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Starting with the Iwasawa-type decomposition of a first-order optical system (or ABCD system) as a cascade of a lens, a magnifier, and an orthosymplectic system (a system that is both symplectic and orthogonal), a further decomposition of the or[...]texto impreso
Based on the eigenvalues of the ray transformation matrix, a classification of ABCD systems is proposed and some nuclei (i.e., elementary members) in each class are described. In the one-dimensional case, possible nuclei are the magnifier, the l[...]texto impreso
Based on the ray transformation matrix formalism, we propose a simple method for the identification of the dynamic and geometric parts of the Gouy phase, acquired by an appropriate Gaussian-type beam while propagating through a first-order optic[...]texto impreso
We analyze the evolution of the vortex and the asymmetrical parts of orbital angular momentum during its propagation through separable first-order optical systems. We find that the evolution of the vortex part depends on only parameters a(x), a([...]texto impreso
It is shown that a lossless first-order optical system whose real symplectic ray transformation matrix can be diagonalized and has only unimodular eigenvalues is similar to a separable fractional Fourier transformer in the sense that the ray tra[...]texto impreso
Calvo Padilla, María Luisa ; Alieva, Tatiana Krasheninnikova ; Bastiaans, Martin J. ; Rodrigo Martín-Romo, José Augusto ; Rodríguez Merlo, D. | SPIE--The International Society for Optical Engineering | 2004We present a short overview on the application of fractional cyclic and linear canonical transformations to optical signal processing and dedicate some of the discussions to the particular features found in the fractional Fourier transform domain.texto impreso
Bastiaans, Martin J. ; Alieva, Tatiana Krasheninnikova ; Calvo Padilla, María Luisa | Hindawi Publishing Corporation | 2005-07-01We 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-v[...]texto impreso
The relationship between the mode content and the fractional Fourier and fractional Hankel transforms of a function is established. It is shown that the Laguerre-Gauss spectrum of a rotationally symmetric wave front can be determined from the wa[...]texto impreso
A Collins transformation maps an orthonormal set of Hermite-Gaussian modes into an orthonormal set of beams with a Gaussian envelope. Among these beams are Laguerre-Gaussian beams and the recently introduced Hermite-Laguerre-Gaussian beams. Comp[...]texto impreso
The Wigner distribution of rotationally symmetric partially coherent light is considered, and the constraints for its moments are derived. Although all odd-order moments vanish, these constraints lead to a drastic reduction in the number of para[...]texto impreso
A family of orthonormal mode sets arises when Hermite-Gauss modes propagate through lossless first-order optical systems. It is shown that the modes at the output of the system are eigenfunctions for the symmetric fractional Fourier transformati[...]texto impreso
We introduce the orbital Stokes parameters as a linear combination of a beam's second-order moments. Similar to the ones describing the field polarization and associated with beam energy and its spin angular momentum, the orbital Stokes paramete[...]texto impreso
Alieva, Tatiana Krasheninnikova ; Calvo Padilla, María Luisa ; Bastiaans, Martin J. | SPIE--The International Society for Optical Engineering | 2003The main properties of n-th order power filtering in the fractional Fourier domain and its relationship to the differentiation operation are considered. The. application of power filtering for solving the phase retrieval problem is proposed.texto impreso
Bastiaans, Martin J. ; Alieva, Tatiana Krasheninnikova ; Calvo Padilla, María Luisa | IOP Publishing | 2002-09-13The main properties of the power filtering operation in the fractional Fourier domain and its relationship to the differentiation operation are considered. The application of linear power filtering for solving the phase retrieval problem from in[...]texto impreso
We provide a general expression and different classification schemes for the general two-dimensional canonical integral transformations that describe the propagation of coherent light through lossless first-order optical systems. Main theorems f[...]
