Wave-particle complementarity and reciprocity of Gauss sums on Talbot effects

Foundations of Physics Letters

Volumn 16, Issue 4, 2003, Pages 325-341

  Matsutani, Shigeki ^a   Ônishi, Yoshihiro ^b  

^a Iwate University ^*  (Japan)

^b IWATE UNIVERSITY   (Japan)

Author keywords

Complementarity; Gauss sums; Reciprocity; Talbot effects

Indexed keywords

EID: 0042881147     PISSN: 08949875     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1025309708569     Document Type: Article

References (27)

1. K. Banaszek, K. Wodkiewicz, and W. P. Schleich, "Fractional Talbot effect in phase space: a compact summation formula," Optics Express 2, 169-172 (1998).
2. M. J. Bastiaans, "The Wigner distribution function applied to optical signals and system," Optics Commun. 25, 26-30 (1978).
3. M. V. Berry, "Quantum fractals in boxes," J. Phys. A: Math. & Gen. 29, 6617-6629 (1996).
4. M. V. Berry and S. Klein, "Integer, fractional and fractal Talbot effects," J. Mod. Opt. 43, 2139-2164 (1996).
5. M. V. Berry and C. Upstill, "Catastrophe optics: morphologies of caustics and their diffraction patterns," Progress in Optics XVIII, 258-346 (1980).
6. N. Bohr "The quantum postulate and the recent development of atomic theory," Nature 121, 580-90 (1928).
7. M. Born and E. Wolf, Principles of Optics, 5th edn. (Pergamon, Oxford, 1975).
8. V. Guillemin and S. Sterngerg, Symplectic Techniques in Physics (Cambridge University Press, Cambridge, 1984).
9. J. H. Hannay and M. V. Berry, "Quantization of linear maps on a torus-Fresnel diffraction by periodic grating," Physica 1D, 267-290 (1980).
10. E. Hecke, Lectures on the Theory of Algebraic Numbers GTM 77 (Springer, Berlin, 1981).
11. F. Klein, Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert I (Springer, Berlin, 1926).
12. S. Ishiwata, S. Matsutani and Y. Ônishi, "Localized state of hard core chain and cyclotomic polynomial: hard core limit of diatomic Toda lattice," Phys. Lett A 231, 208-216 (1997).
13. K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, 2nd edn. (Springer, Berlin, 1990).
14. V. P. Maslov, Théorie des Perturbations et Méthodes Asymptotiques (Dunod, Paris, 1972).
15. 2/2g," Rev. Math. Phys. 9, 943-991 (1997).
16. S. Matsutani, "p-adic difference-difference Lotka-Volterra equation and ultra-discrete limit," Int. J. Math, and Math. Sci. 27, 251-260 (2001).
17. NZ," J. Phys. A: Gen. & Math. 34, 10737-10744 (2001).
18. E. Noponen and J. Turunen, "Electromagnetic theory of Talbot imaging," Optics Commun. 98, 132-140 (1993).
19. K. I. Oskolkov, "Schrodinger equation and oscillatory Hilbert transforms of second degrees," J. Fourier Anal. Appl. 3, 341-356 (1998).
20. K. Patorski, "The Self-imaging phenomenon and its applications," Progress in Optics XXVII, 10-110 (1989).
21. J. S. Sánchez and K. B. Wolf, Lie Methods in Optics, LNP 250 (Springer, Berlin, 1985).
22. L. S. Schulman, Techniques and Applications of Path Integration (John Wiley, New York, 1981).
23. W.H.F. Talbot, "Facts relating to optical sciences. No. IV," Phil. Mag. 9, 401-407 (1838).
24. K. Tanaka, "Paraxial theory in optical design in terms of Gaussian brackets patterns," Progress in Optics XXIII, 63-112 (1986).
25. M. Testorf, and J. Ojeda-Castañeda, "Fractional Talbot effect: analysis in phase space." J Opt Soc. Am. A 13, 119-125 (1996).
26. A. Weil, "Sur certains groupes d'opérateurs unitaires," Acta Math. 111, 143-211 (1964).
27. J. T. Winthrop and C. R. Worthington, "Theory of Fresnel images. I. plane periodic objects in monochromatic light," J. opt. Soc. Am. 55, 373-381 (1965).