OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry M. Van Driel
  • Vol. 25, Iss. 4 — Apr. 1, 2008
  • pp: 555–563

Dependence of nonlinearity enhancement on power density in photonic crystals characterized by numerical Z-scan experiments based on the finite-difference time-domain technique

Zi-Ming Meng, Hai-Ying Liu, Qiao-Feng Dai, Li-Jun Wu, Qi Guo, Wei Hu, Song-Hao Liu, Sheng Lan, and V. A. Trofimov  »View Author Affiliations


JOSA B, Vol. 25, Issue 4, pp. 555-563 (2008)
http://dx.doi.org/10.1364/JOSAB.25.000555


View Full Text Article

Enhanced HTML    Acrobat PDF (500 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We investigate the enhancement of nonlinearity in one-dimensional (1D) photonic crystals (PCs) with Kerr nonlinearity by numerical Z-scan experiments based on the finite-difference time-domain technique. Focused Gaussian beams with well-defined waists and Rayleigh lengths necessary for Z-scan experiments are generated through a conjugated manipulation of the Gaussian beams propagating in free space. The Z-scan measurements used for bulk materials are naturally extended to 1D PCs after incorporating the frequency- and power-density-dependent reflections into their linear and nonlinear absorptions. The closed- and open-aperture Z-scan traces for the 1D PCs are obtained and a symmetric method is employed to modify the asymmetric closed-aperture traces. The nonlinearity enhancement factors at different frequencies in the first and second bands are derived numerically and analytically. A good agreement is found between the numerical and analytical results in the case of weak nonlinearity. Moreover, the dependences of the enhancement factor on the incident power density for different frequencies in the 1D PCs are extracted and they are found to be much different from those in bulk materials. It is revealed that the variation of the group velocity with increasing power density is responsible for the power-density dependence of the enhancement factor. It indicates that in practice one must deliberately choose the working frequency and power density of PC-based devices in order to achieve a maximum enhancement of nonlinearity.

© 2008 Optical Society of America

OCIS Codes
(190.3270) Nonlinear optics : Kerr effect
(190.4390) Nonlinear optics : Nonlinear optics, integrated optics

ToC Category:
Photonic Crystals

History
Original Manuscript: December 7, 2007
Manuscript Accepted: January 14, 2008
Published: March 21, 2008

Citation
Zi-Ming Meng, Hai-Ying Liu, Qiao-Feng Dai, Li-Jun Wu, Qi Guo, Wei Hu, Song-Hao Liu, Sheng Lan, and V. A. Trofimov, "Dependence of nonlinearity enhancement on power density in photonic crystals characterized by numerical Z-scan experiments based on the finite-difference time-domain technique," J. Opt. Soc. Am. B 25, 555-563 (2008)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-25-4-555


Sort:  Year  |  Journal  |  Reset  

References

  1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987). [CrossRef] [PubMed]
  2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486-2489 (1987). [CrossRef] [PubMed]
  3. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819-1821 (1999). [CrossRef] [PubMed]
  4. J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic crystals: putting a new twist on light,” Nature 386, 143-149 (1997). [CrossRef]
  5. S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608-610 (2000). [CrossRef] [PubMed]
  6. M. Loncǎr, D. Nedeljkovic, T. Doll, J. Vuckovic, A. Scherer, and T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77, 1937-1939 (2000). [CrossRef]
  7. S. Lan, S. Nishikawa, H. Ishikawa, and O. Wada, “Design of impurity band-based photonic crystal waveguides and delay lines for ultrashort optical pulses,” J. Appl. Phys. 90, 4321-4327 (2001). [CrossRef]
  8. Y. Sugimoto, S. Lan, S. Nishikawa, N. Ikeda, H. Ishikawa, and K. Asakawa, “Design and fabrication of impurity band-based photonic crystal waveguides for optical delay lines,” Appl. Phys. Lett. 81, 1946-1948 (2002). [CrossRef]
  9. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096-R10099 (1998). [CrossRef]
  10. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals: toward microscale lightwave circuits,” J. Lightwave Technol. 17, 2032-2038 (1999). [CrossRef]
  11. L. J. Wu, M. Mazilu, and T. F. Krauss, “Beam steering in planar-photonic crystals: from superprism to supercollimator,” J. Lightwave Technol. 21, 561-566 (2003). [CrossRef]
  12. M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368-1371 (1994). [CrossRef] [PubMed]
  13. H. Y. Liu, S. Lan, L. J. Wu, Q. Guo, W. Hu, S. H. Liu, X. S. Lin, and A. V. Gopal, “Self-induced Anderson localization and optical limiting in photonic crystal coupled cavity waveguides with Kerr nonlinearity,” Appl. Phys. Lett. 90, 213507 (2007). [CrossRef]
  14. P. R. Villeneuve, D. S. Abrams, S. Fan, and J. D. Joannopoulos, “Single-mode waveguide microcavity for fast optical switching,” Opt. Lett. 21, 2017-2019 (1996). [CrossRef] [PubMed]
  15. S. Lan, A. V. Gopal, K. Kanamoto, and H. Ishikawa, “Ultrafast response of photonic crystal atoms with Kerr nonlinearity to ultrashort optical pulses,” Appl. Phys. Lett. 84, 5124-5126 (2004). [CrossRef]
  16. Y. H. Liu, X. Y. Hu, D. X. Zhang, B. Y. Cheng, D. Z. Zhang, and Q. B. Meng, “Subpicosecond optical switching in polystyrene opal,” Appl. Phys. Lett. 86, 151102 (2005). [CrossRef]
  17. A. Haché and M. Bourgeois, “Ultrafast all-optical switching in a silicon-based photonic crystal,” Appl. Phys. Lett. 77, 4089-4091 (2000). [CrossRef]
  18. X. Y. Hu, Q. Zhang, Y. H. Liu, B. Y. Cheng, and D. Z. Zhang, “Ultrafast three-dimensional tunable photonic crystal,” Appl. Phys. Lett. 83, 2518-2520 (2003). [CrossRef]
  19. N. S. Zhao, H. Zhou, Q. Guo, W. Hu, X. B. Yang, S. Lan, and X. S. Lin, “Design of highly efficient optical diodes based on the dynamics of nonlinear photonic crystal molecules,” J. Opt. Soc. Am. B 23, 2434-2440 (2006). [CrossRef]
  20. M. Soljacic, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, “Photonic-crystal slow-light enhancement of nonlinear phase sensitivity,” J. Opt. Soc. Am. B 19, 2052-2059 (2002). [CrossRef]
  21. J. Hwang, N. Y. Ha, H. J. Chang, B. Park, and J. W. Wu, “Enhanced optical nonlinearity near the photonic bandgap edges of a cholesteric liquid crystal,” Opt. Lett. 29, 2644-2646 (2004). [CrossRef] [PubMed]
  22. J. Hwang and J. W. Wu, “Determination of optical Kerr nonlinearity of a photonic bandgap structure by Z-scan measurement,” Opt. Lett. 30, 875-877 (2005). [CrossRef] [PubMed]
  23. M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760-769 (1990). [CrossRef]
  24. J. Hwang and J. W. Wu, “Investigation on dispersive properties of photonic crystals for employment of Z-scan method,” Proc. SPIE 6480, 648019 (2007). [CrossRef]
  25. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302-307 (1966). In this paper, a commercial software developed by Rsoft Design Group (http://www.rsoftdesign.com) is used for FDTD simulations. [CrossRef]
  26. J. Hwang, M. J. Kim, J. W. Wu, S. M. Lee, and B. K. Rhee, “Picosecond pump-probe measurement of bandgap changes in SiO2/TiO2 one-dimensional photonic bandgap structures,” Opt. Lett. 31, 377-379 (2006). [CrossRef] [PubMed]
  27. Z. B. Liu, J. G. Tian, W. P. Zang, W. Y. Zhou, C. P. Zhang, and G. Y. Zhang, “Influence of nonlinear absorption on Z-scan measurements of nonlinear refraction,” Chin. Phys. Lett. 20, 509-512 (2003). [CrossRef]
  28. N. C. Panoiu, M. Bahl, and R. M. Osgood, Jr., “Ultrafast optical tuning of a superprism effect in nonlinear photonic crystals,” J. Opt. Soc. Am. B 21, 1500-1508 (2004). [CrossRef]

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