Plane and Guided Wave Effects and Devices Via Quadratic Cascading

  • Gaetano Assanto
  • Katia Gallo
  • Claudio Conti
Part of the NATO Science Series book series (ASHT, volume 61)

Abstract

Quadratic cascading, i. e. the sequence of two second-order nonlinear processes, has assumed an important role in recent years as one of the possibilities for a low power, lossless, ultrafast approach to all-optical processing of signals. [1, 2, 3, 4, 5] The foundation of quadratic cascading is as old as quadratic nonlinear optics itself, but its implications were brought up later on in several theoretical [6, 7, 8, 9, 10, 11, 12, 13, 14, 15] and experimental [16, 17, 18, 19, 20, 21, 22] reports outlining phase effects intrinsic to parametric interactions. More recently, however, it was the second-harmonic generation (SHG) experiment performed by DeSalvo et al. [1] in Potassium Tytanil Phosphate (KTP) the one which triggered a considerable effort in investigating both applications and novel effects of cascading, from switching to modulation, and from solitary waves to gap solitons [3, 4, 5, 23]. It is remarkable the number of papers published on the subject in the past five years, and the rapid progress in a field which is benefitting both from the established knowledge and understanding of cubic nonlinearities and phenomena, and from the advancements of material sciences and technology in the area of noncentrosymmetric crystals for electro-optical and parametric interactions.

Keywords

Fundamental Frequency Lithium Niobate Periodically Pole Lithium Niobate Nonlinear Phase Shift Lithium Niobate Waveguide 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    DeSalvo, R., Hagan, D.J., Sheik-Bahae, M., Stegeman, G., Van Stryland, E.W. and Vanherzeele, H. (1992) Self-focusing and self-defocusing by cascaded second-order effects in KTP, Opt. Lett. 17, 28–30.CrossRefADSGoogle Scholar
  2. 2.
    Stegeman, G.I., Sheik-Bahae, M., VanStryland, E. W. and Assanto, G. (1993) Large nonlinear phase shifts in second-order nonlinear optical processes, Opt. Lett. 18, 13–15.CrossRefADSGoogle Scholar
  3. 3.
    Assanto, G., Stegeman, G.I., Sheik-Bahae, M. and Van Stryland, E. W. (1995) Coherent interactions for all-optical signal processing via quadratic nonlinearities, IEEE J. Quantum Electron. 31, 673–681.CrossRefADSGoogle Scholar
  4. 4.
    Stegeman, G.I., Schiek, R., Tomer, L., Torruellas, W.E., Baek, Y., Baboiu, D., Wang, Z., Van Stryland, E.W., Hagan, D.J. and Assanto, G. (1997) Cascading: a promising approach to nonlinear optical phenomena, in I.C. Khoo, F. Simoni and C. Umeton (eds.), Novel Optical Materials and Applications, John Wiley & Sons, Interscience Div., New York, Ch.2.Google Scholar
  5. 5.
    Stegeman, G.I., Hagan, D.J. and Torner, L., (1996) χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons, J. Opt. & Quantum Electron. 28, 1691–1740.CrossRefGoogle Scholar
  6. 6.
    Ostrovskii, L.A., (1967) Self-action of light in crystals, JETP Lett. 5, 272–275; (1967) ZhETF Pis’ma 5, 331-334.ADSGoogle Scholar
  7. 7.
    Gustafson, T.K., Taran, J.-P.E., Kelley, P.L. and Chiao, R.Y. (1970) Self-modulation of picosecond pulses in electro-optic crystals. Opt. Commun. 2, 17–21.CrossRefADSGoogle Scholar
  8. 8.
    Thomas, J.-M.R. and Taran, J.-P.E. (1972) Pulse distortion in mismatched second harmonic generation, Opt. Commun. 4, 329–334.CrossRefADSGoogle Scholar
  9. 9.
    Klyshko, D.N. and Polkovnikov, B.F., (1974) Phase modulation and self-modulation of light in three-photon processes, Sov. J. Quant. Electron. 3, 324–326.CrossRefADSGoogle Scholar
  10. 10.
    Eckardt, R.C. and Reintjes J. (1984) Phase matching limitations of high efficiency second harmonic generation, IEEE J. Quant. Electron. 20, 1178–1187.CrossRefADSGoogle Scholar
  11. 11.
    Manassah, J.T. (1987) Amplitude and phase of a pulsed second harmonic signal, J. Opt. Soc. Am. B 4, 1235–1240.CrossRefADSGoogle Scholar
  12. 12.
    Bakker, H.J., Planken, P.C.M.,, Kuipers, L. and Lagendijk, A. (1990) Phase modulation in second order nonlinear processes, Phys. Rev. A 42, 4085–4101.CrossRefADSGoogle Scholar
  13. 13.
    Andrews, J.H., Kowalski, K.L. and Singer, K.D. (1992) Pair correlations, cascading, and local-field effects in nonlinear optical susceptibilities, Phys. Rev. A 46, 4172–4184.CrossRefADSGoogle Scholar
  14. 14.
    Pliszka, P. and Banerjee, P.P. (1993) Self-phase modulation in quadratically nonlinear crystals, J. Mod. Opt. 40, 1909–1916.CrossRefADSGoogle Scholar
  15. 15.
    Kalocsai, A.G. and Haus, J.W. (1993) Self-modulation effects in quadratically nonlinear materials, Opt. Commun. 97, 239–244.CrossRefADSGoogle Scholar
  16. 16.
    De Martini, F. (1967); Coherent Raman amplification, II Nuovo Cimento 51 B, 16–41; Coffinet, J.P. and De Martini, F. (1969) Coherent excitation of polaritons in gallium phosphide, Phys. Rev. Lett. 22, 60-64.ADSGoogle Scholar
  17. 17.
    Yablonovitch, E., Flytzanis, C. and Bloembergen, N. (1972) Anisotropic interference of three-wave and double two-wave frequency mixing in GaAs, Phys. Rev. Lett. 29, 865–868.CrossRefADSGoogle Scholar
  18. 18.
    Akhmanov, S.A., Dubovik, A.N., Saltiel, S.M., Tomov, I.V. and Tunkin, V.G. (1974) Nonlinear optical effects of fourth order in the field in a lithium formiate crystal, JETP Lett. 20, 117–118.ADSGoogle Scholar
  19. 19.
    Meredith, G.R. (1981) Cascading in optical third-harmonic generation by crystalline quartz, Phys. Rev. B 24, 5522–5532; (1982) Second-order cascading in third-order nonlinear optical processes, J. Chem. Phys. 77, 5863-5871.CrossRefADSGoogle Scholar
  20. 20.
    Qiu, P., and Penzkofer, A. (1988) Picosecond third-harmonic light generation in ß-BaB2O4, Appl. Phys. B 45, 225–236.CrossRefADSGoogle Scholar
  21. 21.
    Belashenkov, N.R., Gagarskii, S.V., and Inochkin, M.V. (1989) Nonlinear refraction of light on second-harmonic generation, Opt. Spectrosc. 66, 806–808.ADSGoogle Scholar
  22. 22.
    Zgonik, M. and Gunter, P. (1992) Second and third-order optical nonlinearities in ABO3 compounds measured in fast four-wave mixing experiments, Ferroelectrics 126, 33–38.CrossRefGoogle Scholar
  23. 24.
    Hutchings, D.C., Aitchison, J.S. and Ironside, C.N. (1993) All-optical switching based on nondegenerate phase shifts from a cascaded second-order nonlinearity, Opt. Lett. 18, 10–12.CrossRefGoogle Scholar
  24. 25.
    Bosshard, Ch., Spreiter, R., Zgonik, M. and Günter, P. (1995) Kerr nonlinearity via cascaded optical rectification and the linear electro-optic effect, Phys. Rev. Lett. 74, 2816–2819.CrossRefADSGoogle Scholar
  25. 26.
    Danielius, R., Di Trapani, P., Dubietis, A., Piskarskas, A., Podenas, D. and Banfi, G.P. (1993) Self-diffraction through cascaded second-order frequency-mixing effects in ß-barium borate, Opt. Lett. 18, 574–576.CrossRefADSGoogle Scholar
  26. 27.
    Ou, Z.Y. (1995) Observation of nonlinear phase shift in CW harmonic generation, Opt. Commun. 124, 430–437.CrossRefGoogle Scholar
  27. 28.
    Fazio, E., Sibilia, C., Senesi, F. and Bertolotti, M. (1996) All-optical switching during quasi-collinear second-harmonic generation, Opt. Commun. 127, 62–68.CrossRefADSGoogle Scholar
  28. 29.
    Wang, Z., Hagan, D.J., Van Stryland, E.W., Zyss, J., Vidakovic, P. and Torruellas, W.E. (1997) Cascaded second-order effects in N-(4-nitrophenyl)-L-prolinol, in a molecular single crystal, J. Opt. Soc. Am. B 14, 76–86.CrossRefADSGoogle Scholar
  29. 30.
    Vidakovic, P., Lovering, D.J., Levenson,(2) I.A., Webjorn, J. and Russell, P.St.J. (1997) Large nonlinear phase shift owing to cascaded χ(2) in quasi-phase-matched bulk LiNbO3, Opt. Lett. 22, 277–279.CrossRefGoogle Scholar
  30. 31.
    Khurgin, J.B. and Ding, Y.J. (1994) Resonant cascaded surface-emitting second-harmonic generation: a strong third-order nonlinear process, Opt. Lett. 19, 1016–1018.CrossRefADSGoogle Scholar
  31. 32.
    Khurgin, J.B., Obeidat, A., Lee, S.J. and Ding, Y.J. (1997) Cascaded optical nonlinearities: Microscopic understanding as a collective effect, J. Opt. Soc. Am. B 14, 1977–1983.CrossRefADSGoogle Scholar
  32. 33.
    Russell, P.St.J. (1993) All-optical high gain transistor action using second-order nonlinearities, Electron. Lett. 29, 1228–1229.CrossRefADSGoogle Scholar
  33. 34.
    Hagan, D.J., Sheik-Bahae, M., Wang, Z., Stegeman, G.I., Van Stryland, E.W. and Assanto, G. (1994) Phase controlled transistor action by cascading of second-order nonlinearities, Opt. Lett. 19, 1305–1307.CrossRefADSGoogle Scholar
  34. 35.
    Belostotsky, A.L., Leonov, A.S. and Meleshko, A.V. (1994) Nonlinear phase change in type II second-harmonic generation under exact phase-matched conditions, Opt. Lett. 19, 856–858.CrossRefADSGoogle Scholar
  35. 36.
    Nitti, S., Tan, H.M., Banfi, G.P. and Degiorgio, V. (1994) Induced ‘third-order’ nonlinearity via cascaded second-order effects in organic crystals of MBA-NP, Opt. Cammun. 106, 263–268.CrossRefADSGoogle Scholar
  36. 37.
    Asobe, M., Yokohama, I., Itoh, H. and Kaino, T. (1997) All-optical switching by use of cascading of phase-matched sum-frequency-generation and difference-frequency-generation processes in periodically poled LiNbO3, Opt. Lett. 22, 274–276.CrossRefADSGoogle Scholar
  37. 38.
    Assanto, G. and Torelli, I. (1995) Cascading effects in type II second-harmonic generation: applications to all-optical processing, Opt. Commun. 119, 143–148.CrossRefADSGoogle Scholar
  38. 39.
    Kobyakov, A., Peschel, U., Muschall, R., Assanto, G., Torchigin, V.P., and Lederer, F. (1995) An analytical approach to all-optical modulation by cascading, Opt. Lett. 20, 1686–1688.CrossRefADSGoogle Scholar
  39. 40.
    Kobyakov, A., Peschel, U. and Lederer, F. (1996) Vectorial interaction in cascaded quadratic nonlinearities-an analytical approach, Opt. Commun. 124, 184–194.CrossRefADSGoogle Scholar
  40. 41.
    Kobyakov, A. and Lederer, F. (1996) Cascading of quadratic nonlinearities: an analytical study, Phys. Rev.A 54, 3455–3471.CrossRefADSGoogle Scholar
  41. 42.
    Lefort, L. and Barthelemy, A. (1995) All-optical transistor action by polarisation rotation during type-? phase-matched second-harmonic generation, Electron. Lett. 31, 910–911.CrossRefGoogle Scholar
  42. 43.
    Assanto, G., Wang, Z., Hagan, D.J. and Van Stryland, E.W. (1995) All-optical modulation via nonlinear cascading in type II second harmonic generation, Appl. Phys. Lett. 67, 2120–2122.CrossRefADSGoogle Scholar
  43. 44.
    Lefort, L. and Barthelemy, A. (1995) Intensity-dependent polarization rotation associated with type-II phase-matched second-harmonic generation: application to self-induced transparency, Opt. Lett. 20, 1749–1751.CrossRefADSGoogle Scholar
  44. 45.
    Buchvarov, I., Saltiel, S., Iglev, Ch. and Koynov, K. (1997) Intensity dependent change of the polarization state as a result of non-linear phase shift in type II frequency doubling crystals, Opt. Commun. 141, 173–178.CrossRefADSGoogle Scholar
  45. 46.
    Wang, Z., Hagan, D.J., VanStryland, E.W. and Assanto, G. (1996) Phase-insensitive, single wavelength, all-optical transistor based on second-order nonlinearities, Electron. Lett. 32, 1135–1136.CrossRefGoogle Scholar
  46. 47.
    Assanto, G., Hagan, D.J., Stegeman, G.I., Van Stryland, E.W. and Torruellas, W. E. (1996) Vectorial quadratic interactions for all-optical signal processing via second-harmonic generation, Optica Applicata XXVI, 285–291.Google Scholar
  47. 48.
    Wang, Z., Hagan, D.J., Van Stryland, E.W. and Assanto, G. (1996) A phase-insensitive all-optical transistor using second-order nonlinear media, in Int. Quantum Electronics Conf., 1996 OSA 1996, Tech. Dig. Series, Washington D.C., 264–265.Google Scholar
  48. 50.
    Assanto, G. (1995) All-optical switching in integrated structures, in: Nonlinear Optical Materials: Principles and Applications, V. DeGiorgio and C. Flytzanis ed., IOS Press, Amsterdam.Google Scholar
  49. 51.
    Sundheimer, M.L., Bosshard, Ch., Van Stryland, E.W., Stegeman, G.I. and Bierlein, J.D. (1993) Large nonlinear phase modulation in quasi-phase-matched KTP waveguides as a result of cascaded second-order processes, Opt. Lett. 18, 1397–1399.CrossRefADSGoogle Scholar
  50. 52.
    Sundheimer, M.L., Villeneuve, A., Stegeman, G.I. and Bierlein, J.D. (1994) Cascading nonlinearities in KTP waveguides at communications wavelengths, Electron. Lett. 30, 1400–1401.CrossRefGoogle Scholar
  51. 53.
    Schiek, R., Sundheimer, M.L., Kim, D.Y., Baek, Y., Stegeman, G.I., Seibert, H. and Sohler, W. (1994) Direct measurement of cascaded nonlinearity in lithium niobate channel waveguides, Opt. Lett. 19, 1949–1951.CrossRefADSGoogle Scholar
  52. 54.
    Baek, Y., Schiek, R. and Stegeman, G.I. (1995) All-optical switching in a hybrid Mach-Zehnder interferometer as a result of cascaded second-order nonlinearity, Opt. Lett. 20, 2168–2171.CrossRefADSGoogle Scholar
  53. 55.
    Baek, Y., Schiek, R., Krijnen, G., Stegeman, G.I., Baumann, I. and Sohler, W. (1996) All-optical integrated Mach-Zehnder switching in lithium niobate waveguides due to cascaded nonlinearities, Appl. Phys. Lett. 68, 2055–2057.CrossRefADSGoogle Scholar
  54. 56.
    Schiek, R., Baek, Y., Krijnen, G., Stegeman, G.I., Baumann, I. and Sohler W. (1997) All-optical switching in lithium niobate directional couplers with cascaded nonlinearity, Opt. Lett. 21, 940–942.CrossRefADSGoogle Scholar
  55. 57.
    Treviño-Palacios, C.G., Stegeman, G.I., De Micheli, M.P., Baldi, P., Nouh, S., Ostrowsky, D.B., Delacourt, D. and Papuchon, M. (1995) Intensity dependent mode competition in second harmonic generation in multimode waveguides, Appl. Phys. Lett. 67, 170–172.CrossRefADSGoogle Scholar
  56. 58.
    Treviño-Palacios, C.G., Stegeman, G.I. and Baldi, P. (1996) Spatial nonreciprocity in waveguide second-order processes, Opt. Lett. 21, 1442–1444.CrossRefADSGoogle Scholar
  57. 59.
    Kim, D.Y., Torruellas, W.E., Kang, J., Bosshard, C., Stegeman, G.I., Vidakovic, P., Zyss, J., Moerner, W.E., Twieg, R. and Bjorklund, G. (1994) Second-order cascading as the origin of large third-order effects in organic single-crystal-core fibers, Opt. Lett. 19, 868–870; Torruellas, W.E., Krijnen, G., Kim, D.Y., Schiek, R., Stegeman, G.I., Vidakovic, P. and Zyss, J. (1994) Cascading nonlinearities in an organic single crystal core fiber: the Cerenkov regime, Opt. Commun. 112, 122-130.CrossRefADSGoogle Scholar
  58. 60.
    Bortz, M.L., Fujimura, M. and Fejer, M.M. (1994) Increased acceptance bandwidth for quasi phase-matched second harmonic generation in LiNbO3 waveguides, Electron. Lett. 30, 34–35.CrossRefGoogle Scholar
  59. 61.
    Mizuuchi, K., Yamamoto, K., Kato, M. and Sato, H. (1994) Broadening of the phase matching bandwith in quasi-phase matched second harmonic generation, IEEE J. Quantum Electron. 30, 1596–1604.CrossRefADSGoogle Scholar
  60. 62.
    See, for example, Guided Wave Nonlinear Optics, D.B. Ostrowsky and R. Reinisch eds., Kluwer Academic Publ, London (1992)Google Scholar
  61. 63.
    Stegeman, G.I. (1990) Overview of nonlinear integrated optics, in Nonlinear Waves in Solid State Physics, A.D. Boardman, M. Bertolotti, T. Twardowski eds., Plenum Press, New York.Google Scholar
  62. 64.
    Suhara, T. and Nishihara, H. (1990) Theoretical analysis of waveguide second-harmonic generation phase matched with uniform and chirped gratings, IEEE J. Quantum Electron. 26, 1265–1276.CrossRefADSGoogle Scholar
  63. 65.
    Gase, T. and Karthe, W. (1997) Quasi-phase matched cascaded second order processes in poled organic polymer waveguides, Opt. Commun. 133, 549–556.CrossRefADSGoogle Scholar
  64. 66.
    Kelaidis, C., Hutchings, D.C. and Arnold, J.M. (1994) Asymmetric two-step GaAlAs quantum well for cascaded second-order processes, IEEE Trans, on Quantum Electron. 30, 2998–3006.CrossRefADSGoogle Scholar
  65. 67.
    Tan, H., Banfi, G.P. and Tomaselli, A. (1993) Optical frequency mixing through cascaded second-order processes in ß-barium borate, Appl. Phys. Lett. 63, 2472–2474.CrossRefADSGoogle Scholar
  66. 68.
    Gorbounova, O., Ding, Y.J., Khurgin, J.B., Lee, S.J. and Craig, A.E. (1996) Optical frequency shifters based on cascaded second-order nonlinear processes, Opt. Lett. 21, 558–560.CrossRefADSGoogle Scholar
  67. 69.
    Gallo, K., Assanto, G. and Stegeman, G.I. (1997) Efficient wavelength shifting over the Erbium amplifier bandwidth via cascaded second order processes in Lithium Niobate waveguides, Appl. Phys. Lett. 71, 1020–1022.CrossRefADSGoogle Scholar
  68. 72.
    Assanto, G., Stegeman, G.I., Sheik-Bahae, M. and Van Stryland, E. (1993) All optical switching devices based on large nonlinear phase shifts from second harmonic generation, Appl. Phys. Lett. 62, 1323–1325.CrossRefADSGoogle Scholar
  69. 73.
    Ironside, C.N., Aitchison, J.S. and Arnold, J.M. (1993) An all optical switch employing the cascaded second-order nonlinear effect, IEEE J. Quantum Electron. 29, 2650–2654.CrossRefADSGoogle Scholar
  70. 74.
    Schiek, R., (1993) Nonlinear refraction caused by cascaded second-order nonlinearity in optical waveguide structures, J. Opt. Soc. Am. B 10, 1848–1855.CrossRefADSGoogle Scholar
  71. 75.
    Schiek, R. (1994) All-optical switching in the directional coupler caused by nonlinear refraction due to cascaded second-order nonlinearity, Opt. & Quantum Ekctron. 26, 415–431.CrossRefGoogle Scholar
  72. 76.
    Assanto, G., Laureti-Palma, A., Sibilia, C. and Bertolotti, M. (1994) All-Optical Switching via Second Harmonic Generation in a Nonlinearly Asymmetric Directional Coupler, Opt. Commun. 110, 599–603.CrossRefADSGoogle Scholar
  73. 77.
    Karpierz, M.A. (1996) Directional coupling for solitary waves in quadratic nonlinearity, Optica Applicata XXVI, 391–397.Google Scholar
  74. 78.
    Lee, S.J., Khurgin, J.B. and Ding, Y.J. (1997) Directional couplers based on cascaded second-order nonlinearities in surface-emitting geometry, Opt. Commun. 139, 63–68.CrossRefADSGoogle Scholar
  75. 79.
    De Angelis, C., Laureti-Palma, A., Nalesso, G.F. and Someda, C.G. (1997) On the modelling of nonlinear guided-wave optics for all-optical signal processing, Opt. & Quantum Electron. 29, 217–238.CrossRefGoogle Scholar
  76. 80.
    De Rossi, A., Conti, C. and Assanto, G. (1997) Mode interplay via quadratic cascading in a lithium niobate waveguide for all-optical processing, Opt. & Quantum Electron. 29, 53–63.CrossRefGoogle Scholar
  77. 81.
    Picciau, M., Leo, G. and Assanto, G. (1996) A versatile bistable gate via quadratic cascading in a Bragg periodic structure, J. Opt. Soc. Am. B 13, 661–670.CrossRefADSGoogle Scholar
  78. 82.
    Leo, G., Picciau, M. and Assanto, G. (1995) Guided-wave optical bistability through nonlinear cascading in a phase-matched distributed reflector, Electron. Lett. 31, 1661–1662.CrossRefGoogle Scholar
  79. 83.
    Chen, W. and Mills, D.L. (1987) Gap solitons and the nonlinear optical response of superlattices, Phys. Rev. Lett. 58, 160–163.CrossRefADSGoogle Scholar
  80. 84.
    Conti, C., Trillo, S. and Assanto, G. (1997) Doubly resonant Bragg simultons via second-harmonic generation, Phys. Rev. Lett. 78, 2341–2344.CrossRefADSGoogle Scholar
  81. 85.
    Conti, C., Trillo, S. and Assanto, G. (1997) Bloch function approach for parametric gap solitons, Opt. Lett. 22, 445–447.CrossRefADSGoogle Scholar
  82. 86.
    Peschel, T., Peschel, U., Lederer, F. and Malomed, B.A. (1997) Solitary waves in Bragg gratings with a quadratic nonlinearity, Phys. Rev. E 55, 4730–4739.CrossRefADSGoogle Scholar
  83. 87.
    He H. and Drummond, P. (1997) Ideal Soliton Environment using Parametric Band Gaps, Phys. Rev. Lett. 78, 4311–4314.CrossRefADSGoogle Scholar
  84. 88.
    Schiek, R. (1997) Soliton-like propagation and second harmonic generation in waveguides with second-order optical nonlinearities, AEÜ Int. J. Electron. Commun. 2, 77–86.Google Scholar
  85. 90.
    Conti, C., Assanto, G. and Trillo, S. (1997) Excitation of self-transparency Bragg solitons in quadratic media, Opt. Lett. 22, 1350–1352.CrossRefADSGoogle Scholar
  86. 91.
    Franken, P.A., Hill, A.E., Peters C.W. and Weinreich, G. (1961) Generation of optical harmonics, Phys. Rev. Lett. 7, 118–121.CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • Gaetano Assanto
    • 1
  • Katia Gallo
    • 1
  • Claudio Conti
    • 1
  1. 1.Department of Electronic EngineeringTerza University of RomeRomeItaly

Personalised recommendations