M. L. Calvo

Gyrator transform: properties and applications

In this work we formulate the main properties of the gyrator operation which produces a rotation in the twisting (position - spatial frequency) phase planes. This transform can be easily performed in paraxial optics that underlines its possible application for image processing, holography, beam characterization, mode conversion and quantum information. As an example, it is demonstrated the application of gyrator transform for the generation of a variety of stable modes.

Experimental implementation of the gyrator transform

The gyrator transform (GT) promises to be a useful tool in image processing, holography, beam characterization, mode transformation, and quantum information. We introduce what we believe to be the first flexible optical experimental setup that performs the GT for a wide range of transformation parameters. The feasibility of the proposed scheme is demonstrated on the gyrator transformation of Hermite-Gaussian modes. For certain parameters the output mode corresponds to the Laguerre-Gaussian one.

A photopolymerizable glass with diffraction efficiency near 100% for holographic storage

Permanent holographic storage has been demonstrated in a photopolymerizable organically modified silica glass. The glass was prepared by dispersing a titanocene photoinitiator and a high refractive index acrylic monomer in a porous silica matrix. This glass exhibits unprecedented sensitivity and refractive index change upon a moderate exposure to green light and can be fabricated in thickness up to several millimeters. A photopolymerizable storage medium of such a thickness with good holographic properties is needed for practical holographic storage devices. Lack of such medium has been considered the main obstacle in development of write-once holographic memories. In our glass, we have stored permanent volume holograms of diffraction efficiency approaching 100% and refractive index modulation up to 4.5×10−3, making this photopolymerizable material suitable for use in holographic data storage.

Ultracompact polarization converter with a dual subwavelength trench built in a silicon-on-insulator waveguide.

The design and fabrication of an ultracompact silicon-on-insulator polarization converter is reported. The polarization conversion with an extinction ratio of 16 dB is achieved for a conversion length of only 10 μm. Polarization rotation is achieved by inducing a vertical asymmetry by forming in the waveguide core two subwavelength trenches of different depths. By taking advantage of the calibrated reactive ion etch lag, the two depths are implemented using a single mask and etching process. The measured converter loss is -0.7 dB and the 3 dB bandwidth is 26 nm.

High-resolution Fourier-transform spectrometer chip with microphotonic silicon spiral waveguides

We report a stationary Fourier-transform spectrometer chip implemented in silicon microphotonic waveguides. The device comprises an array of 32 Mach-Zehnder interferometers (MZIs) with linearly increasing optical path delays between the MZI arms across the array. The optical delays are achieved by using Si-wire waveguides arranged in tightly coiled spirals with a compact device footprint of 12 mm2. Spectral retrieval is demonstrated in a single measurement of the stationary spatial interferogram formed at the output waveguides of the array, with a wavelength resolution of 40 pm within a free spectral range of 0.75 nm. The phase and amplitude errors arising from fabrication imperfections are compensated using a transformation matrix spectral retrieval algorithm.

Optical system design for orthosymplectic transformations in phase space

On the basis of a matrix formalism, we analyze the paraxial optical systems composed by generalized lenses and fixed free-space intervals, suitable for orthosymplectic transformations in phase space. Flexible configurations to perform the attractive operations for optical information processing such as image rotation, separable fractional Fourier transformation, and twisting for different parameters are proposed.

Programmable two-dimensional optical fractional Fourier processor

A flexible optical system able to perform the fractional Fourier transform (FRFT) almost in real time is presented. In contrast to other FRFT setups the resulting transformation has no additional scaling and phase factors depending on the fractional orders. The feasibility of the proposed setup is demonstrated experimentally for a wide range of fractional orders. The fast modification of the fractional orders, offered by this optical system, allows to implement various proposed algorithms for beam characterization, phase retrieval, information processing, etc.

Fractional transforms in optical information processing

We review the progress achieved in optical information processing during the last decade by applying fractional linear integral transforms. The fractional Fourier transform and its applications for phase retrieval, beam characterization, space-variant pattern recognition, adaptive filter design, encryption, watermarking, and so forth is discussed in detail. A general algorithm for the fractionalization of linear cyclic integral transforms is introduced and it is shown that they can be fractionalized in an infinite number of ways. Basic properties of fractional cyclic transforms are considered. The implementation of some fractional transforms in optics, such as fractional Hankel, sine, cosine, Hartley, and Hilbert transforms, is discussed. New horizons of the application of fractional transforms for optical information processing are underlined.

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.

Focusing properties of fractal zone plates: experimental implementation with a liquid-crystal display

We report the first experimental results, to our knowledge, with fractal zone plates implemented in a liquid-crystal display. Our results largely agree with theory for the axial irradiance distribution of these lenses. The dependence of the shape and size of the focus points on critical design parameters is discussed. Additional unpredicted features are also described.