Juan Carrasquilla

Spatial coherence wavelets and phase-space representation of diffraction.

The phase-space representation of the Fresnel-Fraunhofer diffraction of optical fields in any state of spatial coherence is based on the marginal power spectrum carried by the spatial coherence wavelets. Its structure is analyzed in terms of the classes of source pairs and the spot of the field, which is treated as the hologram of the map of classes. Negative values of the marginal power spectrum are interpreted as negative energies. The influence of the aperture edge on diffraction is stated in terms of the distortion of the supports of the complex degree of spatial coherence near it. Experimental results are presented.

Young's experiment with electromagnetic spatial coherence wavelets.

We discuss Youngs experiment with electromagnetic random fields at arbitrary states of coherence and polarization within the framework of the electric spatial coherence wavelets. The use of this approach for the electromagnetic spatial coherence theory allows us to envisage the existence of polarization domains inside the observation plane. We show that it is possible to locally control those polarization domains by means of the correlation properties of the electromagnetic wave. To show the validity of this alternative approach, we derive by means of numerical modeling the classical Fresnel-Arago interference laws.

Phase-space representation and polarization domains of random electromagnetic fields

The phase-space representation of stationary random electromagnetic fields is developed by using electromagnetic spatial coherence wavelets. The propagation of the fields power and states of spatial coherence and polarization results from correlations between the components of the field vectors at pairs of points in space. Polarization domains are theoretically predicted as the structure of the field polarization at the observation plane. In addition, the phase-space representation provides a generalization of the Poynting theorem. Theoretical predictions are examined by numerically simulating the Young experiment with electromagnetic waves. The experimental implementation of these results is a current subject of research.

Characterization of the Bose-glass phase in low-dimensional lattices

We study by numerical simulation a disordered Bose-Hubbard model in low-dimensional lattices. We show that a proper characterization of the phase diagram on finite disordered clusters requires the knowledge of probability distributions of physical quantities rather than their averages. This holds in particular for determining the stability region of the Bose-glass phase, the compressible but not superfluid phase that exists whenever disorder is present. This result suggests that a similar statistical analysis should be performed also to interpret experiments on cold gases trapped in disordered lattices, limited as they are to finite sizes.

Definition and invariance properties of the complex degree of spatial coherence

Within the framework of the phase-space representation of random electromagnetic fields provided by electromagnetic spatial coherence wavelets, and by using the Fresnel-Arago laws for interference and polarization as an analysis tool, the meaning of the spatial coherence-polarization tensor and its invariance under transformations is studied. The results give new insight into the definition and properties of the complex degree of spatial coherence by showing that its invariance is not required for properly describing the behavior of random electromagnetic fields within the scope of physically measurable quantities.

Wavemeter based on moiré effect

A moiré-effect-based procedure used to measure the wavelength of coherent sources is shown. Two plane waves, individually coherent but mutually incoherent and located at the entrance pupil of a Michelson interferometer with slightly tilted mirrors, generate a moiré pattern at the output plane. The spatial period of that moiré pattern is determined by the spatial frequencies of the interferograms superimposed on intensity. Thus the spatial frequency of such moiré patterns allows the establishment of a ratio between the wavelengths of the sources that illuminate the interferometer. This ratio can be applied for the accurate determination of determining an unknown wavelength in terms of a reference wavelength, as we show both theoretically and experimentally.

Diffraction spread of spatially partially optical fields along the propagation axis

The spreading properties of the Fraunhofer diffraction patterns of optical fields in any state of spatial coherence along the z‐axis are both theoretically and numerically analysed using the so called spatial coherence wavelets. The numerical analysis is performed by studying the one‐dimensional diffraction pattern produced when a single slit is uniformly illuminated with a Gaussian Schell‐model field. The diffraction pattern is understood as the result of contributions provided by spatial coherence wavelets coming from two different regions within the aperture, called the inner circle and the truncation crown respectively. It is shown that shape‐invariant spots with minimum spreading along the z‐axis can be obtained by properly modulating the spatial coherence properties along the truncation crown. Those spots can be regarded as finger prints of the spatially partially coherent optical field, in the sense that they only depend on the spatial coherence properties and not on the shape of the aperture itsel...

Radiometric analysis of diffraction

A description of Fresnel and Fraunhofer diffraction of quasi‐homogenous optical fields in any state of spatial coherence is presented, which clearly differs from the classical formalism. Instead of the propagation of the cross‐spectral density from the diffracting aperture to the observation plane, the diffracting aperture is regarded as a planar quasi‐homogeneous source, whose generalised radiance is carried by the spatial coherence wavelets, and the power distribution at the observation plane is expressed in terms of the generalised radiant intensity. It allows interpreting the negative values of the generalised radiance as “negative energies” emitted along specific directions and subjected to the achievement of the conservation law of energy. This interpretation is not evident in the classical formalism. Consequently, interference can be thought as resulting of energy transfer over a given wavefront, due to the addition of equal amounts of “positive” and “negative” energies, along specific directions, ...

Full retrieving of the complex degree of spatial coherence through the spot moments

In this work a method for retrieving the magnitude and phase of the complex degree of spatial coherence is shown. To apply it only the recording of the spot intensity is required. Afterwards, centered reduced moments of the spot are calculated, in order to use them as coefficients of a series to expand the complex degree of spatial coherence. Experimental results for Schell-model spots are shown. The Fourier spectra corresponding to the experimentally recorded sots, are calculated in order to show the equivalency between the proposed method and the Fourier one.