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.
Optical diffraction fields have a not easy spatial structure, some times optical diffraction fields can generate a focusing region or caustic region, in this contribution, we describe the focusing region associated with highly symmetric transmittances, we analyze its associated phase function and show that generic features can be studied from a differential equation for a focusing geometry, which is obtained through angular representation for diffraction fields, the diffraction field presents focusing region whose geometry and spatial evolution can be described with the analysis of the phase singularities avoiding the integral representation. We show that in general the diffracted field has a decomposition in optical fields propagating along three optical axis mutually perpendicular. The decomposition is in terms of the Pearcey and Airy functions and generalized Airy function. Experimental results are shown.
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.
The phase function of optical fields collapse on focusing regions generating a discontinuity in the amplitude function, this induces sources or sinks that corresponds with the topological charge. When the previous comments are transferred to the Plasmon optics context, the discontinuity of the electromagnetic field generates a real distribution of electric charge. This distribution has associated a geometry which can be obtained from the boundary condition of the field. A dynamical character can be implemented on the charge distribution using partial coherence processes in the illumination configuration for the synthesis of the Plasmon field, generating local current distributions modifying selectively the electromagnetic field properties. The model is performed using as a prototype the interaction between plasmon fields Pearcey and Airy kind. Both of them have associated a catastrophe function to the phase function, this mathematical representation allows us to identify and quantify the discontinuity of the electromagnetic field. The computational simulations show that the charge/current distributions present non-linear effects, which offers applications for tunable spectroscopy, plasmonic tweezers, etc.
We analyze the scattering field generated by the coherent illumination of a three-dimensional transmittance characterized by a slit-shape curve. Generic features are obtained by using the Frenet-Serret equations which allows a decomposition of the scattering field. The analysis is performed by describing the influence of the curvature and torsion on osculating, normal and rectifying planes. Focusing and bifurcation effects are predicted and corroborated experimentally.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.