The transmittance curves describing effects important in the behavior of the diffracted fields generated by
coherent illuminated. However, when it is performed a spatial transform on a transmittance curve, this can
be done by tilting the screen, for example, the projection of a circle curve is an ellipse as result the diffraction
field is no more a smooth transformation. In this case, the boundary condition may generate regions identified
as singularities regions. In this study, we describe slit-shape transmittance whose diffraction field presented
bifurcation effects and focusing regions know as caustics. The geometric shape of the transmittance allows to
study the structure diffraction fields, where they are organized around focusing regions. We describe singularities
that corresponds to cusp caustics of codimension two and astroid caustics. In the focusing regions are produced
dislocation points on intensity pattern. In particular, in the cusp catastrophe is presented the Pearcey pattern.
The generation of singularities is studied by mean the numerical solution of the paraxial Helmholtz equation.
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 recent years, particle transport at microscopic level has become an important research topic which has led to the
understanding of directed particle transport subjected to thermal fluctuations. Brownian motors (also called ratchet
mechanism) are one of the most interesting phenomena of work generation in nonequilibrium systems under
random external forces. In this work, we report Brownian movement rectification of 0.5 μm diameter latex
particles using pulsating ratchets. In order to implement the ratchets, an asymmetric 2D potential saw tooth phase
pattern is displayed on a spatial phase modulator and then transformed into an intensity pattern by using the phase
contrast method. This pattern is focused down with a 100x microscope objective obtaining a pattern of ~40x40
μm2 at the focal plane. The patterns parameters can be dynamically controlled: periodicity, asymmetry, and
on/off rate, which allows optimization of directed transport. We found that there is an optimum value for the
on/off rate and particle diameter/spatial period obtaining an average speed of 0.6 μm/s. The 2D pattern allow us to
manipulate a large number of particles, in contrast to previous studies were only one particle has been studied,
opening the opportunity to massive sorting of particles.
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.