OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Vol. 17, Iss. 9 — Sep. 1, 2000
  • pp: 1579–1588

Optical kicked system exhibiting localization in the spatial frequency domain

Amir Rosen, Baruch Fischer, Alexander Bekker, and Shmuel Fishman  »View Author Affiliations


JOSA B, Vol. 17, Issue 9, pp. 1579-1588 (2000)
http://dx.doi.org/10.1364/JOSAB.17.001579


View Full Text Article

Enhanced HTML    Acrobat PDF (198 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

An optical kicked system with free-space light propagation along a sequence of equally spaced thin phase gratings is presented and investigated. We show, to our knowledge for the first time in optics, the occurrence of the localization effect in the spatial frequency domain, which suppresses the spreading of diffraction orders formed by the repeated modulation by the gratings of the propagating wave. Resonances and antiresonances of the optical system are described and are shown to be related to the Talbot effect. The system is similar in some aspects to the quantum kicked rotor, which is the standard system in the theoretical studies of the suppression of classical (corresponding to Newtonian mechanics) chaos by interference effects. Our experimental verification was done in a specific regime, where the grating spacing was near odd multiples of half the Talbot length. It is shown that this corresponds to the vicinity of antiresonance in the kicked system. The crucial alignment of the gratings in-phase positioning in the experiment was based on a diffraction elimination property at antiresonance. In the present study we obtain new theoretical and experimental results concerning the localization behavior in the vicinity of antiresonance. The behavior in this regime is related to that of electronic motion in incommensurate potentials, a subject that was extensively studied in condensed matter physics.

© 2000 Optical Society of America

OCIS Codes
(060.5530) Fiber optics and optical communications : Pulse propagation and temporal solitons
(270.1670) Quantum optics : Coherent optical effects

Citation
Amir Rosen, Baruch Fischer, Alexander Bekker, and Shmuel Fishman, "Optical kicked system exhibiting localization in the spatial frequency domain," J. Opt. Soc. Am. B 17, 1579-1588 (2000)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-17-9-1579


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. A. W. Snyder and S. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).
  2. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).
  3. S. Fishman, D. R. Grempel, and R. E. Prange, “Chaos, quantum recurrences, and Anderson localization,” Phys. Rev. Lett. 49, 509–512 (1982); D. R. Grempel, R. E. Prange, and S. Fishman, “Quantum dynamics of a nonintegrable system,” Phys. Rev. A 29, 1639–1647 (1984). [CrossRef]
  4. F. Haake, Quantum Signatures of Chaos (Springer, New York, 1991).
  5. P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109, 1492–1505 (1958). [CrossRef]
  6. For reviews, see D. J. Thouless, “Critical phenomena, random systems, gauge theories,” in Proceedings of the Les-Houches Summer School, K. Osterwalder and R. Stora, eds. (North-Holland, Amsterdam, 1986), p. 681; I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988).
  7. F. L. Moore, J. C. Robinson, C. F. Barucha, B. Sundaram, and M. G. Raizen, “Atom optics realization of the quantum δ-kicked rotor,” Phys. Rev. Lett. 75, 4598–4601 (1995). [CrossRef] [PubMed]
  8. B. G. Klappauf, W. H. Oskay, D. A. Steck, and M. G. Raizen, “Observation of noise and dissipation effects on dynamical localization,” Phys. Rev. Lett. 81, 1203–1206 (1998); H. Ammann, R. Gray, I. Shvarchuck, and N. Christensen, “Quantum delta-kicked rotor: experimental observation of decoherence,” Phys. Rev. Lett. 80, 4111–4115 (1998). [CrossRef]
  9. L. Liu, “Talbot and Lau effects on incident beams of arbitrary wavefront, and their use,” Appl. Opt. 28, 4668–4678 (1989). [CrossRef] [PubMed]
  10. E. Ott, Chaos in Dynamical Systems (Cambridge U. Cambridge, UK, 1993).
  11. P. Bergé, Y. Pomeau, and C. Vidal, Order Within Chaos (Hermann, Paris, 1984).
  12. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, New York, 1983).
  13. A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion (Springer, New York, 1983).
  14. M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, New York, 1990).
  15. M. J. Giannoni, A. Voros, and J. Zinn-Justin, eds., “Chaos and quantum physics,” in Proceedings of the Les-Houches Summer School, Session LII, 1989 (North-Holland, Amsterdam, 1991).
  16. G. L. Oppo, S. M. Barnett, E. Riis, and M. Wilkinson, eds., “Quantum dynamics of simple systems,” in Proceedings of the 44th Scottish Universities Summer School in Physics (Scottish Universities Summer School in Physics Publications and Institute of Physics, Bristol, UK, 1996).
  17. G. Casati, B. V. Chirikov, F. M. Izrailev, and J. Ford, in Stochastic Behavior in Classical and Quantum Hamiltonian Systems, Vol. 93 of Lecture Notes in Physics, G. Casati and J. Ford, eds. (Springer-Verlag, Berlin, 1979), p. 334.
  18. B. V. Chirikov, F. M. Izrailev, and D. L. Shepelyansky, “Dynamical stochasticity in classical and quantum mechanics,” Sov. Sci. Rev. Sect. C 2, 209–267 (1981).
  19. D. L. Shepelyansky, “Localization of quasienergy eigenfunctions in action space,” Phys. Rev. Lett. 56, 677–680 (1986); “Localization of diffusive excitation in multi-level systems,” Physica D 28, 103–114 (1987). [CrossRef] [PubMed]
  20. R. Blumel, S. Fishman, and U. Smilansky, “Excitation of molecular rotation by periodic microwave pulses. A testing ground for Anderson localization,” J. Chem. Phys. 84, 2604–2614 (1986). [CrossRef]
  21. R. Graham, M. Schlautmann, and P. Zoller, “Dynamical localization of atomic-beam deflection by a modulated standing light wave,” Phys. Rev. A 45, R19–R22 (1992); see also R. Graham, M. Schlautmann, and D. L. Shepelyansky, “Dynamical localization in Josephson junctions,” Phys. Rev. Lett. 67, 255–258 (1991), and references therein. [CrossRef] [PubMed]
  22. G. Casati, I. Guarneri, and D. L. Shepelyansky, “Hydrogen atom in monochromatic field: chaos and dynamical photonic localization,” IEEE J. Quantum Electron. 24, 1420–1444 (1988), and references therein; R. Blümel and U. Smilansky, “Microwave ionization of highly excited hydrogen atoms,” Z. Phys. D 6, 83–105 (1987), and references therein; E. J. Galvez, B. E. Sauer, L. Moorman, P. M. Koch, and D. Richards, “Microwave ionization of H atoms: breakdown of classical dynamics for high frequencies,” Phys. Rev. Lett. PRLTAO 61, 2011–2014 (1988); J. E. Bayfield, G. Casati, I. Guarneri, and D. W. Sokol, “Localization of classically chaotic diffusion for hydrogen atoms in microwave fields,” Phys. Rev. Lett. PRLTAO 63, 364–367 (1989), and references therein; R. Blümel, R. Graham, L. Sirko, U. Smilansky, H. Walther, and K. Yamada, “Microwave excitation of Rydberg atoms in the presence of noise,” Phys. Rev. Lett. PRLTAO 62, 341–344 (1989); R. Blümel, A. Buchleitner, R. Graham, L. Sirko, U. Smilansky, and H. Walther, “Dynamical localization in the microwave interaction of Rydberg atoms: the influence of noise,” Phys. Rev. A PLRAAN 44, 4521–4540 (1991), and references therein. [CrossRef] [PubMed]
  23. S. L. McCall, P. M. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, “Microwave propagation in two-dimensional dielectric lattices,” Phys. Rev. Lett. 67, 2017–2020 (1991). [CrossRef] [PubMed]
  24. M. V. Berry and S. Klein, “Transparent mirrors: rays, waves, and localization,” Eur. J. Phys. 18, 222–228 (1997). [CrossRef]
  25. D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671–673 (1997). [CrossRef]
  26. J. Krug, “Optical analog of a kicked quantum oscillator,” Phys. Rev. Lett. 59, 2133–2136 (1987). [CrossRef] [PubMed]
  27. R. E. Prange and S. Fishman, “Experimental realizations of kicked quantum chaotic systems,” Phys. Rev. Lett. 63, 704–707 (1989); O. Agam, S. Fishman, and R. E. Prange, “Experimental realizations of quantum chaos in dielectric waveguides,” Phys. Rev. A 45, 6773–6802 (1992). [CrossRef] [PubMed]
  28. B. Fischer, A. Rosen, and S. Fishman, “Localization in frequency for periodically kicked light propagation in a dispersive single-mode fiber,” Opt. Lett. 24, 1463–1465 (1999). [CrossRef]
  29. B. Fischer, A. Rosen, A. Bekker, and S. Fishman, “Experimental observation of localization in the spatial frequency domain of a kicked optical system,” Phys. Rev. E 61, 4694R–4697R (2000). [CrossRef]
  30. D. R. Grempel, S. Fishman, and R. E. Prange, “Localization in an incommensurate potential: an exactly solvable model,” Phys. Rev. Lett. 49, 833–836 (1982). [CrossRef]
  31. See, for example, A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 7.
  32. I. Dana, E. Eisenberg, and N. Shnerb, “Dynamical localization near quantum antiresonance: exact results and a solvable case,” Phys. Rev. Lett. 74, 686–689 (1995); “Antiresonance and localization in quantum dynamics,” Phys. Rev. E 54, 5948–5963 (1996); E. Eisenberg and I. Dana, “Limited sensitivity to analyticity: a manifestation of quantum chaos,” Found. Phys. FNDPA4 27, 153–170 (1997). [CrossRef] [PubMed]
  33. R. E. Prange, D. R. Grempel, and S. Fishman, “Wave functions at a mobility edge: an example of a singular continuous spectrum,” Phys. Rev. B 28, 7370–7372 (1983); R. E. Prange, D. R. Grempel, and S. Fishman, “Solvable model of quantum motion in an incommensurate potential,” Phys. Rev. B 29, 6500–6512 (1984); R. E. Prange, D. R. Grempel, and S. Fishman, “Long-range resonance in Anderson insulators: finite-frequency conductivity of random and incommensurate systems,” Phys. Rev. Lett. PRLTAO 53, 1582–1585 (1984). [CrossRef]
  34. L. A. Pastur and A. L. Figotin, “Localization in an incommensurate potential: exactly solvable multidimensional model,” JETP Lett. 37, 686–688 (1983).
  35. M. Ya. Azbel, “Energy spectrum of a conduction electron in a magnetic field,” Sov. Phys. JETP 19, 634–645 (1964).
  36. S. Aubry and G. Andre, “Analyticity breaking and Anderson localization in incommensurate lattices,” Ann. Isr. Phys. Soc. 3, 133–164 (1979).
  37. D. J. Thouless and Q. Niu, “Wavefunction scaling in a quasi-periodic potential,” J. Phys. A 16, 1911–1919 (1983). [CrossRef]
  38. M. Wilkinson, “Critical properties of electron eigenstates in incommensurate systems,” Proc. R. Soc. London, Ser. A 391, 305–350 (1984). [CrossRef]
  39. B. Simon, “Almost periodic Schrödinger operators: a review,” Adv. Appl. Math. 3, 463–490 (1982). [CrossRef]
  40. P. Sarnak, “Spectral behavior of quasi periodic potentials,” Commun. Math. Phys. 84, 377–401 (1982). [CrossRef]
  41. J. Avron and B. Simon, “Singular continuous spectrum for a class of almost periodic Jacobi matrices,” Bull. Am. Math. Soc. 6, 81–85 (1982); “Almost periodic Schrödinger operators. II. The integrated density of states,” Duke Math. J. 50, 369–391 (1983). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited