Wigner functions for helmholtz wave fields

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 16, Issue 10, 1999, Pages 2476-2487

  Wolf, Kurt Bernardo ^a   Alonso, Miguel Angel ^b   Forbes, Gregory W ^b  

^a INSTITUTO DE CIENCIAS FÍSICAS   (Mexico)

^b MACQUARIE UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001344129     PISSN: 10847529     EISSN: 15208532     Source Type: Journal    
DOI: 10.1364/JOSAA.16.002476     Document Type: Article

References (13)

1. E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749-759 (1932); H.-W. Lee, “Theory and application of the quantum phase-space distribution functions,” Phys. Rep. 259, 147-211 (1995).
2. A. Walther, “Radiometry and coherence,” J. Opt. Soc. Am. 58, 1256-1259 (1968).
3. A. Walther, “Radiometry and coherence,” J. Opt. Soc. Am. 63, 1622-1623 (1973).
4. R. G. Littlejohn and R. Winston, “Corrections to classical radiometry,” J. Opt. Soc. Am. A 10, 2024-2037 (1993).
5. Yu. A. Kravtsov and Yu. A. Orlov, Geometrical Optics of Inhomogeneous Media (Springer-Verlag, Berlin, 1990), p. 23.
6. The existence of an invertible Fourier transform [Eq. (3)] of a (twice-differentiable) Helmholtz wave field C(q) is ensured by the conditions of the Fourier integral theorem only when it is absolutely integrable and of bounded variation. Plane waves are in this sense limit functions for which Fourier analysis can be extended as usual with Dirac d’s in the p plane and on the unit circle [Eq. (4)]. However, evanescent solutions (i.e., of exponential growth in the plane) do not possess a Fourier transform.
7. P. González-Casanova and K. B. Wolf, “Interpolation for solutions of the Helmholtz equation,” Num. Meth. Partial Diff. Eqs. 11, 77-91 (1995).
8. For other references about flux vortices see, for example, M. V. Berry, “Evanescent and real waves in quantum billiards and Gaussian beams,” J. Phys. A Nucl. Math. Gen. 27, L391-L398 (1994).
9. A. Lohmann, “The Wigner function and its optical production,” Opt. Commun. 42, 32-37 (1980).
10. K. B. Wolf and A. L. Rivera, “Holographic information in the Wigner function,” Opt. Commun. 144, 36-42 (1997).
11. M. Bastiaans, “The Wigner distribution function applied to optical signals and systems,” Opt. Commun. 25, 26-30 (1978); “Wigner distribution function and its application to first-order optics,” J. Opt. Soc. Am. 69, 1710-1716 (1979);“The Wigner distribution function and Hamilton’s characteristics of a geometric-optical system,” Opt. Commun. 30, 321-326 (1979).
12. S. Steinberg and K. B. Wolf, “Invariant inner products on spaces of solutions of the Klein-Gordon and Helmholtz equations,” J. Math. Phys. 22, 1660-1663 (1981).
13. L. M. Nieto, N. M. Atakishiyev, S. M. Chumakov, and K. B. Wolf, “Wigner distribution function for finite systems,” J. Phys. A Nucl. Math. Gen. 31, 3875-3895 (1998).