Brigitte Bidégaray-Fesquet — Optics

Optics is one of my major themes. I am currently following two directions : Quantum Optics and Sub-wavelength optics.

I have studied at length the Maxwell–Bloch model in different aplicative contexts.
See also the Maxwell–Bloch page and Maxwell–Bloch gallery.

• Centro-symmetric materials (gases, glasses).
  We have selected mathematical and numerical midels which correctly (conservation of certain physical variables) account for some relaxation phenomena in Bloch equations [BBR03]. These equations describe matter at the quantum level. The same issues are of interest in the coupling with an electromagnetic wave, yielding the Maxwell–Bloch equations [Bid03], allowing to treat many experimental phenomena [Bid02]. We also have derived asymptotic models from the Bloch equations resulting in rate equations [BCD04] All these works have been exhautively presented in a book at the Master level [Bid06].
• Crystals.
  The case of crystal was the subject of Olivier Saut's PhD to which I contributed concerning the quantum description [BBBDS04]. This new case introduces technical problems dues to (a) the complexity of the derivation of the model for each symmetru class (still to be done, only KDP has been traeted) (b) the eed to have full 3D models to describe anisometries.
• Quantum dots.
  In the case of quantum dots, new theoretical problems arise, due to the fact that we have two species of electron and we have to derive the models in the Heisenberg picture of quatum mechanics (the Schrödinger pitiure was used in the previous studies). A first preliminary work is devoted to degeneracies and the Pauli exclusion principle with a very reduced model [Bid10].

Ongoing work

I am currently working on

• the introduction of Coulomb and electron-phonon interactions (nonlinear effects due to the Hartree–Fock approximation);
• the coupling with the wetting layer (quantum well model);
• the introduction of other phenomenological phenomena;
• the numerical implementation (multi-scale computing).

References

I am responsible of the MADISON (Modèles Asymptotiques pour la DIffraction Sub-longueur d'ONde de surfaces rugueuses) which un funded by the M-STIC pole of the Joseph Fourier University. This funding was aimed at the organization of the pluri-disciplinary workshop Polaritons 2009, but we also work on the study of diffractive phenomena on sub-wavelength surfaces. We more specifically address the asymptotic and numerical analysis of the diffraction by metallic rectangular gratings which are experimentally studied at the Institut Néel.

My colleagues at the LJK have performed the asymptotic study of a system of cavities which allow to replace them, as their width tends to zero, by dipoles [BT10]. This work is using perfect metal boundary conditions to treat the surfaces.

In parallel, I studied with Éric Dumas the impact of surface conditions on the computation of refected modes and cavity modes. These computations suppose a modal expansion of the electromagnetic fields and have been communicated at the Waves 2009 Conference (9th International Conference on Mathematical and Numerical Aspects of Waves) in June 2009 and are submitted to the special issue dediacted to this event [BD09]. This work show that real metal boundary conditions (surface impedance conditions) are more adequate and we explain how asymptotic expansions with respect to the dielectric permittivity of the metal can make computations effectient. We also diplay that for some frequencies (or incident angles) the incident wave is absorbed by the cavities, thus yielding high energy concentrations usueful for applications.

Ongoing work

We are currently working or intend to work on

• the comparison of modal computations with other modal techniques or full Helmholtz finite difference computations;
• the combinaison of our cavity modes with the asymptotic study of equivalent dipoles;
• the derivation of diffractive geometry models when the cavities are fille with nonlinear (Kerr) materials.

References