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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 28, Iss. 4 — Apr. 1, 2011
  • pp: 641–650

Finite signals in planar waveguides

Juvenal Rueda-Paz and Kurt Bernardo Wolf  »View Author Affiliations

JOSA A, Vol. 28, Issue 4, pp. 641-650 (2011)

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We examine the evolution in phase space of an N-point signal, produced and sensed at finite arrays transverse to a planar waveguide within the framework of the finite quantization of geometric optics. We use the Kravchuk coherent states provided by the finite oscillator model to evince the nonlinear transformations that elliptic-profile waveguides produce on phase space by means of the SO ( 3 ) Wigner function.

© 2011 Optical Society of America

OCIS Codes
(080.2720) Geometric optics : Mathematical methods (general)
(070.2025) Fourier optics and signal processing : Discrete optical signal processing

ToC Category:
Fourier Optics and Signal Processing

Original Manuscript: August 26, 2010
Revised Manuscript: January 14, 2011
Manuscript Accepted: January 25, 2011
Published: March 25, 2011

Juvenal Rueda-Paz and Kurt Bernardo Wolf, "Finite signals in planar waveguides," J. Opt. Soc. Am. A 28, 641-650 (2011)

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  1. K. B. Wolf, “Refracting surfaces between fibers,” J. Opt. Soc. Am. A 8, 1389–1398 (1991). [CrossRef]
  2. K. B. Wolf, “Linear transformations and aberrations in continuous and in finite systems,” J. Phys. A 41, 304026 (2008). [CrossRef]
  3. H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).
  4. Ç. Candan, M. A. Kutay, and H. M. Ozaktas, “The discrete fractional Fourier transform,” IEEE Trans. Signal Process. 48, 1329–1337 (2000). [CrossRef]
  5. A. Koç, H. M. Ozaktas, C. Candan, and M. A. Kutay, “Digital computation of linear canonical transforms,” IEEE Trans. Signal Process. 56, 2383–2394 (2008). [CrossRef]
  6. S.-C. Pei and C.-C. Tseng, “Discrete fractional Fourier transform based on orthogonal projections,” IEEE Trans. Signal Process. 47, 1335–1348 (1999). [CrossRef]
  7. J. J. Healy and J. T. Sheridan, “Fast linear canonical transforms,” J. Opt. Soc. Am. A 27, 21–30 (2010). [CrossRef]
  8. K. B. Wolf, Geometric Optics on Phase Space (Springer, 2004).
  9. N. M. Atakishiyev and K. B. Wolf, “Fractional Fourier-Kravchuk transform,” J. Opt. Soc. Am. A 14, 1467–1477 (1997). [CrossRef]
  10. N. M. Atakishiyev, G. S. Pogosyan, and K. B. Wolf, “Finite models of the oscillator,” Phys. Part. Nucl. 36, 521–555 (2005).
  11. N. M. Atakishiyev, S. M. Chumakov, and K. B. Wolf, “Wigner distribution function for finite systems,” J. Math. Phys. 39, 6247–6261 (1998). [CrossRef]
  12. S. T. Ali, N. M. Atakishiyev, S. M. Chumakov, and K. B. Wolf, “The Wigner 23 function for general Lie groups and the wavelet transform,” Ann. Henri Poincaré 1, 685–714 (2000). [CrossRef]
  13. A. J. Dragt, “Lie algebraic theory of geometrical optics and optical aberrations,” J. Opt. Soc. Am. 72, 372–379 (1982). [CrossRef]
  14. A. J. Dragt, E. Forest, and K. B. Wolf, “Foundations of a Lie algebraic theory of geometrical optics.,” in Lie Methods in Optics, Lecture Notes in Physics (Springer, 1986), Vol.  250, pp. 105–158. [CrossRef]
  15. K. B. Wolf, “Discrete systems and signals on phase space,” Appl. Math. Inf. Sci. 4, 141–181 (2010).
  16. R. Gilmore, Lie Groups, Lie Algebras, and Some of Their Applications (Wiley-Interscience, 1978).
  17. L. C. Biedenharn and J. D. Louck, Angular Momentum in Quantum Physics, Encyclopedia of Mathematics and Its Applications (Addison-Wesley, 1981), Vol.  8.
  18. N. M. Atakishiyev, L. E. Vicent, and K. B. Wolf, “Continuous vs. discrete fractional Fourier transforms,” J. Comput. Appl. Math. 107, 73–95 (1999). [CrossRef]
  19. M. Krawtchouk, “Sur une généralization des polinômes d’Hermite,” C. R. Acad. Sci. Paris Ser. IV 189, 620–622 (1929).
  20. A. F. Nikiforov, S. K. Suslov, and V. B. Uvarov, Classical Orthogonal Polynomials of a Discrete Variable, Springer Series in Computational Physics (Springer, 1991).
  21. N. M. Atakishiyev and S. K. Suslov, “Difference analogs of the harmonic oscillator,” Theor. Math. Phys. 85, 1055–1062 (1990). [CrossRef]
  22. N. M. Atakishiyev, G. S. Pogosyan, and K. B. Wolf, “Contraction of the finite one-dimensional oscillator,” Int. J. Mod. Phys. A 18, 317–327 (2003). [CrossRef]
  23. K. B. Wolf and G. Krötzsch, “Geometry and dynamics in the fractional discrete Fourier transform,” J. Opt. Soc. Am. A 24, 651–658 (2007). [CrossRef]
  24. S. H. Cheng, N. J. Higham, C. S. Kenney, and A. J. Laub, “Approximating the logarithm of a matrix to a specified accuracy,” SIAM J. Matrix Anal. Appl. 22, 1112–1125 (2001). [CrossRef]
  25. L. M. Nieto, N. M. Atakishiyev, S. M. Chumakov, and K. B. Wolf, “Wigner distribution function for Euclidean systems,” J. Phys. A 31, 3875–3895 (1998). [CrossRef]
  26. C. A. Muñoz, J. Rueda-Paz, and K. B. Wolf, “Discrete repulsive oscillator wavefunctions,” J. Phys. A 42, 485210(2009). [CrossRef]
  27. K. B. Wolf and G. Krötzsch, “Metaxial correction of fractional Fourier transformers,” J. Opt. Soc. Am. A 16, 821–830 (1999). [CrossRef]
  28. E. P. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749–759 (1932). [CrossRef]
  29. H.-W. Lee, “Theory and applications of the quantum phase-space distribution functions,” Phys. Rep. 259, 147–211 (1995). [CrossRef]

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