Dispersion of short pulses: Guigay matrix

Abstract

By employing Guigay coefficients, one can describe in an elegant and useful manner the Fresnel diffraction patterns of a periodic structure. Here, we relate Guigay formulation with the classical Fourier series treatment of first order dispersion. Then, we propose the use of a remarkably simple matrix for describing first order dispersion.

Full Text: PDF

References

1. A.W. Lohmann and D.A. Silvia, "An interferometer based on the Talbot effect", Opt. Comm. 2,71 (1971). CrossRef
2. S. Yokozeiki and T. Suzuki, Appl. Optics 10, 1575 (1971). CrossRef
3. A. W. Lohmann, Optik 79, 41 (1988).
4. V. Arrizon and J. Ojeda-Castaneda, "Talbot array illuminators with binary phase gratings", Opt. Lett. 18, 1 (1993). CrossRef
5. J. Ojeda-Castaneda and E. E. Sicre, "Theta-modulation decoder based on the Lau effect", Opt. Comm. 59, 87 (1986). CrossRef
6. J. Ojeda-Castaneda, P. Andres and J. C. Barreiro, "Abbe-Porter experiment and logic operations", Opt. Comm. 7l, 145 (1989). CrossRef
7. S. Chitraleka, K. V. Avudainayagam, and S. V. Pappu, "Sensitivity of Lau fringes to grating rotation: theoretical analysis", Appl. Opt. 29, 125 (1990). CrossRef
8. J. C. Barreiro and J. Ojeda-Castaneda, "Degree of coherence: a lensless measuring technique", Opt. Lett. 18, 302 (1993). CrossRef
9. A. W. Lohmann and J. Ojeda-Castaneda, "Fresnel similarity", Opt. Comm. 249, 39 (2005). CrossRef
10. Tomasz Jannson and Joanna Jannson, "Information capacity of Bragg holograms in planar optics", J. Opt. Soc. Am. 71, 1373 (1981). CrossRef
11. J. Ojeda-Castaneda, P. Andrés and O. Mendoza-Yero, "Tailoring temporal intensities at first- and second-dispersion order", Optical Memory and Neural Networks 18, 260 (2009). CrossRef
12. J. Ojeda-Casta-eda and C. M. Gómez-Sarabia, "Optical processor arrays for controlling focal length or for tuning the depth of field ", Photonics Lett. of Poland 2, 165 (2010). CrossRef
13. Jean-Pierre Guigay, "On Fresnel Diffraction by One-dimensional Periodic Objects, with Application to Structure Determination of Phase Objects", Optica Acta 18, 677 (1971). CrossRef
14. J. T. Winthrop and C. R. Worthington, "Theory of Fresnel Images. I. Plane Periodic Objects in Monochromatic Light", J. Opt. Soc. Am. 55, 373 (1965). CrossRef
15. R. Evans and B. Berndt, "The determination of Gauss sums", Bull. Amer. Math. Soc. 5, 107 (1981). CrossRef
16. V. Arrizón and J. Ojeda-Casta-eda, "Fresnel diffraction of substructured gratings: matrix description", Opt. Lett. 20, 118 (1995). CrossRef
17. J. Ojeda-Castaneda and C. M. Gómez-Sarabia, "Optical processor arrays for controlling focal length or for tuning the depth of field ", Photonics Lett. of Poland 2, 159 (2010) CrossRef