In this work we calculate the effect caused by roughness on the light reflected by an optical surface like a mirror, the numerical calculation is carry out within the Rayleigh approximation. We focus our study in the comparison of the results obtained numerically using different roughness parameters and calculate its effect on the aberrations of the wavefront, which without the effect of the roughness is considered a ideal surface.
Diffraction fields many times can generate a focusing region, we describe the focusing region associated with symmetric transmittances, analyzing its associated phase function. We show that some generic features, it can be obtained from a differential equation for a focusing geometry, which is obtained through angular representation for diffraction fields, the diffraction field presents a new focusing region whose geometry and spatial evolution can be described with the analysis of the phase singularities avoiding the integral diffraction calculation.
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.
Tunable lenses have become very popular elements due their capacity of change their focal length by only modifying their shape. This characteristic is very useful in different applications in the field of optics. The development of tunable lenses consists on several phases: first, to find a suitable material, second, to obtain an optimal analysis and design, and third, to find the way to change the lens shape and characterization. In this work we present the characterization of a tunable lens, formed by spherical profiled elastic membranes and a liquid medium between them. The proposed liquidfilled tunable has a design such that the spherical aberration is the least to different focus. The development of an optomechanical system to change the lens shape is presented.
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.
In this work we calculate the effect caused by roughness on the light reflected by an optical surface like a mirror, the numerical calculation is carry out within the Rayleigh approximation. We focus our study in the comparison of the results obtained numerically using different roughness parameters and calculate its effect on the aberrations of the wavefront, which without the effect of the roughness is considered perfect surface.
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.
Optical diffraction fields have in general a spatial complex structure and some times can generate focusing regions, in
this work we describe the focusing region associated with highly symmetric transmittances, analyzing its associated
phase function. We show that generic features can be studied from a differential equation for a focusing geometry, which
is obtained through angular representation for diffraction fields, according to the choice of the parameters involved, the
diffraction field presents a new focusing region whose geometry and spatial evolution can be described with the only
analysis of the phase singularities avoiding the integral representation.
In this work we describe a dipole wave propagation through a two-dimensional nanoparticles array, where the array is doped with magnetic impurities randomly distributed. The effect of impurities is a trajectory resorting in the wave propagation; this phenomenon is described by means of the percolation theory.
In this work we describe a resonant interaction between nanoparticles considering the geometric parameters using
a multidisciplinary approach to mode coupling theory. The study groups are differentiable equations describing
the resonant processes.
We use the profile of a parabolic mirror to calculate the scattered electromagnetic field, this mirror can be used
in the design and construction of a reflector telescope. We calculate the effect caused by the roughness on the
performance of this optical elements, the calculation is done within the Rayleigh approximation. In another work
presented in this meeting we show a comparison of the results obtained numerically using different roughness
parameters and calculate its effect on the aberrations of the wavefront.
Recently in the micro-optical engineering area has been a grown in use of tunable liquid lenses because this
lenses us allow versatility in the focusing range, also an easy handling and implementation. In the literature,
many tunable lens models have been reported, but most of this work has been on describing the optical quality
of the images, the opto-mechanical analysis is neglected. In this paper, an analysis of opto-mechanical of a
tunable liquid lens is presented, for this; we show a finite element simulation of mechanical behavior and
estimate how this influences in the optical performance of the lens. The liquid lens is composed of two elastic
transparent membranes and of a cylindrical metallic mount.
In this paper we show the results as well as the description of the followed process to calculate the electromagnetic
field scattered by optical surface elements, where the optical surface is not considered as a flat surface that follows
a shape, but as a rough one, roughness that in general may be regarded as random. We use the profile of a
parabolic mirror to calculate the scattered electromagnetic field, this mirror can be used in the design and
construction of a reflector telescope. We calculate the effect caused by the roughness on the performance of
this optical elements, the calculation is done within the Rayleigh approximation. In another work presented in
this meeting we show a comparison of the results obtained numerically using different roughness parameters and
calculate its effect on the wavefront.
In this study, the opto-mechanical design and functional characterization of a Variable Focal
Liquid Length Lens (VFLLL) are presented. This VFLLL is formed by a hydro-pneumatic
system, a mount with two elastic membranes and the liquid medium between them. The hydropneumatic
system allows the entrance and exit of the liquid at any moment to change the shape
of the surfaces as well as the axial thickness of the lens. The functional characterization consists
in measure the spherical aberrations present in VFLLL when changes on the amount of liquid
medium are made. We used the Zygo interferometer to measure the spherical aberration. The
changes of aberration as function of the focal length are shown. Finally the experimental results
Surface plasmon modes can be considered as the analogous to plane waves for homogeneous media. The extension
to partially coherent surface plasmon beams is obtained by means of the incoherent superposition of the
interference between surface plasmon modes whose profile is controlled associating a probability density function
to the structural parameters implicit in their representation. We show computational simulations for cosine,
Bessel, gaussian and dark hollow surface plasmon beams.
Today elastic membranes are being used more frequent as optical surfaces in the science or in the industry. This
due to the advantages that they display in their handling and in their cost of production. These characteristics
make them ideals to apply them in micro-optical components and Tunable Focus Liquid Filled Length Lens
(TFLFLL). In order to know if a membrane of PDMS (PDMS Sylgard 184) is feasible for a specific application
within the field of the optics, it is necessary to know its mechanical, optical and chemical properties. In this
work the parametric membrane characterization is reported for an optical application. An important factor in
the performance of these membranes is related with their scattering factor that is produced due to the roughness
and impurities (micro-bubbles or dust particles). These membranes are used as refractive surface in TFLFLL. Experimental results of the characterization process and device performance are presented.
In this work, we describe the behavior of the electromagnetic field on a Nanostructured interface using the
coupled mode theory. The study is performed by associating time-dependent parameters to a set of polarized
particles randomly distributed on an dielectric substrate. As a result, we obtain the conditions to generate a
negative refractive index as a function of the distance between two particles in harmonic oscillation, in this way
we show the possibility to synthetize Metamaterials from the nanoparticles arrays.
The inability of an optical spherometer to measure large curvature radii in optical convex surfaces is well known. This is
because the movement of the optical component or the instrument cannot be physically carried out since this would
involve crossing each other. This study proposes the opto-mechanical design of a spherometer that will have a source
light, a beam splitter, and a liquid lens composed of a plane surface and a transparent elastic membrane with a liquid
medium between them. By changing the volume of the liquid the shape of the membrane and the thickness of the lens
will change. The present study offers a paraxial analysis of the relationships obtained to measure the curvature radius
together with its uncertainty as a function of changes in the volume. The study also presents the work range of the
instrument. The instrument is focused on the vertex of the surface and on the center of curvature with aid an intensity
We describe the synthesis of diffraction free beams (DFB) and quasi diffraction free beams (qDFB) with features
easily tunable using a holographic techniques. The hologram plate transmittance is generated by interfering two
zero order Bessel beams with non-common axis. Spatial filtering techniques are implemented by controlling the
kind of illumination during the reconstruction process. The experimental results are for illumination with the
same kind of illumination that the recording process, obtaining a set of diffracting free beams. One of these
propagates quasi-parallel to the surface hologram. For illumination with a plane wave we obtain dark hollow
beam propagating in same direction that reconstruction beam. Experimental results are shown in both cases.
We describe the mode solutions for the Helmholtz Equation using the operator formalism. The study is extended
to the structural solution for the focused non-linear Schrödinger equation (NLSE). With this treatment, we obtain
for the NLSE a reduced partial differential equation, whose characteristic solution has an eikonal structure
which allows us a geometrical analysis. Focusing region in non-linear media is described by means of an envelope
region of eikonal trajectories establishing similar behaviors with caustic structures. In particular, if the boundary
condition consists of a slit shape curve, the focusing profile corresponds with the evolute of the curve. In general,
the profile satisfies a non-linear partial differential equation whose structure remains non-variable under changes
of variables which may represents scaling or rotations. This feature permits us to extend the analysis to other
kind of focusing regions, such as focusing vortex.
Working with big mirrors always is a great challenge, even more if the surfaces have great roughness. In this work we present a technique to verify the quality for surfaces around 3 meters in diameter and with roughness around 30 microns. In order to reach our goal we made an analysis of the grating pitch to avoid the roughness and we implement a common source light, which is independent of the angle of illumination of the surface under test. Also we implement the shadow moire and the phase shift method to obtain the wave front aberrations.