OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Vol. 21, Iss. 8 — Aug. 1, 2004
  • pp: 1509–1521

Counterpropagating quasi-phase matching: a generalized analysis

Gary D. Landry and Theresa A. Maldonado  »View Author Affiliations


JOSA B, Vol. 21, Issue 8, pp. 1509-1521 (2004)
http://dx.doi.org/10.1364/JOSAB.21.001509


View Full Text Article

Acrobat PDF (615 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The system of four differential equations governing counterpropagating quasi-phase matching are recast in a Hamiltonian form that leads to immediate insight into the nonlinear mixing process by inspection for all possible boundary conditions. A reduced Hamiltonian is found using conservation relations that are dependent on only two normalized field efficiencies and two aggregate phases. Hamiltonian contours are plotted in a series of phase-space cross sections to provide insight into the generalized behavior. The nonlinear eigenmodes are found, and their stability is examined. Finally, two specific counterpropagating quasi-phase-matching configurations, i.e., mirrored and mirrorless, are analyzed using this general Hamiltonian with the appropriate boundary conditions.

© 2004 Optical Society of America

OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(190.1450) Nonlinear optics : Bistability
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.3100) Nonlinear optics : Instabilities and chaos

Citation
Gary D. Landry and Theresa A. Maldonado, "Counterpropagating quasi-phase matching: a generalized analysis," J. Opt. Soc. Am. B 21, 1509-1521 (2004)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-21-8-1509


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. N. R. Belashenkov, S. V. Gagarskii, and M. V. Inochkin, “Nonlinear refraction of light on second-harmonic generation,” Opt. Spectrosc. 66, 806–808 (1989).
  2. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28–30 (1992).
  3. M. L. Sundheimer, C. Bosshard, E. W. Van Stryland, G. I. Stegeman, and J. D. Bierlein, “Large nonlinear phase modulation in quasi-phase-matched KTP waveguides as a result of cascaded second-order processes,” Opt. Lett. 18, 1397–1399 (1993).
  4. G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
  5. G. Stegeman, R. Schiek, L. Torner, W. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. Van Stryland, D. Hagan, and G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I. C. Khoo, F. Simoni, and C. Umeton, eds. (Wiley, New York, 1997).
  6. L. A. Ostrovskii, “Self-action of light in crystals,” JETP Lett. 5, 272–275 (1967).
  7. J. M. R. Thomas and J. P. E. Taran, “Pulse distortions in mismatched second harmonic generation,” Opt. Commun. 4, 329–334 (1972).
  8. G. R. Meredith, “Second-order cascading in third-order nonlinear optical processes,” J. Chem. Phys. 77, 5863–5871 (1982).
  9. Y. Fukuchi, T. Sakamoto, K. Taira, K. Kikuchi, D. Kunimatsu, A. Suzuki, and H. Ito, “Speed limit of all-optical gate switched using cascaded second-order nonlinear effect in quasi-phase-matched LiNbO3 devices,” IEEE Photonics Technol. Lett. 13, 1267–1269 (2002).
  10. Y. Fukuchi and K. Kikuchi, “Novel design method for all-optical ultrafast gate switches using cascaded second-order nonlinear effect in quasi-phase matched LiNbO3 devices,” IEEE Photonics Technol. Lett. 14, 1409–1411 (2002).
  11. B. Chen, C. Q. Xu, B. Zhou, and X. H. Tang, “Analysis of cascaded second-order nonlinear interaction based on quasi-phase-matched optical waveguides,” IEEE J. Sel. Top. Quantum Electron. 8, 675–680 (2002).
  12. M. Houe and P. D. Townsend, “An introduction to methods of periodic poling for second-harmonic generation,” J. Phys. D 28, 1747–1763 (1995).
  13. J. Pierce and D. Lowenthal, “Periodically poled materials and devices,” Laser Optoelektron. 16, 25–27 (1997).
  14. J. A. Armstrong, N. Bloembergen, J. Ducuino, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
  15. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
  16. G. D. Miller, R. G. Batchko, W. M. Tulloch, D. R. Weise, M. M. Fejer, and R. L. Byer, “42%-efficient single-pass cw second-harmonic generation in periodically poled lithium niobate,” Opt. Lett. 22, 1834–1836 (1997).
  17. D. Taverner, P. Britton, P. G. R. Smith, D. J. Richardson, G. W. Ross, and D. C. Hanna, “Highly efficient second-harmonic and sum-frequency generation of nanosecond pulses in a cascaded erbium-doped fiber: periodically poled lithium niobate source,” Opt. Lett. 23, 162–164 (1998).
  18. W. R. Bosenberg, A. Drobshoff, J. I. Alexander, L. E. Myers, and R. L. Byer, “93% pump depletion, 3.5-W continuous-wave, singly resonant optical parametric oscillator,” Opt. Lett. 21, 1336–1338 (1996).
  19. P. Vidakovic, D. J. Lovering, J. A. Levenson, J. Webjorn, and P. St. J. Russell, “Large nonlinear phase shift owing to cascaded χ(2) in quasi-phase-matched bulk LiNbO3,” Opt. Lett. 22, 277–279 (1997).
  20. T. Gase and W. Karthe, “Quasi-phase matched cascaded second order processes in poled organic polymer waveguides,” Opt. Commun. 133, 549–556 (1997).
  21. R. Normandin, R. L. Williams, and F. Chatenoud, “Enhanced surface emitting waveguides for visible, monolithic semiconductor laser sources,” Electron. Lett. 26, 2088–2089 (1990).
  22. S. Janz, F. Chatenoud, and R. Normandin, “Quasi-phase-matched second-harmonic generation from asymmetric coupled quantum wells,” Opt. Lett. 19, 622–624 (1994).
  23. G. D’Alessandro, P. S. J. Russell, and A. A. Wheeler, “Nonlinear dynamics of a backward quasi-phase-matched second-harmonic generator,” Phys. Rev. A 55, 3211–3218 (1997).
  24. K. Daneshvar and D. H. Kang, “A novel method for laser-induced periodic domain reversal in LiNbO3,” IEEE J. Quantum Electron. 36, 85–88 (2000).
  25. K. Mizuuchi, K. Yamamoto, and M. Kato, “Generation of ultraviolet light by frequency doubling of a red laser diode in a first-order periodically poled bulk LiTaO3,” Appl. Phys. Lett. 70, 1201–1203 (1997).
  26. Y. Shuto, T. Watanabe, S. Tomaru, I. Yokohama, M. Hikita, and M. Amano, “Quasi-phase-matched second-harmonic generation in diazo-dye- substituted polymer channel waveguides,” IEEE J. Quantum Electron. 33, 349–357 (1997).
  27. N. Hashizume, T. Tsuruzono, T. Kondo, and R. Ito, “Fabrication of periodic waveguides using organic crystals and fluorinated polyimides for quasi-phase-matched second-harmonic generation,” Opt. Rev. 4, 316–320 (1997).
  28. S. Montant, H. Guillet de Chatellus, and E. Freysz, “Laser-induced quasi-phase matching in thermally poled glasses,” Opt. Lett. 26, 837–839 (2001).
  29. V. Shur, E. Rumyantsev, R. Batchko, G. Miller, M. Fejer, and R. Byer, “Physical basis of the domain engineering in the bulk ferroelectrics,” Ferroelectrics 221, 157–167 (1999).
  30. H. Liu, N. Zhu, Y. Y. Zhu, N. B. Ming, X. C. Lin, W. J. Ling, A. Y. Yao, and Z. Y. Xu, “Multiple-wavelength second-harmonic generation in aperiodic optical superlattices,” Appl. Phys. Lett. 81, 3326–3328 (2002).
  31. H. O. Wagner, M. Kühnelt, G. Wein, B. Hahn, W. Genhardt, D. Eisert, G. Bacher, and A. Forchel, “Phase matched second harmonic generation using a χ(2) modulated ZnTe/ZnSe optical waveguide,” J. Lumin. 72, 87–89 (1997).
  32. Y. Paltiel, D. Mahalu, H. Shtrikman, G. Bunin, and U. Meirav, “Short-period surface superlattices formed by plasma etching,” Semicond. Sci. Technol. 12, 987–990 (1997).
  33. A. Saher Helmy, D. C. Hutchings, T. C. Kleckner, J. H. Marsh, A. C. Bryce, J. M. Arnold, C. R. Stanley, J. S. Aitchison, C. T. A. Brown, K. Moutzouris, and M. Ebrahimzadeh, “Quasi phase matching in GaAs AlAs superlattice waveguides through bandgap tuning by use of quantum-well intermixing,” Opt. Lett. 25, 1370–1372 (2000).
  34. D. C. Hutchings and T. C. Kleckner, “Quasi phase matching in semiconductor waveguides by intermixing: optimization considerations,” J. Opt. Soc. Am. B 19, 890–894 (2002).
  35. X. Gu, R. Y. Korotkov, Y. J. Ding, J. U. Kang, and J. B. Khurgin, “Backward second-harmonic generation in periodically-poled lithium niobate,” J. Opt. Soc. Am. B 15, 1561–1566 (1998).
  36. J. U. Kang, Y. J. Ding, W. K. Burns, and J. S. Melinger, “Backward second-harmonic generation in periodically poled bulk LiNbO3,” Opt. Lett. 22, 862–864 (1997).
  37. X. Gu, M. Makarov, Y. J. Ding, J. B. Khurgin, and W. P. Risk, “Backward second-harmonic and third-harmonic generation in a periodically poled potassium titanyl phosphate waveguide,” Opt. Lett. 24, 127–129 (1999).
  38. K. Gallo, P. Baldi, M. De Micheli, D. B. Ostrowsky, and G. Assanto, “Cascading phase shift multivalued response in counterpropagating frequency-nondegenerate parametric amplifiers,” Opt. Lett. 25, 966–968 (2000).
  39. M. C. Booth, M. Atature, G. Di Giuseppe, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Counterpropagating entangled photons in a periodically poled nonlinear waveguide,” in Proceedings of 2002 Lasers and Electro-Optics Society Annual Meeting (IEEE, Piscataway, N.J., 2002), Vol. 1, pp. 83–84.
  40. P. M. Lushnikov, P. Lodahl, and M. Saffman, “Transverse modulational instability of counterpropagating quasi-phase-matched beams in a quadratically nonlinear medium,” Opt. Lett. 23, 1650–1652 (1998).
  41. K. Y. Kolossovski, A. V. Burak, and R. A. Sammut, “Quadratic solitary waves in a counterpropagating quasi-phase-matched configuration,” Opt. Lett. 24, 835–837 (1999).
  42. Y. J. Ding and J. B. Khurgin, “Second-harmonic generation based on quasi-phase matching: a novel configuration,” Opt. Lett. 21, 1445–1447 (1996).
  43. G. D. Landry and T. A. Maldonado, “Efficient nonlinear phase shifts due to cascaded second order processes in a counter-propagating quasi-phase-matched configuration,” Opt. Lett. 22, 1400–1402 (1997).
  44. G. D. Landry and T. A. Maldonado, “Second harmonic generation and cascaded second order processes in a counterpropagating quasi-phase-matched device,” Appl. Opt. 37, 7809–7820 (1998).
  45. G. D. Landry and T. A. Maldonado, “Pulse simulations of a mirrored counterpropagating-QPM device,” Opt. Express 5, 176–187 (1999).
  46. G. D. Landry and T. A. Maldonado, “Switching and second harmonic generation using counterpropagating quasi-phase-matching in a mirrorless configuration,” J. Lightwave Technol. 17, 316–327 (1999).
  47. S. Trillo, S. Wabnitz, R. Chisari, and G. Cappellini, “Two-wave mixing in a quadratic nonlinear medium: bifurcations, spatial instabilities, and chaos,” Opt. Lett. 17, 637–639 (1992).
  48. S. Trillo and S. Wabnitz, “Nonlinear parametric mixing instabilities induced by self-phase and cross-phase modulation,” Opt. Lett. 17, 1572–1574 (1992).
  49. P. S. J. Russell, “Theoretical study of parametric frequency and wavefront conversion in nonlinear holograms,” IEEE J. Quantum Electron. 27, 830–835 (1991).
  50. Y. Qin, S. N. Pietranlunga, and M. Martinelli, “Quasi-phase-matched (QPM) difference frequency generation in a mirrorless counterpropagating configuration,” J. Lightwave Technol. 19, 1298–1306 (2001).
  51. Y. Qin, S. N. Pietranlunga, and M. Martinelli, “Correction to quasi-phase-matched (QPM) difference frequency generation in a mirrorless counterpropagating configuration,” J. Lightwave Technol. 19, 1794 (2001).
  52. S. J. B. Yoo, “Wavelength conversion technology for WDM network applications,” J. Lightwave Technol. 14, 955–966 (1996).
  53. J. M. Manley and H. E. Rowe, “General energy in nonlinear reactances,” Proc. IRE 47, 2115 (1959).
  54. H. Goldstein, Classical Mechanics, 2nd ed. (Addison-Wesley, Reading, Mass., 1980).
  55. D. Zwillinger, Handbook of Differential Equations, 2nd ed. (Academic, San Diego, 1992).
  56. G. Nicolis, Introduction to Nonlinear Science (Cambridge University, Cambridge, UK, 1995).

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