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Nonlinear optical beam propagation and solitons in photorefractive media

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La Rivista del Nuovo Cimento (1978-1999) Aims and scope

Conclusions

The last few years have witnessed a great renewal of interest in the photorefractive effect thanks to the realization of the possibility of propagating stable 2D spatial solitons at very low optical powers in PR crystals. This result, besides possessing a great scientific relevance in itself, associated with the first experimental demonstration of a non-diffracting two-dimensional pencil of light, has also an interesting applicative potential thanks to the guidance properties of the waveguide associated with the soliton, which survives in the dark also after the soliton has been turned off. In this paper, we have tried to present a self-contained approach to the theory of self-trapped nonlinear propagation, which is far from being definitive, together with the most important experimental demonstrations obtained in the last few years. The novelty of the field, and the fact that it is still undergoing a rapid growth, has made our task not an easy one and we apologize to the readers for the many inevitable omissions both in the subjects we have chosen to emphasize and in the references.

We cannot conclude this review without mentioning self-trapping of planar optical beams by the use of the PR effect in a semiconductor (InP:Fe) [94, 95], the main advantages over standard PR materials being associated with its sensitivity in the range of the near-infrared wavelengths and faster response time.

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References

  1. Bloembergen N.,Nonlinear Optics (Addison-Wesley, Reading, Mass.) 1991;Encounters in Nonlinear Optics: selected Papers of Nicolaas Bloembergen, edited by N. Bloembergen (World Scientific, NJ), 1996; Shen Y. R.,The Principles of Nonlinear Optics (Wiley, New York) 1984.

    Google Scholar 

  2. Chiao R. Y., Garmire E. andTownes C. H.,Phys. Rev. Lett.,13 (1964) 479.

    Article  ADS  Google Scholar 

  3. Zakharov V. E. andShabat A. B.,Sov. Phys. JETP,34 (1972) 62.

    MathSciNet  ADS  Google Scholar 

  4. See,e.g.,Agrawal G. P.,Nonlinear Fiber Optics (Academic Press, New York) 1989.

    Google Scholar 

  5. See,e.g.,Hasegawa A. andKodama Y.,Solitons in Optical Communications (Clarendon Press, Oxford) 1995.

    Google Scholar 

  6. See,e.g.,Infeld E. andRowlands G.,Nonlinear Waves, Solitons and Chaos (Cambridge University Press, Cambridge) 1990.

    Google Scholar 

  7. Temporal solitons were first demonstrated byMollenhauer L. F., Stolen R. H. andGordon J. P.,Phys. Rev. Lett.,45 (1980) 1095.

    Article  ADS  Google Scholar 

  8. See.,e.g., the first observation of spatial solitons in solids,Aitchison J. S., Weiner A. M., Silberberg Y., Oliver M. K., Jackel J. L., Leaird D. E., Vogel E. M. andSmith P. W.,Opt. Lett.,15 (1990) 471.

    Article  ADS  Google Scholar 

  9. Kelley P. L.,Phys. Rev. Lett.,15 (1964) 1005.

    Article  ADS  Google Scholar 

  10. Zakharov V. E. andRubenchik A. M.,Sov. Phys. JETP,38 (1974) 494.

    ADS  Google Scholar 

  11. We use the term “soliton” in conjunction with non-diffracting self-trapped optical beams,i.e. we use the broader definition of solitons including those in non-integrable systems, as defined byZakharov V. E. andMalomed B. A., inPhysical Encyclopedia, edited byA. M. Prokhorov (Great Russian Encyclopedia, Moscow) 1994.

    Google Scholar 

  12. Segev M., Crosignani B., Yariv A. andFischer B.,Phys. Rev. Lett.,68 (1992) 923.

    Article  ADS  Google Scholar 

  13. Duree G. C., Shultz J. L., Salamo G. J., Segev M., Yariv A., Crosignani B., Di Porto P., Sharp E. J., Neurgaonkar R. R.,Phys. Rev. Lett.,71 (1993) 533.

    Article  ADS  Google Scholar 

  14. Torruellas W. E., Wang Z., Hagan D. J., Van Stryland E. W., Stegeman G. L., Torner L. andMenyuk C. R.,Phys. Rev. Lett.,74 (1995) 5036.

    Article  ADS  Google Scholar 

  15. Tikhonenko V., Christou J. andLuther-Davies B.,Phys. Rev. Lett 76 (1996) 2698; one related obserevation was reported much earlier:Bjorkholm J. E. andAshkin A.,Phys. Rev. Lett.,32 (1974) 129.

    Article  ADS  Google Scholar 

  16. Ashkin A., Boyd G. D., Dziedzic J. M., Smith R. G., Ballman A. A., Levinstein J. J. andNassau K.,Appl. Phys. Lett.,9 (1966) 72.

    Article  ADS  Google Scholar 

  17. Yariv A.,Optical Electronics, 5th edition (Wiley, New York) 1995.

    Google Scholar 

  18. Yeh P.,Introduction to Photorefractive Nonlinear Optics (Wiley, New York) 1993.

    Google Scholar 

  19. Solymar L., Webb D. J. andGrunnet-Jepsen A.,The Physics and Applications of Photorefractive Materials (Clarendon Press, Oxford) 1996.

    Google Scholar 

  20. Vinetski V. L. andKukhtarev N. V.,Sov. Phys. Solid State,16 (1975) 2414.

    Google Scholar 

  21. Kukhtarev N. V., Markov V. B., Odulov S. G., Soskin M. S. andVinetski V. L.,Ferroelectrics,22 (1979) 961.

    Article  Google Scholar 

  22. The necessity of having a number NA of acceptors impurities, which permanently trap a corresponding number of electrons, is due to the role they play in determining the Debye length lD of the crystal. In fact, if not for the presence of acceptors, the Debye length would scale with 1/√(Ne) instead of the much smaller quantity 1/√(NA) and thus would become too large for the purpose of recording optical information.

  23. Crosignani B., Di Porto P., DeGasperis A., Segev M. andTrillo S.,J. Opt. Soc. Am. B,14 (1997) 3078.

    Article  ADS  Google Scholar 

  24. This term can be shown to be responsible for a self-bending of the self-trapped beam which does not alter its shape; see,e.g.,Singh S.R. andChristodoulides D. N.,Opt. Commun.,118 (1995) 569.

    Article  ADS  Google Scholar 

  25. Segev M., Valley G., Crosignani B., Di Porto P. andYariv A.,Phys. Rev. Lett.,73 (1994) 3211.

    Article  ADS  Google Scholar 

  26. Segev M., Shih M. andValley G.,J. Opt. Soc. Am. B,13 (1996) 706.

    Article  ADS  Google Scholar 

  27. Christodoulides D. N. andCarvalho M. I.,J. Opt. Soc. Am. B,12 (1995) 1628.

    Article  ADS  Google Scholar 

  28. Segev M., Yariv A., Salamo, G., Shultz J., Crosignani B. andDi Porto P.,Opt Photonics News,4(12) (1993) 8.

    Article  ADS  Google Scholar 

  29. Duree G. C., Morin M., Salamo G. J., Segev M., Crosignani B., Di Porto P., Sharp E. andYariv A.,Phys. Rev. Lett.,74 (1995) 1978.

    Article  ADS  Google Scholar 

  30. Segev M., Salamo G. J., Duree G. C., Morin M., Crosignani B., Di Porto P. andYariv A.,Opt. Photonics News,5(12) (1994) 9.

    Article  ADS  Google Scholar 

  31. Duree G. C., Salamo G. J., Segev M., Yariv A., Crosignani B., Di Porto P. andSharp E.,Opt. Lett.,16 (1994) 1195.

    Article  ADS  Google Scholar 

  32. Segev M., Crosignani B., Di Porto P., Yariv A., Duree G. C., Salamo G. J. andSharp E.,Opt. Lett.,17 (1994) 1296.

    Article  ADS  Google Scholar 

  33. Morin M., Duree G., Salamo G. andSegev M.,Opt. Lett.,20 (1995) 2066.

    Article  ADS  Google Scholar 

  34. Gómez Sarabia C. M., Márquez Aquilar P. A., Sánchez Mondragón J. J., Stepanov S. andVysloukh V.,J. Opt. Soc. Am. B,13 (1996) 2767.

    Article  Google Scholar 

  35. Crosignani B., Segev M., Engin D., Di Porto P., Yariv A. andSalamo G.,J. Opt. Soc. Am. B,10 (1993) 446.

    Article  ADS  Google Scholar 

  36. Christodoulides D. N. andCarvalho M. L.,Opt. Lett.,19 (1994) 1714.

    Article  ADS  Google Scholar 

  37. Fressengeas N., Maufoy J. andKugel G.,Phys. Rev. E,54 (1996) 6866.

    Article  ADS  Google Scholar 

  38. Segev M., Crosignani B., Salamo G., Duree G., Di Porto P. andYariv A.,Photorefractive spatial solitons, inPhotorefractive Effects and Materials, edited byD. Nolte (Kluwer, Boston) 1995, Chapt. 4.

    Google Scholar 

  39. Glass A. M., von der Linde D. andNegran T. J.,Appl. Phys. Lett.,25 (1974) 233.

    Article  ADS  Google Scholar 

  40. Sturman B. I. andFridkin V. M.,The Photovoltaic and Photorefractive Effect in Non-Centrosymmetric Materials (Gordon and Breach, Philadelphia) 1992.

    Google Scholar 

  41. Valley G. C., Segev M., Crosignani B., Yariv A., Fejer M. M. andBashaw M.,Phys. Rev. A 50 (1994) R4457.

    Article  ADS  Google Scholar 

  42. Segev M., Valley G. C., Bashaw M. C., Taya M. andFejer M. M.,J. Opt. Soc. Am. B,14 (1997) 1772.

    Article  ADS  Google Scholar 

  43. Taya M., Bashaw M. C., Fejer M. M., Segev M. andValley G. C.,Phys. Rev. A,52 (1995) 3095.

    Article  ADS  Google Scholar 

  44. Taya M., Bashaw M. C., Fejer M. M., Segev M. andValley G. C.,Opt. Lett.,21 (1996) 943.

    Article  ADS  Google Scholar 

  45. Chen Z., Segev M., Wilson D. W., Muller R. E. andMaker P. D.,Phys. Rev. Lett.,78 (1997) 2948.

    Article  ADS  Google Scholar 

  46. Bian S., Frejlich J. andRinghofer K. H.,Phys. Rev. Lett.,78 (1997) 4035.

    Article  ADS  Google Scholar 

  47. Iturbe-Castillo M. D., Marquez-Aguilar P. A., Sanchez-Mondragon J. J., Stepanov S. andVysloukh V.,Appl. Phys. Lett.,64 (1994) 408.

    Article  ADS  Google Scholar 

  48. Shih M., Segev M., Valley G. C., Salamo G., Crosignani B. andDi Porto P.,Electron. Lett.,31 (1995) 826.

    Article  ADS  Google Scholar 

  49. Shih M., Leach P., Segev M., Garret M. H., Salamo G. andValley G. C.,Opt Lett.,21 (1996) 324.

    Article  ADS  Google Scholar 

  50. Kos K., Meng H., Salamo G., Shih M., Segev M. andValley G. C.,Phys. Rev. E,53 (1996) R4330.

    Article  ADS  Google Scholar 

  51. Mamaev A. V., Saffman M., Anderson D. Z. andZozulya A. A.,Phys. Rev. A,54 (1996) 870. In this paper, it is claimed that both bright and dark photorefractive solitons suffer from transverse instabilities and are unstable. But the experimental results presented in the same paper clearly show “self-trapped channel of light” that donot exhibit transverse instabilities (figs. 5d and 14b). Instability was observed only when further “increasing the nonlinearity” (see discussion on page 874 there). The similarity between the experimental and the numerical results showing the development of the instability in that paper is misleading: the experimental results (figs. 5 and 14) show sequences of output intensity distributions (at a fixed propagation distance) for different levels of applied voltages (i.e. different levels of nonlinearity),only one of which corresponds to that of a soliton (that is on the existence curve), whereas the simulations (figs. 1 and 9) show the near field intensity evolution for different propagation distances for a fixed set of parameters (i.e. at a fixed voltage) that greatlydiffers from that of a soliton.

    Article  ADS  Google Scholar 

  52. Infeld E. andLenkowska-Czerwinska T.,Phys. Rev. E,55 (1997) 6101.

    Article  ADS  Google Scholar 

  53. Zozulya A. A. andAnderson D. Z.,Phys. Rev. A,51 (1995) 1520.

    Article  ADS  Google Scholar 

  54. Zozulya A. A. andAnderson D. Z.,Opt. Lett.,20 (1995) 837.

    Article  ADS  Google Scholar 

  55. Burak D. andNasalski W.,Appl. Opt,33 (1994) 6393.

    Article  ADS  Google Scholar 

  56. Chen Z., Mitchell M., Shih M., Segev M., Garret M. H. andValley G. C.,Opt. Lett.,21 (1996) 629.

    Article  ADS  Google Scholar 

  57. Swartzlander G. A., Andersen D. R., Regan J. J., Yin H. andKaplan A. E.,Phys. Rev. Lett.,66 (1991) 1583.

    Article  ADS  Google Scholar 

  58. Allan G. R., Skinner S. R., Andersen D. R. andSmirl A. L.,Opt. Lett.,16 (1991) 156.

    ADS  Google Scholar 

  59. Iturbe-Castillo M. D., Sanchez-Mondragon J. J., Stepanov S. I., Klein M. B. andWechsler B. A.,Opt. Commun.,118 (1995) 515.

    Article  ADS  Google Scholar 

  60. Chen Z., Mitchell M. andSegev M.,Opt. Lett.,21 (1996) 716.

    Article  ADS  Google Scholar 

  61. Chen Z., Segev M., Singh S. R., Coskun T. andChristodoulides D. N.,J. Opt Soc. Am. B,14 (1997) 1407.

    Article  ADS  Google Scholar 

  62. Mamaev A. V., Saffman M. andZozulya A. A.,Phys. Rev. Lett.,77 (1996) 4544.

    Article  ADS  Google Scholar 

  63. Chen Z., Shih M., Segev, Wilson D. W., Muller R. E. andMaker P. D.,Opt Lett.,22 (1997) 1751.

    Article  ADS  Google Scholar 

  64. Askar’yan G. A.,Sov. Phys. JETP,15 (1962) 1088.

    Google Scholar 

  65. Snyder A. W., Mitchell D. J., Poladian L. andLadouceur F.,Opt. Lett.,16 (1991) 21.

    Article  ADS  Google Scholar 

  66. Snyder A. W., Mitchell D. J. andKivshar Y. S.,Mod. Phys. Lett. B,9 (1995) 1479.

    Article  ADS  Google Scholar 

  67. Mitchell D. J., Snyder A. W. andPoladian L.,Opt. Commun.,41 (1991) 59.

    Google Scholar 

  68. De La Fuente R., Barthelemy A. andFroehly C.,Opt. Lett.,16 (1991) 793.

    Article  ADS  Google Scholar 

  69. Luther-Davies B. andYang X.,Opt Lett.,17 (1992) 496; 1755.

    Article  ADS  Google Scholar 

  70. Bosshard C., Mamyshev P. V. andStegeman G.,Opt. Lett.,19 (1994) 90.

    Article  ADS  Google Scholar 

  71. Swatrzlander G. A. andLaw C. T.,Phys. Rev. Lett.,69 (1992) 2503.

    Article  ADS  Google Scholar 

  72. Shih M., Segev M. andSalamo G.,Opt Lett.,21 (1996) 931.

    Article  ADS  Google Scholar 

  73. Shih M., Chen Z., Mitchell M., Segev M., Lee H., Feigelson R. andWilde J.,J. Opt. Soc. Am. B,14 (1997) 3091.

    Article  ADS  Google Scholar 

  74. Lan S., Shih M. andSegev M.,Opt. Lett.,22 (1997) 1467.

    Article  ADS  Google Scholar 

  75. Zabusky N. J. andKruskal M. D.,Phys. Rev. Lett.,15 (1965) 240.

    Article  ADS  Google Scholar 

  76. Snyder A. W. andSheppard A. P.,Opt. Lett. 18 (1993) 482.

    Article  ADS  Google Scholar 

  77. Polodian L., Snyder A. W. andMitchell D. J.,Opt. Commun.,85 (1991) 59.

    Article  ADS  Google Scholar 

  78. Shih M. andSegev M.,Opt. Lett.,21 (1996) 1538.

    Article  ADS  Google Scholar 

  79. Krolikowski W. andHolmstrom S. A.,Opt. Lett.,22 (1997) 369.

    Article  ADS  Google Scholar 

  80. Shih M., Segev M. andSalamo G.,Phys. Rev. Lett.,78 (1997) 2551.

    Article  ADS  Google Scholar 

  81. Barthelemy A., Maneuf S. andFroehly C.,Opt. Commun.,55 (1985) 201; Reynaud F. and Barthelemy A.,Europhys. Lett.,12 (1990) 401.

    Article  ADS  Google Scholar 

  82. Aitchison J. S., Weiner A. M., Silberberg Y., Oliver M. K., Jackel J. L., Leaird D. E., Vogel E. M. andSmith P. W.,Opt. Lett.,15 (1990) 471;16 (191) 15.

    Article  ADS  Google Scholar 

  83. Gatz S. andHerrmann J.,IEEE J. Quant. Electron,28 (1992) 1732.

    Article  ADS  Google Scholar 

  84. Snyder A. W. andSheppard A. P.,Opt. Lett.,18 (1993) 482.

    Article  ADS  Google Scholar 

  85. Shih M., Chen Z., Segev M., Coskun T. andChristodoulides D. N.,Appl. Phys. Lett.,69 (1996) 4151.

    Article  ADS  Google Scholar 

  86. Meng H., Salamo G., Shih M. andSegev M.,Opt. Lett.,22 (1997) 448.

    Article  ADS  Google Scholar 

  87. Garcia-Quirino G. S., Iturbe-Castillo M. D., Vysloukh V., Sanchez-Mondragon J. J., Stepanov S. L., Lugo-Martinez G. andTorres-Cisneros G. E.,Opt. Lett.,22 (1997) 154.

    Article  ADS  Google Scholar 

  88. Tikhonenko V., Christou J. andLuther-Davies B.,Phys. Rev. Lett.,76 (1996) 2698.

    Article  ADS  Google Scholar 

  89. Shih M., Segev M., Salamo G. andKivshar Y.,Opt. Photonics News,8(12) (1997) 43.

    Article  ADS  Google Scholar 

  90. Mitchell M., Chen Z., Shih M. andSegev M.,Phys. Rev. Lett.,77 (1996) 490.

    Article  ADS  Google Scholar 

  91. Mitchell M. andSegev M.,Nature,387 (1997) 880; See also commentary on this article in theNews and Views section of the same issue:Boardman A.,Nature,387 (1997) 854.

    Article  ADS  Google Scholar 

  92. Christodoulides D. N., Coskun T. H., Mitchell M. andSegev M.,Phys. Rev. Lett.,78 (1997) 646.

    Article  ADS  Google Scholar 

  93. Mitchell M., Segev M., Coskun T. andChristodoulides D. N.,Phys. Rev. Lett.,79 (1997) 4990.

    Article  ADS  Google Scholar 

  94. Chauvet M., Hawkins S. A., Salamo G. J., Segev M., Bliss D. F. andBryant G.,Opt. Lett.,21 (1996) 1333.

    Article  ADS  Google Scholar 

  95. Chauvet M., Hawkins S. A., Salamo G. J., Segev M., Bliss D. F. andBryant G.,Appl. Phys. Lett.,70 (1996) 2499.

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Fisica, Università dell’Aquila, 67010, L’Aquila, Italy

    B. Crosignani & P. Di Porto

  2. Istituto Nazionale di Fisica della Materia, Unità di Roma 1, Roma, Italy

    B. Crosignani & P. Di Porto

  3. Electrical Engineering Department, Princeton University, 08544, Princeton, NJ, USA

    M. Segev

  4. Physics Department, University of Arkansas, 72701, Fayetteville, AR, USA

    G. Salamo

  5. Applied Physics Department, California Institute of Technology, 91125, Pasadena, CA, USA

    A. Yariv

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  1. B. Crosignani
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Crosignani, B., Di Porto, P., Segev, M. et al. Nonlinear optical beam propagation and solitons in photorefractive media. Riv. Nuovo Cim. 21, 1–37 (1998). https://doi.org/10.1007/BF02874290

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