Alejandro Cámara

Characterization of holographically generated beams via phase retrieval based on Wigner distribution projections

In this work, we propose a robust and versatile approach for the characterization of the complex field amplitude of holographically generated coherent-scalar paraxial beams. For this purpose we apply an iterative algorithm that allows recovering the phase of the generated beam from the measurement of its Wigner distribution projections. Its performance is analyzed for beams of different symmetry: Laguerre-Gaussian, Hermite-Gaussian and spiral ones, which are obtained experimentally by a computer generated hologram (CGH) implemented on a programmable spatial light modulator (SLM). Using the same method we also study the quality of their holographic recording on a highly efficient photopolymerizable glass. The proposed approach is useful for the creation of adaptive CGH that takes into account the peculiarities of the SLM, as well as for the quality control of the holographic data storage.

Optical coherenscopy based on phase-space tomography

Partially coherent light provides attractive benefits in imaging, beam shaping, free-space communications, random medium monitoring, among other applications. However, the experimental characterization of the spatial coherence is a difficult problem involving second-order statistics represented by four-dimensional functions that cannot be directly measured and analyzed. In addition, real-world applications usually require quantitative characterization of the local spatial coherence of a beam in the absence of a priori information, together with fast acquisition and processing of the experimental data. Here we propose and experimentally demonstrate a technique that solves this problem. It comprises an optical setup developed for automatized video-rate measurement and a method -phase-space tomographic coherenscopy- allowing parallel data acquisition, processing, and analysis. This technique significantly simplifies the spatial coherence analysis and opens up new perspectives for the development of tools exploiting the degrees of freedom hidden into light coherence.

Partially coherent stable and spiral beams

Stable and spiral coherent beams, which do not change the form of their intensity distribution apart from possible scaling and rotation during propagation and therefore possess self-healing properties, are widely applied in science and technology. On the other hand, it has been found that partially coherent light often provides better output than coherent light. Here we consider two methods for the design and experimental generation of partially coherent stable and spiral beams.

Phase-space tomography with a programmable Radon–Wigner display

We show the adaptation of a multifunctional optical system consisting of two spatial light modulators for the optimal measurement of the Radon-Wigner transform of one-dimensional signals. The proposed Radon-Wigner display allows reconstructing the Wigner distribution and the phase or the mutual intensity of fully or partially coherent fields, respectively. It is also suitable for the analysis of two-dimensional rotationally symmetric or separable in Cartesian coordinates optical fields. The feasibility of the proposed scheme is experimentally demonstrated in several examples.

Phase-space tomography for characterization of rotationally symmetric beams

The experimental measurement of light field correlations is a difficult problem because, even in the monochromatic scalar case, the spatial coherence state of light is described by four-dimensional functions. Additional information about the field symmetry or coherence state allows reduction of the complexity of the problem. Here, we present a simplified coherence-agnostic phase-space tomography method for the experimental characterization of the widely used class of rotationally symmetric beams, which includes as a particular case partially coherent vortices. It is based on the reconstruction of the beam ambiguity function from the intensity distributions measured in the antisymmetric fractional Fourier transform domains. The experimental data can be acquired using an optical setup consisting of four cylindrical lenses and a digital camera located in fixed positions. The feasibility of the proposed method is experimentally demonstrated.

The Linear Canonical Transformations in Classical Optics

In this chapter we consider the application of the linear canonical transformations (LCTs) for the description of light propagation through optical systems. It is shown that the paraxial approximation of ray and wave optics leads to matrix and integral forms of the two-dimensional LCTs. The LCT description of the first-order optical systems consisting of basic optical elements: lenses, mirrors, homogeneous and quadratic refractive index medium intervals and their compositions is discussed. The applications of these systems for the characterization of the completely and partially coherent monochromatic light are considered. For this purpose the phase space beam representation in the form of the Wigner distribution (WD), which reveals local beam coherence properties, is used. The phase space tomography method of the WD reconstruction is discussed. The physical meaning and application of the second-order WD moments for global beam analysis, classification, and comparison are reviewed. At the similar way optical systems used for manipulation and characterization of optical pulses are described by the one-dimensional LCTs.

Optical systems and algorithms for phase-space tomography of one- and two-dimensional beams

The application of partially coherent optical beams for imaging, free space communication, random medium analysis requires controlling its mutual intensity. This task can be done using the phase-space tomography method consisting on the reconstruction of the Wigner distribution (WD), and therefore the mutual intensity, from its projections associated with the fractional power spectra. We propose two schemes that apply spatial light modulators (SLMs) for the measurements of the required WD projections in the case of one- and two-dimensional optical signals. The use of the SLMs allows rapid data acquisition and operative change of the projection number. Moreover, the measured intensity distributions do not require further rescaling, which accelerates the WD reconstruction algorithm and improves its efficiency. The developed numerical methods provide different ways for data analysis such as the reconstruction of the WD using the inverse Radon transform and its visualization for the case of one-dimensional signals; the determination of the mutual intensity for two fixed points without previous reconstruction of the entire WD for two-dimensional signals, etc. The validity of the proposed approaches has been verified experimentally for the test signals and the results are in a good agreement with the numerical simulations.

Synthesis and characterization of complex partially-coherent beams

Partially coherent light provides attractive benefits for different applications in microscopy, astronomy, telecommunications, optical lithography, etc. However, design and generation of partially coherent beams with desirable properties is challenging. Moreover, the experimental characterization of the spatial coherence is a difficult problem involving second-order statistics represented by four-dimensional functions that cannot be directly measured and analyzed. We discuss the techniques for design and generation of partially coherent structurally stable beams and the recently developed phase-space tomography methods supported by simple experimental setups for practical quantitative characterization of partially coherent light spatial structure, including its local coherence properties.

Radon-Wigner Display

In some situations it is not possible, or not desirable, to perform a full characterization of the spatial structure of 2D beams since under certain hypothesis the analysis of 1D beam profiles is more convenient.

Characterization of Beams Separable in Cartesian Coordinates

As we have discussed in Chap. 1, the characterization of 2D beams is a complex problem requiring the acquisition and processing of huge volume of data. Any hypothesis about the beam spatial structure, and specially those that can be experimentally checked, has to be used in order to simplify this task.