing the Local Field at Metallic Antennas Using Single Particle Luminescence,” Journal of Physics D, Vol. 100, 2008, p. 052038.

[22]   B. Lamprecht, J. R. Krenn, G. Schider, H. Ditlbacher, M. Salerno, N. Felidj, A. Leitner, F. R. Aussenegg and J. C. Weeber, “Surface Plasmon Propagation in Microscale Metal Stripes,” Applied Physics Letters, Vol. 79, No. 1, 2001, p. 51. doi:10.1063/1.1380236

[23]   S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel and A. A. G. Requicha, “Local Detection of Electromagnetic Energy Transport below the Diffraction Limit in Metal Nanoparticle Plasmon Waveguides,” Nature Materials, Vol. 2, 2003, pp. 229-232. doi:10.1038/nmat852

[24]   B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. R. Aussenegg, A. Leitner and J. R. Krenn, “Dielectric Stripes on Gold as Surface Plasmon Waveguides,” Applied Physics Letters, Vol. 88, No. 9, 2006, p. 094104. doi:10.1063/1.2180448

[25]   H. Ditlbacher, A. Hohenau, D. Wagner, U. Krebig, M. Rogers, F. Hofer, F. R. Aussenegg and J. R. Krenn, “Silver Nanowires as Surface Plasmon Resonators,” Physical Review Letters, Vol. 95, No. 25, 2005, p. 257403. doi:10.1103/PhysRevLett.95.257403

[26]   Y. G. Sun, Y. D. Yin, B. T. Mayers, T. Herricks and Y. N. Xia, “Uniform Silver Nanowires Synthesis by Reducing AgNO3 with Ethylene Glycol in the Presence of Seeds and Poly (Vinil Pyrrolidone),” Chemistry of Materials, Vol. 14, No. 11, 2002, pp. 4736-4745. doi:10.1021/cm020587b

[27]   G. Schider, J. R. Krenn, W. Gotschy, B. Lamprecht, H. Ditlbacher, A. Leitner and F. R. Aussenegg, “Optical Properties of Ag and Au Nanowire Gratings,” Journal of Applied Physics, Vol. 90, No. 8, 2001, pp. 3825-3830. doi:10.1063/1.1404425

[28]   R. Petit, “Electromagnetic Theory of Gratings,” Springer- Verlag, Berlin, 1980, p. 128. doi:10.1007/978-3-642-81500-3

[29]   L. Salomon, F. de Fornel and P. M. Adam, “Analysis of the Near Field and the Far Field Diffracted by a Metallized Grating at and beyond the Plasmon Resonance,” Journal of the Optical Society of America A, Vol. 16, No. 11, 1999, pp. 2695-2704. doi:10.1364/JOSAA.16.002695

[30]   L. Salomon, C. Charbonnier, F. de Fornel, P. M. Adam, P. Guérin and F. Carcenac, “Near-Field Optical Study of Mesoscopic Au Periodic Samples: Effect of the Polarization and Comparison between Different Imaging Modes,” Physical Review B, Vol. 62, 2000, pp. 17072-17083. doi:10.1103/PhysRevB.62.17072

[31]   H. Boutaleb, L. Salomon, G. Bassou and M. Z. Chekroun, “A Study of a Differential Method for a Field Diffracted by a Rough Surface,” Journal of Molecular Structure Theochem, Vol. 777, No. 1-3, 2006, pp. 139-143. doi:10.1016/j.theochem.2006.08.042

[32]   M. Y. Mahmoud, et al., “Near-Field Study with a Photon Scanning Tunneling Microscope: Comparison between Dielectric Nanostructure and Metallic Nanostructure,” Materials Science and Engineering B, Vol. 142, No. 1, 2007, pp. 37-45. doi:10.1016/j.mseb.2007.06.008

[33]   S. Goumri-Said, et al., “Numerical Study of Photolithography System: Electromagnetic Differential Method,” Journal of Materials Processing Technology, Vol. 148, No. 1, 2004, pp. 50-56. doi:10.1016/j.jmatprotec.2004.01.039

[34]   S. Goumri-Said, et al., “Numerical Simulations of Photon Scanning Tunneling Microscopy: Role of a Probe Tip Geometry in Image Formation,” Optics Communications, Vol. 244, No. 1-6, 2005, pp. 245-258. doi:10.1016/j.optcom.2004.09.024

[35]   L. Li, “Formulation and Comparison of Two Recursive Matrix Algorithms for Modeling Layered Diffraction Gratings,” Journal of the Optical Society of America A, Vol. 13, No. 5, 1996, pp. 1024-1035. doi:10.1364/JOSAA.13.001024

[36]   F. Montiel, M. Nevière and P. Peyrot, “Waveguide Confinement of Cerenkov Second-Harmonic Generation through a Graded-Index Grating Coupler: Electromagnetic Optimization,” Journal of Modern Optics, Vol. 45, No. 10, 1998, pp. 2169-2186. doi:10.1080/09500349808231753

[37]   L. Li, “Use of Fourier Series in the Analysis of Discontinuous Periodic Structures,” Journal of the Optical Society of America A, Vol. 13, No. 9, 1996, pp. 1870-1876. doi:10.1364/JOSAA.13.001870

[38]   J. Tevro, et al., “Efficient Bragg Wave-Guide Grating Analysis by Quasi-Rigorous Approach Based on Redheffer’s Star Product,” Optics Communications, Vol. 198, 2001, pp. 265-272.

[39]   B. Saswateeect, “Analysis of Near Field Characteristics of a Diffractive Optical Laser Beam Profile Shaper Using a High Accuracy Finite Difference Time Domain Method,” Proceedings of SPIE, Vol. 4832, 2002, pp. 454- 465. doi:10.1117/12.486445

[40]   N. Ya, Z. Wang, C. Zhou, et al., “Mode-Matching Analysis of Deep Etched Phase Gratings,” Journal of Optical Communications and Networking, Vol. 21, No. 6, 2000, pp. 229-231. doi:10.1515/JOC.2000.21.6.229

[41]   Y. Ohkawa, Y. Tsuji and M. Koshiba, “Analysis of Anisotropic Dielectric Grating Diffraction Using the Finite-Element Method,” Journal of the Optical Society of America A, Vol. 13, No. 5, 1996, pp. 1006-1012. doi:10.1364/JOSAA.13.001006

[42]   M. G. Moharam and T. K. Gaylord, “Rigorous Couple- Wave Analysis of Planar-Grating Diffraction,” Journal of the Optical Society of America A, Vol. 71, No. 7, 1981, pp. 811-818doi:10.1364/JOSA.71.000811

[43]   L. F. Li, “Multilayer Modal Method for Diffraction Gratings of Arbitrary Profile, Depth and Permittivity,” Journal of the Optical Society of America A, Vol. 10, No. 12, 1993, pp. 2581-2591. doi:10.1364/JOSAA.10.002581

[44]   M. G. Moharam, D. A. Pommet and E. B. Grann, “Stable Implementation of the Rigorous Coupled-Wave Analysis for Surface-Relief Gratings: Enhanced Transmittance Matrix Approach,” Journal of the Optical Society of America A, Vol. 12, No. 5, 1995, pp. 1077-1086. doi:10.1364/JOSAA.12.001077

[45]   E. D. Palik, “Handbook of Optical Constants of Solid,” Academic Press, New York, 1985, p. 355.

[46]   D. Gérard, L. Salomon, F. de Fornel and A. Zayats, “Analysis of the Bloch Mode Spectra of Surface Polaritonic Crystals in the Weak and Strong Coupling Regimes: Grating-Enhanced Transmission at Oblique Incidence and Suppression of SPP Radiative Losses,” Optics Express, Vol. 12, No. 16, 2004, pp. 3652-3663. doi:10.1364/OPEX.12.003652

[47]   A. Benabbas, et al., “Analytical Model of the Optical Response of Periodically Structured Metallic Films,” Optics Express, Vol. 13, No. 22, 2005, pp. 8730-8745. doi:10.1364/OPEX.13.008730

[48]   D. Gérard, L. Salomon, F. de Fornel and A. V. Zayats, “Ridge-Enhanced Optical Transmission through a Continuous Metal Film,” Physical Review B, Vol. 69, No. 11, 2004, p. 113405. doi:10.1103/PhysRevB.69.113405

[49]   A. Giannattasio, I. R. Hooper and W. L. Barnes, “Dependence on Surface Profile in Grating-Assisted Coupling of Light to Surface Plasmon-Polaritons,” Optics Communications, Vol. 261, No. 2, 2006, pp. 291-295. doi:10.1016/j.optcom.2005.12.016

[50]   N. García, “Exact Calculations of P-Polarized Electromagnetic Fields Incident on Grating Surfaces: Surface Polariton Resonances,” Optics Communications, Vol. 45, No. 5, 1983, pp. 307-310. doi:10.1016/0030-4018(83)90254-7

[51]   P. Vincent, “Electromagnetic Theory of Gratings,” Topics in Current Physics, Vol. 22, 1980, pp. 101-121. doi:10.1007/978-3-642-81500-3_4

[52]   R. C. Mac Phedran, G. H. Derrick, M. Nevière and D. Maystre, ‘‘Metallic Crossed Grating,’’ Journal of the Optics, Vol. 29, 1982, pp. 209-218.

[53]   R. C. Mac Phedran, “Electromagnetic Theory of Gratings,” Topics in Current Physics, Vol. 22, 1980, pp. 227- 276.

 
 
Top