Geovanni Arenas Muñoz, Ilsse I. Cazares Aguilar, Elizabeth Saldivia Gomez, Juan C. Atenco Cuautle, Fabian Cubillos Morales, Andrea Garcia Guzman, Patricia Martinez Vara, Gabriel Martinez Niconoff
In this paper, the expression for the dispersion relation function for evanescent waves (EWs) is obtained. This expression establishes the basis of the two-dimensional optics where EWs are involved. We make use of the nonhomogeneous character of these types of waves. The dispersion relation function was implemented to analyze the interference effects showing that the resulting optical field has easily tunable polarization features, which were characterized through a set of Poincare’s spheres with its corresponding coherence matrix representation. The interference model was generalized to describe the diffraction effects by proposing the angular spectrum model with EWs. The analysis was further extended to describe the synthesis of evanescent self-imaging optical fields.
We analyze the diffraction field when changes in the curvature function of the boundary condition are implemented. The study is performed using differential geometry models with a curvature function displaying local behavior. Depending on the sign of curvature, we classify the diffraction field as elliptic, hyperbolic, or parabolic. In particular, it is shown that the optical field is organized around the parabolic regions, which correspond to focusing regions. The model is experimentally corroborated by applying a coordinate transformation to the transmittance of a zone plate. The reason to use this transmittance comes from the fact that its diffraction field displays multiple foci allowing identification, description, and control of bifurcations and morphogenesis effects, which are studied using the curvature function.
The properties of optical surfaces generated by diffraction are studied analyzing the changes in the curvature function of the boundary condition. The study leads to establish a classification for the optical fields as elliptical, hyperbolical or parabolic. The elliptical regions are separated from hyperbolic regions by a region of parabolic type, which corresponds to optical focusing regions. The main result of the analysis leads us to describe and to control bifurcations and vortices effects allowing to geometrize and to control the topological properties of the optical field. For this feature is important to control the geometry of the parabolic region, obtained by controlling the curvature function in the boundary condition. The model is implemented experimentally applying a linear transformation in transmittances of zone plate type. The experimental results corroborate the theoretical predictions.
We analyze the resonant interaction between cumulus of nano-particles distributed on a two-dimensional array controlling the polarization states on the illumination, this allows controlling the dipole moment induced in a tunable-way obtaining an analytic expression for the refractive index. The resonant effects depend on the parameters that characterize the spatial distribution of the particle arrangement. We present two cases, firstly the interaction is described using a linear polarization on a linear particle array, and secondly it is obtained using circular polarization inducing resonant interaction between ring-particle kind structures. The refractive index associated to both configurations is implemented in the Fresnel equations for the study of the reflectivity and transmittance of optical fields. As a main result of the analysis is that we can to identify and control the parameters required for the synthesis of metamaterials. Computer simulations are presented.
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