Abstract

The two-dimensional (2-D) iterative finite difference beam-propagation method (IFD-BPM) is modified to model the cylindrically symmetric three-dimensional (quasi-3-D) second-order nonlinear wavelength conversion in quasi-phase-matched condition. The study shows that the difference between the 2-D and 3-D schemes is small for the guided waves but large for the nonguided beams. The comparison with experimental results shows that the quasi-3-D IFD-BPM is closer to reality than the 2-D scheme. In addition, simulation using the quasi-3-D IFD-BPM reveals that plane-wave and Gaussian-beam assumptions are not sufficient for estimating the nonlinear conversion and beam propagation in second-order nonlinear devices.

© 2001 IEEE

PDF Article

References

  • View by:
  • |

  1. R. L. Byer, "Quasiphase-matched nonlinear interactions and devices", J. Nonlinear Opt. Phys. Mater., vol. 6, pp. 549-592, 1997.
  2. L. E. Myers, R. C. Eckardt, M. M. Fejer and R. L. Byer, "Quasiphase-matched optical parametric oscillations in bulk periodically poled LiNbO3", J. Opt. Soc. Amer. B, vol. 12, pp. 2102-2116, 1995.
  3. C. Baron, H. Cheng and M. C. Gupta, "Domain inversion in LiTaO3 and LiNbO3 by electric field application on chemically patterned crystals", Appl. Phys. Lett. , vol. 68, pp. 481-483, 1996.
  4. M. L. Bortz and M. M. Fejer, "Annealed proton exchanged LiNb O3 waveguides", Opt. Lett., vol. 6, pp. 1844-1846, 1991.
  5. D. Eger, M. Oron, M. Kartz and A. Zussman, "Highly efficient blue light generation in KTiOPO4 waveguides", Appl. Phys. Lett. , vol. 64, pp. 3208-3209, 1994.
  6. M. M. Fejer, G. A. Magel, D. H. Jundt and R. L. Byer, "Quasiphase-matched second harmonic generation: Tuning and tolerances", IEEE J. Quantum Electron., vol. 28, pp. 2631-2654, 1992.
  7. J. Webjorn, S. Siala, D. K. Nam, R. G. Waarts and R. J. Lang, "Visible laser sources based on frequency doubling in nonlinear waveguides", IEEE J. Quantum Electron., vol. 33, pp. 1673-1685, 1997.
  8. O. Pfister, J. S. Wells, L. Hollberh, L. Zink, D. A. Van Baak, M. D. Levenson and W. R. Bosnberg, "Continuous-wave frequency tripling and quadrupling by simultaneous tree-wave mixing in periodically poled crystal: Application to a two-step 1.19-10.71µ m frequency bridge", Opt. Lett., vol. 22, pp. 1211 -1213, 1997.
  9. L. Goldberg, W. K. Burns and R. W. McElhanon, "Wide accceptance bandwidth difference frequency generation in quasiphase-matched LiNbO3 ", Appl. Phys. Lett., vol. 67, no. 20, pp. 2910-2912, 1995 .
  10. S. Sanders, R. J. Lang, L. E. Myers, M. M. Fejer and R. L. Byer, "Broadly tunable mid-IR radiation source based on difference frequency mixing of high power wavelength-tunable laser diodes in bulk periodically poled LiNbO3", Electron. Lett., vol. 32, pp. 218-219, 1996.
  11. C. Q. Xu, H. Okayama and T. Kamijoh, "Broadband multichannel wavelength conversions for optical communication systems using quasiphase matched difference frequency generation", J. Appl. Phys., vol. 34, pp. L1543-L1545, 1995.
  12. M. L. Sundheimer, Ch. Bosshard, E. W. Van Stryland and G. I. Stegeman, "Large nonlinear phase modulation in quasiphase-matched KTP waveguides as a result of cascaded second-order process", Opt. Lett., vol. 18, pp. 1397-1399, 1993.
  13. C. N. Ironside, J. S. Aitchison and J. M. Arnold, "An all-optical switch employing the cascaded second-order nonlinear effect", IEEE J. Quantum Electron., vol. 29, pp. 2650-2654, 1993.
  14. M. A. Arbore, O. Marco and M. M. Fejer, "Pulse compression during second-harmonic generation in aperiodic quasiphase-matching gratings", Opt. Lett., vol. 22, pp. 865-867, 1997.
  15. J. D. McMullen, "Optical parametric interactions in isotropic materials using a phase-corrected stack of nonlinear dielectric plates", J. Appl. Phys., vol. 46, pp. 3076-3081, 1975.
  16. C. Q. Xu, H. Okayama and M. Kawahara, "Optical frequency conversions in nonlinear medium with periodically medulated linear and nonlinear optical parameters", IEEE J. Quantum Electron., vol. 31, pp. 981-987, 1995.
  17. V. Mahalakshmi, M. R. Shenoy and K. Thyagarajan, "Evolution of the intensity profile of Cerenkov second-harmonic radiation with propagation distance in planar waveguides", IEEE J. Quantum Electron., vol. 32, pp. 137-144, 1996.
  18. M. Vaya, K. Thyagarajan and A. Kumar, "Leaky-waveguide configuration for quasiphase-matched second-harmonic generation", J. Opt. Soc. Amer. B, vol. 15, pp. 1322-1328, 1998.
  19. H. J. W. M. Hoekstra, "On beam propagation methods for modeling in integrated optics", Opt. Quantum Electron., vol. 29, pp. 157-171, 1997.
  20. B. Hermansson, D. Yevick and L. Thylen, "A propagation beam method analysis of nonlinear effects in optical waveguides", Opt. Quantum Electron., vol. 16, pp. 525-534, 1984.
  21. K. Hayata and M. Koshiba, "Numerical study of guide-wave sum-frequency generation through second-order nonlinear parametric processes", J. Opt. Soc. Amer. B, vol. 8, pp. 449-458, 1991.
  22. K. Hayata and M. Koshiba, "Three-dimentional simulation of guided-wave second-harmonic generation in the form of coherent Cerenkov radiation", Opt. Lett., vol. 16, pp. 1563-1565, 1991.
  23. F. A. Katsriku, B. B. A. Rahman and K. T. V. Grattan, "Numerical modeling of second harmonic generation in optical waveguides using the finite element method", IEEE J. Quantum Electron., vol. 33, pp. 1727-1733, 1997.
  24. P. S. Weitzman and U. Osterberg, "A modified beam propagation method to model second harmonic generation in optical fibers", IEEE J. Quantum Electron., vol. 29, pp. 1437-1443, 1993.
  25. H. M. Masoudi and J. M. Arnold, "Modeling second-order nonlinear effects in optical waveguides using a parallel-processing beam propagation method", IEEE J. Quantum Electron., vol. 31, pp. 2107 -2113, 1995.
  26. H. M. Masoudi and J. M. Arnold, "Parallel beam propagation methed for the analysis of second harmonic generation", IEEE Photon. Technol. Lett., vol. 7, pp. 400-402, 1995.
  27. G. J. M. Krijnen, W. Torruellas, G. I. Stegeman, H. J. W. M. Heoskstra and P. V. Lambeck, "Optimization of second harmonic generation and nonlinear phase-shifts in the Cerenkov regime", IEEE. J. Quantum Electron., vol. 32, pp. 729-738, 1996.
  28. H. J. W. M. Heoskstra, O. Noordman, G. J. M. Krijnen, R. K. Varshney and E. Henselmans, "Beam-propagation method for second-harmonic generation in waveguides with birefringent materials", J. Opt. Soc Amer. B, vol. 14, pp. 1823-1830, 1997.
  29. H.-F. Chou, C.-F. Lin and G.-C. Wang, "An iterative finite difference beam propagation method for modeling second-order nonlinear effects in optical waveguides", J. Lightwave Technol., vol. 16, pp. 1686-1693, 1998.
  30. H.-F. Chou, C.-F. Lin and S. Mou, "Comparisons of finite difference beam propagarion methods for modeling second-order nonlinear effects", J. Lightwave Technol. , vol. 17, pp. 1481-1486, 1998.
  31. Y. Chung and N. Dagli, "An assessment of finite difference beam propagation method", IEEE J. Quantum Electron., vol. 26, pp. 1335 -1339, 1990.
  32. H.-F. Chou, "A study of quasiphase-matched second-order nonlinear effects", Masters thesis, National Taiwan University, 1998.
  33. W. Koechner, Solid-State Laser Engineering, New York: Springer-Verlag, 1976.
  34. W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing ,: U.K.: Cambridge Univ. Press, 1992.
  35. J. W. Thomas, Numerical Partial Differential Equations: Finete Difference Methods , New York: Springer-Verlag, 1995 .
  36. S. Nakamura, Applied Numerical Methods with Software, Englewood Cliffs, NJ: Prentice-Hall, 1991.
  37. D. G. Zill and M. R. Cullen, Advanced Engineering Mathematics,: PWS, 1992.

J. Lightwave Technol.

Opt. Lett.

Other

J. D. McMullen, "Optical parametric interactions in isotropic materials using a phase-corrected stack of nonlinear dielectric plates", J. Appl. Phys., vol. 46, pp. 3076-3081, 1975.

C. Q. Xu, H. Okayama and M. Kawahara, "Optical frequency conversions in nonlinear medium with periodically medulated linear and nonlinear optical parameters", IEEE J. Quantum Electron., vol. 31, pp. 981-987, 1995.

V. Mahalakshmi, M. R. Shenoy and K. Thyagarajan, "Evolution of the intensity profile of Cerenkov second-harmonic radiation with propagation distance in planar waveguides", IEEE J. Quantum Electron., vol. 32, pp. 137-144, 1996.

M. Vaya, K. Thyagarajan and A. Kumar, "Leaky-waveguide configuration for quasiphase-matched second-harmonic generation", J. Opt. Soc. Amer. B, vol. 15, pp. 1322-1328, 1998.

H. J. W. M. Hoekstra, "On beam propagation methods for modeling in integrated optics", Opt. Quantum Electron., vol. 29, pp. 157-171, 1997.

B. Hermansson, D. Yevick and L. Thylen, "A propagation beam method analysis of nonlinear effects in optical waveguides", Opt. Quantum Electron., vol. 16, pp. 525-534, 1984.

K. Hayata and M. Koshiba, "Numerical study of guide-wave sum-frequency generation through second-order nonlinear parametric processes", J. Opt. Soc. Amer. B, vol. 8, pp. 449-458, 1991.

L. Goldberg, W. K. Burns and R. W. McElhanon, "Wide accceptance bandwidth difference frequency generation in quasiphase-matched LiNbO3 ", Appl. Phys. Lett., vol. 67, no. 20, pp. 2910-2912, 1995 .

S. Sanders, R. J. Lang, L. E. Myers, M. M. Fejer and R. L. Byer, "Broadly tunable mid-IR radiation source based on difference frequency mixing of high power wavelength-tunable laser diodes in bulk periodically poled LiNbO3", Electron. Lett., vol. 32, pp. 218-219, 1996.

C. Q. Xu, H. Okayama and T. Kamijoh, "Broadband multichannel wavelength conversions for optical communication systems using quasiphase matched difference frequency generation", J. Appl. Phys., vol. 34, pp. L1543-L1545, 1995.

D. Eger, M. Oron, M. Kartz and A. Zussman, "Highly efficient blue light generation in KTiOPO4 waveguides", Appl. Phys. Lett. , vol. 64, pp. 3208-3209, 1994.

M. M. Fejer, G. A. Magel, D. H. Jundt and R. L. Byer, "Quasiphase-matched second harmonic generation: Tuning and tolerances", IEEE J. Quantum Electron., vol. 28, pp. 2631-2654, 1992.

J. Webjorn, S. Siala, D. K. Nam, R. G. Waarts and R. J. Lang, "Visible laser sources based on frequency doubling in nonlinear waveguides", IEEE J. Quantum Electron., vol. 33, pp. 1673-1685, 1997.

F. A. Katsriku, B. B. A. Rahman and K. T. V. Grattan, "Numerical modeling of second harmonic generation in optical waveguides using the finite element method", IEEE J. Quantum Electron., vol. 33, pp. 1727-1733, 1997.

P. S. Weitzman and U. Osterberg, "A modified beam propagation method to model second harmonic generation in optical fibers", IEEE J. Quantum Electron., vol. 29, pp. 1437-1443, 1993.

H. M. Masoudi and J. M. Arnold, "Modeling second-order nonlinear effects in optical waveguides using a parallel-processing beam propagation method", IEEE J. Quantum Electron., vol. 31, pp. 2107 -2113, 1995.

H. M. Masoudi and J. M. Arnold, "Parallel beam propagation methed for the analysis of second harmonic generation", IEEE Photon. Technol. Lett., vol. 7, pp. 400-402, 1995.

G. J. M. Krijnen, W. Torruellas, G. I. Stegeman, H. J. W. M. Heoskstra and P. V. Lambeck, "Optimization of second harmonic generation and nonlinear phase-shifts in the Cerenkov regime", IEEE. J. Quantum Electron., vol. 32, pp. 729-738, 1996.

H. J. W. M. Heoskstra, O. Noordman, G. J. M. Krijnen, R. K. Varshney and E. Henselmans, "Beam-propagation method for second-harmonic generation in waveguides with birefringent materials", J. Opt. Soc Amer. B, vol. 14, pp. 1823-1830, 1997.

C. N. Ironside, J. S. Aitchison and J. M. Arnold, "An all-optical switch employing the cascaded second-order nonlinear effect", IEEE J. Quantum Electron., vol. 29, pp. 2650-2654, 1993.

R. L. Byer, "Quasiphase-matched nonlinear interactions and devices", J. Nonlinear Opt. Phys. Mater., vol. 6, pp. 549-592, 1997.

L. E. Myers, R. C. Eckardt, M. M. Fejer and R. L. Byer, "Quasiphase-matched optical parametric oscillations in bulk periodically poled LiNbO3", J. Opt. Soc. Amer. B, vol. 12, pp. 2102-2116, 1995.

C. Baron, H. Cheng and M. C. Gupta, "Domain inversion in LiTaO3 and LiNbO3 by electric field application on chemically patterned crystals", Appl. Phys. Lett. , vol. 68, pp. 481-483, 1996.

H.-F. Chou, C.-F. Lin and S. Mou, "Comparisons of finite difference beam propagarion methods for modeling second-order nonlinear effects", J. Lightwave Technol. , vol. 17, pp. 1481-1486, 1998.

Y. Chung and N. Dagli, "An assessment of finite difference beam propagation method", IEEE J. Quantum Electron., vol. 26, pp. 1335 -1339, 1990.

H.-F. Chou, "A study of quasiphase-matched second-order nonlinear effects", Masters thesis, National Taiwan University, 1998.

W. Koechner, Solid-State Laser Engineering, New York: Springer-Verlag, 1976.

W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing ,: U.K.: Cambridge Univ. Press, 1992.

J. W. Thomas, Numerical Partial Differential Equations: Finete Difference Methods , New York: Springer-Verlag, 1995 .

S. Nakamura, Applied Numerical Methods with Software, Englewood Cliffs, NJ: Prentice-Hall, 1991.

D. G. Zill and M. R. Cullen, Advanced Engineering Mathematics,: PWS, 1992.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.