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Theory of optics in confined geometry

The physics of optical evanescent waves which is the central concept used in near-field optics ( NFO) instrumentation has been familiar in traditional optics for a long time. In modern physics, the control of such peculiar light fields provides an interesting and versatile tool that generates powerful applications in nanoscience (surface imaging, molecule addressing, light guiding, localized plasmons excitations, ....). Other applications can be found in the field of ultracold atoms manipulations. For example, in laser cooled atoms physics such optical phenomena can be used as adjustable ``atomic mirrors''. The accurate description of the optical field distribution, prior to its local detection or manipulation, is mandatory for describing properly the image formation mechanisms in NFO but also to describe many others near-field optical phenomena. The main difficulties in achieving this goal are inherent to the complexity of the geometries investigated in NFO (non-periodic objects, localized surface defects, nanometer size holes, ...) as well as to the need of accounting for a large spectra of non-radiative optical field components. Particularly, corners, sharp edges and angular regions much smaller than the incident wavelength, generate specific difficulties for most of the theoretical schemes and numerical methods for solving Maxwell's equations.

In our group, this problem has been treated from a peculiar adaptation of the integral representation of Maxwell's equations by introducing the concept of Green Dyadic Functions. In our formalism, the photonic Green Dyadic function associated with the system under study, is calculated by solving iteratively the Dyson equation. This allows a generalized propagator to be defined for the system. This propagator is then applied to compute the light field everywhere, namely inside and outside the nanostructures. Figure 1 gives an example of such computations near lithographically designed dielectric nanostructure (see for example `` The physics of the near-field'' Report on Progress in Physics Vol. 63, 893 (2000) and Phys. Rev. E65, 036701 (2002)).

(1) The theory of Green Dyadic Functions (Field-Suceptibility)

When a finite line of individual gold particles are coupled together (cf. figure 3), the spatial intensity distribution is different from that for a single particle. The squeezing of the optical near--field due to plasmon coupling is well reproduced. This computation is based on a the knowledge of the formula of the Green's dyadic associated with a reference system which, in this problem, is a flat glass surface. The numerical procedure considers any object deposited on the surface as a localized perturbation which is discretized in direct space. In a first step, the electric field is determined self-consistently inside the eventually disconnected perturbations.

A renormalization associated to the depolarization effect is applied to take care of the self-interaction of each discretization cell. The final step relies on the Huygens--Fresnel principle to compute the electric field anywhere on the basis of the knowlegde of the field inside the localized perturbations. In the computational results presented in figure 3, the incoming field is defined as the PSTM experiments with a TM polarization. Relatively to the incident wavelength of 633 nm used in this simulation, this narrowing correspond to an important squeezing of the optical near--field along the chain.

2) The differential Theory of Gratings (DTG).

When working with periodic surface structures, the localized Green's function method described above becomes unappropriate. In the case of periodically patterned surfaces, the near-field optical distributions can be investigated with a second class of methods called the differential theory of gratings (DTG).

This method was originally developed in the Group of Michel Nevière (Marseille University) twenty years ago to predict the efficiencies of two--dimensional diffraction gratings. Recently, it was also adapted by J. C. Weeber (LPUB Dijon) for near-field optical applications.

Based on a rigorous treatment of Maxwell's equations, this method can also be used efficiently to determine the optical near--field scattered by three dimensional periodic objects (figure 4 illustrates the capability of this method for near-field optical appliquations). In collaboration with the Group of J. Weiner (LCAR/CNRS Toulouse), we have applied this technique to simulate atomic diffraction experiments performed in the vicinity of nanostructured optical potential. In figure 4, we have represented an example of nanostructured optical potential near a grating made of TiO2 posts microfabricated on a silica surface (cf ``Atomic diffraction from nanostructured optical potentials'', Phys. Rev. A65, 053615 (2002)).