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Introduction to Nonlinear Optics in Photorefractive Media

  • Giuseppe Di DomenicoEmail author
Chapter
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Part of the Springer Theses book series (Springer Theses)

Abstract

In this chapter nonlinear optical beams are introduced and specialized to spatial solitons in photorefractive media. In particular, we present the electro-optic effect, ferroelectricity, relaxor ferroelectrics, the mechanism of photorefraction, and the physics underlying photorefractive solitons.

References

  1. 1.
    Brosi JM, Koos C, Andreani LC, Waldow M, Leuthold J, Freude W (2008) High-speed low-voltage electro-optic modulator with a polymer-infiltrated silicon photonic crystal waveguide. Opt Express 16(6):4177–4191ADSCrossRefGoogle Scholar
  2. 2.
    Ouskova E, Sio LD, Vergara R, White TJ, Tabiryan N, Bunning TJ (2014) Ultra-fast solid state electro-optical modulator based on liquid crystal polymer and liquid crystal composites. Appl Phys Lett 105(23):231122ADSCrossRefGoogle Scholar
  3. 3.
    Qianfan X, Schmidt B, Pradhan S, Lipson M (2005) Micrometre-scale silicon electro-optic modulator. Nature 435(7040):325–327ADSCrossRefGoogle Scholar
  4. 4.
    Roth M, Tseitlin M, Angert N (2005) Oxide crystals for electro-optic Q-switching of lasers. Glass Phys. Chem. 31:86–95CrossRefGoogle Scholar
  5. 5.
    Malinowski A, Vu KT, Chen KK, Nilsson J, Jeong Y, Alam S, Lin D, Richardson DJ (2009) High power pulsed fiber MOPA system incorporating electro-optic modulator based adaptive pulse shaping. Opt Express 17(23):20927–20937ADSCrossRefGoogle Scholar
  6. 6.
    Goetz PG, Rabinovich WS, Mahon R, Murphy JL, Ferraro MS, Suite MR, Smith WR, Burris HR, Moore CI, Schultz WW et al (2012) Modulating retro-reflector lasercom systems for small unmanned vehicles. IEEE J Sel Areas Commun 30(5):986–992CrossRefGoogle Scholar
  7. 7.
    Guarino A, Poberaj G, Rezzonico D, Degl’Innocenti R, Günter P (2007) Electro-optically tunable microring resonators in lithium niobate. Nat Photonics 1(7):407–410ADSCrossRefGoogle Scholar
  8. 8.
    Wang M, Yingxin X, Fang Z, Liao Y, Wang P, Chu W, Qiao L, Lin J, Fang W, Cheng Y (2017) On-chip electro-optic tuning of a lithium niobate microresonator with integrated in-plane microelectrodes. Opt Express 25(1):124–129ADSCrossRefGoogle Scholar
  9. 9.
    Goodby JW, Collings PJ, Kato T, Tschierske C, Gleeson HF, Raynes P (2014) Handbook of liquid crystals. Wiley-VCH, WeinheimCrossRefGoogle Scholar
  10. 10.
    Ashkin A, Boyd GD, Dziedzic JM, Smith RG, Ballman AA, Levinstein JJ, Nassau K (1966) Optically-induced refractive index inhomogeneities in LiNbO\(_3\) and LiTaO\(_3\). Appl Phys Lett 9(1):72–74Google Scholar
  11. 11.
    Cavalieri AL, Fritz DM, Lee SH, Bucksbaum PH, Reis DA, Rudati J, Mills DM, Fuoss PH, Stephenson GB, Kao CC et al (2005) Clocking femtosecond X rays. Phys Rev Lett 94(11):114801ADSCrossRefGoogle Scholar
  12. 12.
    Yariv A, Yeh P (1984) Optical waves in crystals, vol 10. Wiley, New YorkGoogle Scholar
  13. 13.
    Born M, Wolf E (1980) Principles of optics: electromagnetic theory of propagation, interference and diffraction of light. Elsevier, AmsterdamzbMATHGoogle Scholar
  14. 14.
    Aillerie M, Theofanous N, Fontana MD (2000) Measurement of the electro-optic coefficients: description and comparison of the experimental techniques. Appl Phys B 70(3):317–334ADSCrossRefGoogle Scholar
  15. 15.
    Park S-E, Shrout TR (1997a) Characteristics of relaxor-based piezoelectric single crystals for ultrasonic transducers. IEEE Trans Ultrason Ferroelectr Freq Control 44(5):1140–1147Google Scholar
  16. 16.
    Shrout TR, Park SE, Lopath PD, Meyer RJ, Ritter TA, Shung KK (1998) Innovations in piezoelectric materials for ultrasound transducers. In: Medical imaging 1998: ultrasonic transducer engineering, vol 3341. SPIE-International Society for Optical Engineering, pp 174–184Google Scholar
  17. 17.
    Uchino K (1996) Piezoelectric actuators and ultrasonic motors, vol 1. Springer Science & Business Media, BerlinCrossRefGoogle Scholar
  18. 18.
    Dong WD, Finkel P, Amin A, Lynch CS (2012) Giant electro-mechanical energy conversion in [011] cut ferroelectric single crystals. Appl Phys Lett 100(4):042903ADSCrossRefGoogle Scholar
  19. 19.
    Booth ER, Wilbur ML (2004) Acoustic aspects of active-twist rotor control. J Am Helicopter Soc 1(49):3–10CrossRefGoogle Scholar
  20. 20.
    Bokov AA, Ye Z-G (2006) Recent progress in relaxor ferroelectrics with perovskite structure. Frontiers of ferroelectricity. Springer, Berlin, pp 31–52Google Scholar
  21. 21.
    Shvartsman VV, Lupascu DC (2012) Lead-free relaxor ferroelectrics. J Am Ceram Soc 95(1):1–26CrossRefGoogle Scholar
  22. 22.
    Ahart M, Somayazulu M, Cohen RE, Ganesh P, Dera P, Mao H-K, Hemley RJ, Ren Y, Liermann P, Wu Z (2008) Origin of morphotropic phase boundaries in ferroelectrics. Nature 451(7178):545–548ADSCrossRefGoogle Scholar
  23. 23.
    Lummen TTA, Gu Y, Wang J, Lei S, Xue F, Kumar A, Barnes AT, Barnes E, Denev S, Belianinov A et al (2014) Thermotropic phase boundaries in classic ferroelectrics. Nat Commun 5:3172Google Scholar
  24. 24.
    Borisevich AY, Eliseev EA, Morozovska AN, Cheng C-J, Lin J-Y, Chu Y-H, Kan D, Takeuchi I, Nagarajan V, Kalinin SV (2012) Atomic-scale evolution of modulated phases at the ferroelectric–antiferroelectric morphotropic phase boundary controlled by flexoelectric interaction. Nat Commun 3:775ADSCrossRefGoogle Scholar
  25. 25.
    Kutnjak Z, Petzelt J, Blinc R (2006) The giant electromechanical response in ferroelectric relaxors as a critical phenomenon. Nature 441(7096):956–959ADSCrossRefGoogle Scholar
  26. 26.
    Tian H, Meng X, Hu C, Tan P, Cao X, Shi G, Zhou Z, Zhang R (2016) Origin of giant piezoelectric effect in lead-free K\(_{1-x}\)Na\(_x\)Ta\(_{1-y}\)Nb\(_y\)O\(_3\) single crystals. Sci Rep 6Google Scholar
  27. 27.
    Park S-E, Shrout TR (1997b) Ultrahigh strain and piezoelectric behavior in relaxor based ferroelectric single crystals. J Appl Phys 82(4):1804–1811ADSCrossRefGoogle Scholar
  28. 28.
    Samara GA (2003) The relaxational properties of compositionally disordered ABO\(_3\) perovskites. J Phys Condens Matter 15(9):R367Google Scholar
  29. 29.
    Lang SB, Chan HLW (2007) Frontiers of ferroelectricity: a special issue of the journal of materials science. Springer Science & Business Media, BerlinGoogle Scholar
  30. 30.
    Glinchuk MD, Eliseev EA, Morozovska AN (2008) Superparaelectric phase in the ensemble of noninteracting ferroelectric nanoparticles. Phys Rev B 78(13):134107ADSCrossRefGoogle Scholar
  31. 31.
    Rivera I, Kumar A, Ortega N, Katiyar RS, Lushnikov S (2009) Divide line between relaxor, diffused ferroelectric, ferroelectric and dielectric. Solid State Commun 149(3):172–176ADSCrossRefGoogle Scholar
  32. 32.
    Toulouse J, DiAntonio P, Vugmeister BE, Wang XM, Knauss LA (1992) Precursor effects and ferroelectric macroregions in KTa\(_{1--x}\)Nb\(_x\)O\(_3\) and K\(_{1- y}\)Li\(_y\)TaO\(_3\). Phys Rev Lett 68(2):232Google Scholar
  33. 33.
    Xu G, Zhong Z, Bing Y, Ye ZG, Shirane G (2006) Electric-field-induced redistribution of polar nano-regions in a relaxor ferroelectric. Nat Mater 5(2):134–140ADSCrossRefGoogle Scholar
  34. 34.
    Xu G, Wen J, Stock C, Gehring PM (2008) Phase instability induced by polar nanoregions in a relaxor ferroelectric system. Nat Mater 7(7):562–566ADSCrossRefGoogle Scholar
  35. 35.
    Akbarzadeh AR, Prosandeev S, Walter EJ, Al-Barakaty A, Bellaiche L (2012) Finite-temperature properties of Ba (Zr, Ti) O\(_3\) relaxors from first principles. Phys Rev Lett 108(25):257601Google Scholar
  36. 36.
    Kleemann W (2014) Relaxor ferroelectrics: cluster glass ground state via random fields and random bonds. Phys Status Solidi B 251(10):1993–2002ADSCrossRefGoogle Scholar
  37. 37.
    Manley ME, Lynn JW, Abernathy DL, Specht ED, Delaire O, Bishop AR, Sahul R, Budai JD (2014) Phonon localization drives polar nanoregions in a relaxor ferroelectric. Nat Commun 5:3683ADSCrossRefGoogle Scholar
  38. 38.
    Phelan D, Stock C, Rodriguez-Rivera JA, Chi S, Leão J, Long X, Xie Y, Bokov AA, Ye ZG, Ganesh P et al (2014) Role of random electric fields in relaxors. Proc Natl Acad Sci 111(5):1754–1759ADSCrossRefGoogle Scholar
  39. 39.
    Pirc R, Kutnjak Z (2014) Electric-field dependent freezing in relaxor ferroelectrics. Phys Rev B 89(18):184110ADSCrossRefGoogle Scholar
  40. 40.
    Pirc R, Blinc R (1999) Spherical random-bond-random-field model of relaxor ferroelectrics. Phys Rev B 60(19):13470ADSCrossRefGoogle Scholar
  41. 41.
    Bokov AA, Ye Z-G (2012) Dielectric relaxation in relaxor ferroelectrics. J Adv Dielectr 2(02):1241010CrossRefGoogle Scholar
  42. 42.
    Ishai PB, De Oliveira CEM, Ryabov Y, Feldman Y, Agranat AJ (2004) Glass-forming liquid kinetics manifested in a KTN: Cu crystal. Phys Rev B 70(13):132104ADSCrossRefGoogle Scholar
  43. 43.
    Ishai PB, Agranat AJ, Feldman Y (2006) Confinement kinetics in a KTN: Cu crystal: experiment and theory. Phys Rev B 73(10):104104ADSCrossRefGoogle Scholar
  44. 44.
    Viehland D, Jang SJ, Cross LE, Wuttig M (1990) Freezing of the polarization fluctuations in lead magnesium niobate relaxors. J Appl Phys 68(6):2916–2921ADSCrossRefGoogle Scholar
  45. 45.
    Wang S, Yi M, Bai-Xiang X (2016) A phase-field model of relaxor ferroelectrics based on random field theory. Int J Solids Struct 83:142–153CrossRefGoogle Scholar
  46. 46.
    Pirc R, Blinc R (2007) Vogel-fulcher freezing in relaxor ferroelectrics. Phys Rev B 76(2):020101ADSCrossRefGoogle Scholar
  47. 47.
    Prosandeev S, Wang D, Akbarzadeh AR, Dkhil B, Bellaiche L (2013) Field-induced percolation of polar nanoregions in relaxor ferroelectrics. Phys Rev Lett 110(20):207601Google Scholar
  48. 48.
    Pugachev AM, Kovalevskii VI, Surovtsev NV, Kojima S, Prosandeev SA, Raevski IP, Raevskaya SI (2012) Broken local symmetry in paraelectric batio 3 proved by second harmonic generation. Phys Rev Lett 108(24):247601ADSCrossRefGoogle Scholar
  49. 49.
    Yokota H, Uesu Y, Malibert C, Kiat J-M (2007) Second-harmonic generation and x-ray diffraction studies of the pretransitional region and polar phase in relaxor K\(_{(1--x)}\)Li\(_x\)TaO\(_3\). Phys Rev B 75(18):184113Google Scholar
  50. 50.
    Chang Y-C, Wang C, Yin S, Hoffman RC, Mott AG (2013a) Giant electro-optic effect in nanodisordered KTN crystals. Opt Lett 38(22):4574–4577ADSCrossRefGoogle Scholar
  51. 51.
    Chang Y-C, Wang C, Yin S, Hoffman RC, Mott AG (2013b) Kovacs effect enhanced broadband large field of view electro-optic modulators in nanodisordered KTN crystals. Opt Express 21(15):17760–17768ADSCrossRefGoogle Scholar
  52. 52.
    Gumennik A, Kurzweil-Segev Y, Agranat AJ (2011) Electrooptical effects in glass forming liquids of dipolar nano-clusters embedded in a paraelectric environment. Opt Mater Express 1(3):332–343ADSCrossRefGoogle Scholar
  53. 53.
    Yeh P (1993) Introduction to photorefractive nonlinear optics, vol 14. Wiley-Interscience, HobokenGoogle Scholar
  54. 54.
    Boyd RW (2003) Nonlinear optics. Handbook of laser technology and applications (three-volume set). Taylor & Francis, Abingdon, pp 161–183Google Scholar
  55. 55.
    Kukhtarev NV, Markov VB, Odulov SG, Soskin MS, Vinetskii VL (1978) Holographic storage in electrooptic crystals. I. steady state. Ferroelectrics 22(1):949–960CrossRefGoogle Scholar
  56. 56.
    Crosignani B, Di Porto P, Degasperis A, Segev M, Trillo S (1997) Three-dimensional optical beam propagation and solitons in photorefractive crystals. JOSA B 14(11):3078–3090ADSCrossRefGoogle Scholar
  57. 57.
    DelRe E, Ciattoni A, Crosignani B, Tamburrini M (1998a) Approach to space-charge field description in photorefractive crystals. JOSA B 15(5):1469–1475ADSCrossRefGoogle Scholar
  58. 58.
    DelRe E, Crosignani B, Di Porto P (2009) Photorefractive solitons and their underlying nonlocal physics. Prog Opt 53:153–200ADSCrossRefGoogle Scholar
  59. 59.
    DelRe E, D’Ercole A, Palange E (2005) Mechanisms supporting long propagation regimes of photorefractive solitons. Phys Rev E 71(3):036610ADSCrossRefGoogle Scholar
  60. 60.
    Agrawal GP (2007) Nonlinear fiber optics. Academic Press, CambridgezbMATHGoogle Scholar
  61. 61.
    Segev M, Valley GC, Crosignani B, Diporto P, Yariv A (1994) Steady-state spatial screening solitons in photorefractive materials with external applied field. Phys Rev Lett 73(24):3211ADSCrossRefGoogle Scholar
  62. 62.
    Duree GC Jr, Shultz JL, Salamo GJ, Segev M, Yariv A, Crosignani B, Di Porto D, Sharp EJ, Neurgaonkar RR (1993) Observation of self-trapping of an optical beam due to the photorefractive effect. Phys Rev Lett 71(4):533ADSCrossRefGoogle Scholar
  63. 63.
    Segev M, Agranat AJ (1997) Spatial solitons in centrosymmetric photorefractive media. Opt Lett 22(17):1299–1301ADSCrossRefGoogle Scholar
  64. 64.
    Chen Z, Garrett MH, Valley GC, Mitchell M, Shih M-F, Segev M (1996) Steady-state dark photorefractive screening solitons. Opt Lett 21(9):629–631ADSCrossRefGoogle Scholar
  65. 65.
    Wan W, Jia S, Fleischer JW (2007) Dispersive superfluid-like shock waves in nonlinear optics. Nat Phys 3(1):46–51CrossRefGoogle Scholar
  66. 66.
    DelRe E, D’Ercole A, Agranat AJ (2003) Emergence of linear wave segments and predictable traits in saturated nonlinear media. Opt Lett 28(4):260–262ADSCrossRefGoogle Scholar
  67. 67.
    DelRe E, Crosignani B, Tamburrini M, Segev M, Mitchell M, Refaeli E, Agranat AJ (1998b). One-dimensional steady-state photorefractive spatial solitons in centrosymmetric paraelectric potassium lithium tantalate niobate. Opt Lett 23(6):421–423ADSCrossRefGoogle Scholar
  68. 68.
    Fressengeas N, Wolfersberger D, Maufoy J, Kugel G (1998) Build up mechanisms of (1+ 1)-dimensional photorefractive bright spatial quasi-steady-state and screening solitons. Opt Commun 145(1):393–400ADSCrossRefGoogle Scholar
  69. 69.
    Zozulya AA, Anderson DZ (1995) Nonstationary self-focusing in photorefractive media. Opt Lett 20(8):837–839ADSCrossRefGoogle Scholar
  70. 70.
    Dari-Salisburgo C, DelRe E, Palange E (2003) Molding and stretched evolution of optical solitons in cumulative nonlinearities. Phys Rev Lett 91(26):263903ADSCrossRefGoogle Scholar
  71. 71.
    DelRe E, Palange E (2006) Optical nonlinearity and existence conditions for quasi-steady-state photorefractive solitons. JOSA B 23(11):2323–2327ADSCrossRefGoogle Scholar
  72. 72.
    Christodoulides DN, Coskun TH, Mitchell M, Segev M (1997) Theory of incoherent self-focusing in biased photorefractive media. Phys Rev Lett 78(4):646ADSCrossRefGoogle Scholar
  73. 73.
    Mitchell M, Segev M, Coskun TH, Christodoulides DN (1997) Theory of self-trapped spatially incoherent light beams. Phys Rev Lett 79(25):4990ADSCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.School of Electrical EngineeringTel Aviv UniversityTel AvivIsrael

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