Oscar G. Rodríguez-Herrera

Complete polarization and phase control for focus-shaping in high-NA microscopy

We show that, in order to attain complete polarization control across a beam, two spatially resolved variable retardations need to be introduced to the light beam. The orientation of the fast axes of the retarders must be linearly independent on the Poincaré sphere if a fixed starting polarization state is used, and one of the retardations requires a range of 2π. We also present an experimental system capable of implementing this concept using two passes on spatial light modulators (SLMs). A third SLM pass can be added to control the absolute phase of the beam. Control of the spatial polarization and phase distribution of a beam has applications in high-NA microscopy, where these properties can be used to shape the focal field in three dimensions. We present some examples of such fields, both theoretically calculated using McCutchens method and experimentally observed.

Generation of achromatic, uniform-phase, radially polarized beams.

Axially symmetric half-wave plates have been used to generate radially polarized beams that have constant phase in the plane transverse to propagation. However, since the retardance introduced by these waveplates depends on the wavelength, it is difficult to generate radially polarized beams achromatically. This paper describes a technique suitable for the generation of achromatic, radially polarized beams with uniform phase. The generation system contains, among other optical components, an achromatic, axially symmetric quarter-wave plate based on total internal reflection. For an incident beam with a constant phase distribution, the system generates a beam with an extra geometrical phase term. To generate a beam with the correct phase distribution, it is therefore necessary to have an incident optical vortex with an azimuthally varying phase distribution of the form exp( + iθ). We show theoretically that the phase component of radially polarized beam is canceled out by the phase component of the incident optical vortex, resulting in a radially polarized beam with uniform phase. Additionally, we present an experimental setup able to generate the achromatic, uniform-phase, radially polarized beam and experimental results that confirm that the generated beam has the correct phase distribution.

Generalized van Cittert–Zernike theorem for the cross-spectral density matrix of quasi-homogeneous planar electromagnetic sources

A generalized van Cittert-Zernike theorem for the cross-spectral density matrix of quasi-homogeneous planar electromagnetic sources is introduced. We present theoretical examples of using this theorem to generate fields with interesting polarization and spatial coherence properties by choosing the appropriate spectral density distribution of the source. We found that under certain conditions, a quasi-homogeneous, polarized source may produce a beam in the far field that is unpolarized in the typical one-point sense but polarized in the two-point, mutual polarization sense.

Satellite-Derived Tropical Cyclone Intensity in the North Pacific Ocean Using the Deviation-Angle Variance Technique

AbstractThe deviation-angle variance technique (DAV-T), which was introduced in the North Atlantic basin for tropical cyclone (TC) intensity estimation, is adapted for use in the North Pacific Ocean using the “best-track center” application of the DAV. The adaptations include changes in preprocessing for different data sources [Geostationary Operational Environmental Satellite-East (GOES-E) in the Atlantic, stitched GOES-E–Geostationary Operational Environmental Satellite-West (GOES-W) in the eastern North Pacific, and the Multifunctional Transport Satellite (MTSAT) in the western North Pacific], and retraining the algorithm parameters for different basins. Over the 2007–11 period, DAV-T intensity estimation in the western North Pacific results in a root-mean-square intensity error (RMSE, as measured by the maximum sustained surface winds) of 14.3 kt (1 kt ≈ 0.51 m s−1) when compared to the Joint Typhoon Warning Center best track, utilizing all TCs to train and test the algorithm. The RMSE obtained when t...

Spatial chirp in the focusing of few-optical-cycle pulses by a mirror

We calculate the electric field of few-optical-cycle pulses at the focus of a perfectly conducting mirror by adding coherently the Airy diffraction patterns for each pulse frequency. We will show that the pulse suffers temporal spreading generated by a change in the spectrum of the pulse as a function of position in the focal plane, which introduces spatial chirp to the pulse. A double pulse appears near to the diffraction minima of the carrier frequency due to the variations in the spectra.

Tropical Cyclogenesis Detection in the North Pacific Using the Deviation Angle Variance Technique

AbstractThe deviation angle variance technique (DAV-T) for genesis detection is applied in the western and eastern North Pacific basins. The DAV-T quantifies the axisymmetric organization of cloud clusters using infrared brightness temperature. Since axisymmetry is typically correlated with intensity, the technique can be used to identify relatively high levels of organization at early stages of storm life cycles associated with tropical cyclogenesis. In addition, the technique can be used to automatically track cloud clusters that exhibit signs of organization. In the western North Pacific, automated tracking results for the 2009–11 typhoon seasons show that for a false alarm rate of 25.6%, 96.8% of developing tropical cyclones are detected with a median time of 18.5 h before the cluster reaches an intensity of 30 knots (kt; 1 kt = 0.51 m s−1) in the Joint Typhoon Warning Center best track at a DAV threshold of 1750°2. In the eastern North Pacific, for a false alarm rate of 38.0%, the system detects 92.9...

Automatic Tracking of Pregenesis Tropical Disturbances Within the Deviation Angle Variance System

The deviation angle variance (DAV) method is an objective tool for estimating the intensity of tropical cyclones (TCs) using geostationary infrared (IR) brightness temperature data. At early stages in TC development, the DAV signal can be also a robust predictor of tropical cyclogenesis. However, one of the problems with using the DAV method at these early stages is that the operator has to subjectively track potentially developing cloud systems, sometimes before they are clearly identifiable. Here, we present a method that allows us to automatically track the evolution of cloud clusters using only the raw IR imagery and the resulting DAV maps. We have compared our objective method with results manually obtained on a limited data set spanning a 12-day period during the 2010 hurricane season in the western North Pacific and tuned the performance of the method to the manual results. The performance of the method was then tested by comparing the results with best track and invest files produced by the Joint Typhoon Warning Center for the four-year period 2009-2012. The long-term results agree well with the best track and invest files for the disturbances analyzed in terms of start time, end time, and locations of disturbances. The automatic tracking method presented in this letter may be used to reduce the dependence of tropical cyclogenesis DAV analyses on the expertise and ability of the operator.

Temporal widening of a short polarized pulse focused with a high numerical aperture aplanatic lens

We present a theoretical analysis of the field distribution in the focal plane of a dispersionless, high numerical aperture (NA) aplanatic lens for an x-polarized short pulse. We compare the focused pulse spatial distribution with that of a focused continuous wave (CW) field and its temporal distribution with the profile of the incident pulse. Regardless of the aberration free nature of the focusing aplanatic lens, the temporal width of the focused pulse widens considerably for incident pulses with durations on the order of a few cycles due to the frequency-dependent nature of diffraction phenomena, which imposes a temporal diffraction limit for focused short pulses. The spatial distribution of the focused pulse is also affected by this dependence and is altered with respect to the diffraction limited distribution of the CW incident field. We have analyzed pulses with flat top and Gaussian spatial irradiance profiles and found that the focused pulse temporal widening is less for the Gaussian spatial irradiance pulse, whereas the spatial distribution variation is similar in both cases. We present results of the focused pulsewidth as a function of the NA for the two spatial irradiance distributions, which show that the Gaussian irradiance pulse outperforms the flat top pulse at preserving the incident pulse duration.

Optical concatenation of a large number of beads with a single-beam optical tweezer

Optical tweezers consist of the spatial confinement of microscopic dielectric particles by the action of forces produced by the change in momentum of the photons of a highly focused laser beam that are deviated by the particle. In experiments that use a single laser beam, it is common to capture not only one but a few particles in the optical trap. However, to our knowledge, the formation of a long chain of beads optically confined with a single laser beam has never been reported. In this work, up to 73 silica spheres immersed in water are seen concatenated along the propagation direction of a 976-nm wavelength Gaussian laser of 300 mW of power. This long chain of beads is obtained when the laser is focused through an oil-immersion DIN microscope objective with 100× magnification and a numerical aperture of 1.25. When performing the same experiment using an infinity-corrected UplanFLN 100× objective with a numerical aperture of 1.3, the maximum number of concatenated beads is only 14. Our results suggest that the mechanisms responsible for the observed phenomena involve successive refocusing of the laser beam by each trapped sphere, optically induced dipole coupling (commonly referred to as optical binding), and aberrations generated by the DIN microscope objective.

Monostatic measurement of the polarized bidirectional reflection distribution function

The polarized bidirectional reflection distribution function (pBRDF) is widely used to characterize the scattering properties of materials and to model remote sensing engagements. Knowledge of a material’s pBRDF enables estimation of the signatures within a scene by adding information about the source-targetsensor geometry. The pBRDF (or its scalar cousin, the unpolarized BRDF) is generally used as a modeling tool, but it is also a powerful identifier that can be used to discriminate objects of interest in complicated scenes. In these situations, we could compare an experimentally measured scattering distribution with a pBRDF library, as is currently done for hyperspectral imaging. Unfortunately, remote measurement of the pBRDF is simply not possible in most real-world scenarios where the target is far away and not under the control of the sensing system. Typically, we measure the pBRDF of a target using goniometric (angle-measuring) setups, where we move the detection arm around the object to measure the light scattered at different angles for each angular position of the illumination arm. Figure 1 is a diagram of the goniometric configuration. We then use the measurements obtained at different angles of incidence to compute the pBRDF of the object. In remote sensing applications, the source of illumination and detector are enclosed in a single compact case (as in an artificial satellite, for example) that cannot be freely moved around a scene. Furthermore, in this case the illumination and detection arms are, by any practical means, parallel. Therefore, measurement of the pBRDF in real-life scenarios imposes more restrictions than its measurement in the laboratory, and ideally it should be obtained from monostatic measurements (using a radar system in which transmitter and receiver are collocated). To achieve this goal, we Figure 1. Diagram representing a typical configuration used to measure the polarized bidirectional reflection distribution function (pBRDF) of a sample object with area A. ‚i;r , ˆi;r are the polar and azimuth angles of the incident and reflected beams.