NONLINEAR OPTICS



When I was studying at the Scuola Normale Superiore my research focused on theoretical Nonlinear Optics. Together with my advisor, Prof. Bassani , I worked on the analitical and asymptotic properties of the general nonlinear susceptibilities functions describing various nonlinear optical phenomena. In particular I focused on the Harmonic generation processes and on the odd nonlinear susceptibilities related to the Pump and Probe configuration. My goal was discussing if in nonlinear optics it was possible to explicitely derive properties of the nonlinear susceptibilities such as Kramers-Kroenig relations and sum rules, which in linear Optics have played such a great role, having proved to be fundamental tools both in fundamental and applied research. The idea was that since those properties come directly from the causality principle and are not model dependent, it was possible to explore their nonlinear extension beginning with simple classical model of light-matter interaction. We moved our steps from the important results obtained by Bassani and Scandolo in the early '90s. A very great deal of work in this subject has been done by the team chiefed by K.E: Peiponen of the University of Joensuu, in Finland. This team has probably contributed the most to the theory of Nonlinear Kramers-Kroenig relations and sum rules by improving the general theoretical results, by introducing algorithms to perform the calculations in both conceptual and more realistic models, and by specifying the results to many real physical systems. Other contributions to this field of Nonlinear Optics have been given by the group led by M. Sheik-Bahae at the University of New Mexico.
In 1998-1999 we worked on the nonlinear extension of the classical Lorentz oscillator model: During the year 2000 we worked on the same problems from a rigorous quantum mechanical perspective keeping a totally general approach thanks to the use of the density matrix formalism and of the general nonlinear response function theory applied to the light-matter interaction. The velocity gauge proved to be more convenient for the toiling calculations we had to get through, and finally we obtained totally general results for the process of harmonic generation. These results match perfectly with the classical ones previously obtained in the first paper once the correct correspondences between quantum and classical physical parameters are estlablished: this is another confirmation of the fact that the properties we have studied are more intrinsic than the model we use to describe the phenomena, since they directly come from the causality principle. We have then presented these results to the Laser Optics 2000 Congress held in St. Petersburg in july 2000. Another paper about linear sum rules where relativistic and nonlocal effects have been taken into account has been prepared during 2000 and then published the following year. During the year 2000 I also worked on the Electromagnetic Induced Transparency, one of the hottest topics in Optics today, and developed together with I. Carusotto a mechanical analogue to the microphysical phenomena, so to have a clearer understanding of the main features of the process. Before fully developing this idea I moved to the US to enter the MIT PhD Program of Atmosphere, Ocean and Climate.
Well, now in 2003, during my staying in Florence, I have developed a full collaboration with the group of Peiponen of the University of Joensuu, Finland, and have published and submitted some papers on the verification of Kramers Kronig relations and sum rules to experimental data (polymers) and on the theoretical generalization of the results obtained in the previous papers. The collaboration was so successful that I have been admitted to discuss a PhD thesis in September 2003.

Publications:

  1. General properties of optical harmonic generation from a simple oscillator model : F. Bassani and V. Lucarini, Il Nuovo Cimento D 20, 1117 (1998)
  2. Pump and probe nonlinear processes: new modified sum rules from a simple oscillator model : F. Bassani and V. Lucarini, European Physical Journal B 12, 323 (1999)
  3. Asymptotic behaviour and general properties of harmonic generation susceptibilities : F. Bassani and V. Lucarini, European Physical Journal B 17, 567 (2000)
  4. Harmonic Generation processes - Paper presented at the Laser Optics 2000 Congress: published in the SPIE reports (2000)
  5. Spatial dispersion and relativistic effects in the optical sum rules : S.Scandolo, F. Bassani, and V. Lucarini, European Physical Journal B 23, 319 (2001)
  6. Multiply subtractive Kramers-Kronig relations for arbitrary-order harmonic generation susceptibilities, V. Lucarini, J.J. Saarinen, and K.-E. Peiponen, Opt. Commun. 218, 409, (2003)
  7. Verification of generalized Kramers-Kronig relations and sum rules on experimental data of third harmonic generation on polymers, V. Lucarini and K.-E. Peiponen, J. Chem. Phys. 119, 620 (2003)
  8. My final thesis
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