Content

Simulation and modeling

Leader: Demetrio Macias

 

Members :

Demetrio Macias, Alexandre Vial, Elena Ionescu

Past PhD students : Anne-Sophie Grimault, Montacer Dridi, Huan Wang, Loic Le Cunff

 

Activity description:

The research activity of this group is devoted to the modelling of the interaction between light and metallic nano-structures through the employment of different numerical or semi-analytic approaches such as  the Finite-Differences Time-Domain Method (FDTD),  the Boundary-Elements Method (BEM) or Mie's Theory, to name but a few examples, and to the resolution of inverse problems by means of stochastic optimization techniques like Simulated Annealing or Evolutionary Algorithms, for instance.  

The strong collaboration between the different research groups at the LNIO, whose activities are mainly experimental, and the modelling axis conferes to the latter a noteworthy transverse character that, broadly speaking, serves to foresee and characterize the behavior of a particular experiment, through the employment of the numerical simulation and optimization techniques mentioned in the previous paragraph.

A representative example that illustrates one part our research activities is the study of the problems associated with the description of the dielectric constant of metals, frequently  described by means of Drude-Lorentz' model [5,6,8,11]. However, the number of terms required to achieve an accurate representation of the permittivity,  within a large spectral interval, makes of this approach prohibitive in terms of computing time and memory. To circumvent this limitation, we have focused our attention on the Critical Points Method (CPM) [7], that  provides, with a  limited  number of terms, a better and less computationally expensive description of the permitivity of different metals such as, for instance, gold, silver, aluminum or copper [9-10].  This has opened the way  to carry on spectroscopic studies in which not only it is possible to consider large spectral intervals, but also it is possible to have different kinds of metals in the system studied.  Several works employing  this approach,  have been conducted in collaboration with teams 1 and 2 [12-15].

We have also investigated two fundamental facets of the inverse problem. In the first of them we were interested on the retrieval of some unknown geometrical or material parameters of a nano-structure, e.g. its size or dielectric constant, and also on  the illumination and detection conditions, for example, the polarization, the angle of incidence or  the angles of detection [1-4]. For this, although the choice is not restrictive and we could have used any other direct method, we employed the FDTD together with a  Stochastic Optimization method known as  Evolutionary Algorithms. This is a  population-based technique that mimics the process of variation and selection that take place in nature through the "genetic operators" of recombination, mutation and selection. Recently, we have used our inversion method to explore the other aspect of the inverse problem that consists in the optimization of certain characteristics of scattered near-field as the visibility of a plasmons interference pattern or the near-field scattered intensity, through the controlled variation of the  geometry and illumination conditions of the sample.

 

Selected publications:
  1. D. Macías, A. Vial, and D. Barchiesi. Application of evolution strategies for the solution of an inverse problem in near-field optics. J. Opt. Soc. Am. A, 21: 1465–1471, 2004.
  2. D. Macías and D. Barchiesi. Identification of unknown experimental parameters from noisy A-SNOM data with an evolutionary procedure.  Optics letters, 30: 2557-2559, 2005.
  3. E. Méndez and D. Macías. Inverse problems in optical scattering. In: MARADUDIN, A. Light Scattering and Nanoscale Surface Roughness. New York: Springer, 2006. p. 435-465.
  4. D. Macias and A. Vial. Optimal design of plasmonic nanostructures for plasmon-interference assisted lithography. Appl. Phys. B-Lasers Opt., 93(1): 159-163, 2008.
  5. A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, and M. Lamy de la Chapelle. Improved analytical fit of gold dispersion : application to the modelling of extinction spectra with the FDTD method. Phys. Rev. B, 71(8): 085416–085422, 2005.
  6. A.-S. Grimault, A. Vial, and M. Lamy de la Chapelle. Modeling of regular gold nanostructures arrays for sers applications using a 3D FDTD method. Appl. Phys. B-Lasers Opt., 84(1-2): 111–115, 2006.
  7. A. Vial. Implementation of the critical points model in the recursiveconvolution method for dispersive media modeling with the FDTD method. J. Opt. A: Pure Appl. Opt., 9(7): 745–748, 2007. (PDF)
  8. T. Laroche, A. Vial and M. Roussey. Crystalline structure's influence on the Near-field optical properties of single plasmonic nanowires. Appl. Phys. Lett., 91(12): 123101, 2007.
  9. A. Vial and T. Laroche. Description of dispersion properties of metals by mean of thecritical points model and application to the study of resonantstructures using the FDTD method. J. Phys. D: Appl. Phys., 40(22): 7152-7158, 2007. (PDF)
  10. A. Vial and T. Laroche. Comparison of gold and silver dispersion laws suitable for FDTD simulations. Appl. Phys. B-Lasers Opt., 93(1): 139-143, 2008.
  11. A.-S. Grimault, A. Vial, J. Grand and M. Lamy de la Chapelle. Modeling of the near-field of metallic nanoparticle gratings: Localized Surface Plasmon Resonance and SERS applications. J. Microscopy, 229(3): 428-432, 2008.
  12. C. Hubert, A. Rumyantseva,G. Lérondel, J. Grand,S. Kostcheev, L.Billot, A. Vial,R. Bachelot, P. Royer, S.H. Chang, S.K. Gray,G.P.Wiederrecht, and G. C. Schatz. Near-fieldphotochemical imaging of noble metal nanostructures. Nanolett., 5(4):615–619, 2005.
  13. J. Grand,M. Lamy de la Chapelle, J.-L.Bijeon, P.-M. Adam, A. Vial, and P. Royer. Role of localized suface plasmons in surface enhanced raman scattering ofshape-controlled metallic particles in regular arrays. Phys. Rev. B,72(3): 033407, 2005.
  14. J. Grand, P.-M. Adam, A.-S. Grimault,A. Vial, M. Lamy de la Chapelle,J.-L. Bijeon, S. Kostcheev, and P. Royer. Optical extinction spectroscopy of oblate, prolate and ellipsoid shaped goldnanoparticles: experiments and theory. Plasmonics, 1(2-4): 135–140, 2006.
  15. H. Ibn El Ahrach, R. Bachelot, A. Vial, G.Lérondel, J. Plain, P. Royer and O. Soppera. Spectral degeneracy breaking of the plasmon resonance of single metalnanoparticles by nanoscale near-field photopolymerization. Phys. Rev. Lett., 98(10): 107402, 2007.