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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 19, Iss. 9 — Sep. 1, 2002
  • pp: 2075–2082

Parametric nonlinear interaction in centrosymmetric three-dimensional photonic crystals

Jordi Martorell  »View Author Affiliations

JOSA B, Vol. 19, Issue 9, pp. 2075-2082 (2002)

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The parametric quadratic nonlinear interaction is considered within three-dimensional photonic crystals. A theoretical model that includes the full three-dimensional aspect of such nonlinear interaction is developed. Results from the study prove that second-order processes are possible in centrosymmetric three-dimensional photonic crystals and that the contribution to this nonlinear interaction is localized at the interfaces separating the two materials of the photonic lattice. In fact, such structures provide an independent solution to some of the most basic requirements for an efficient second-order nonlinear interaction: a nonvanishing interaction in the dipole approximation, a phase-matching mechanism, and a high nonlinear susceptibility not linked to the specific properties of the crystalline structure. Numerical results show that efficient parametric processes are achievable by use of short three-dimensional photonic crystals when realistic parameters for such nonlinear structures are used.

© 2002 Optical Society of America

OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

Jordi Martorell, "Parametric nonlinear interaction in centrosymmetric three-dimensional photonic crystals," J. Opt. Soc. Am. B 19, 2075-2082 (2002)

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  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 in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987). [CrossRef] [PubMed]
  3. J. Martorell and N. M. Lawandy, “Observation of inhibited spontaneous emission in a periodic dielectric structure,” Phys. Rev. Lett. 65, 1877–1880 (1990). [CrossRef] [PubMed]
  4. For a recent review see, for instance, C. M. Soukoulis, ed., Photonic Crystals and Light Localization in the 21st Century (Kluwer Academic, Dordrecht, The Netherlands, 2001).
  5. C. J. Herbert, W. S. Capinski, and M. S. Malcuit, “Optical power limiting with nonlinear periodic structures,” Opt. Lett. 17, 1037–1039 (1992). [CrossRef] [PubMed]
  6. C. J. Herbert and M. S. Malcuit, “Optical bistability in nonlinear periodic structures,” Opt. Lett. 18, 1783–1785 (1993). [CrossRef] [PubMed]
  7. J. Martorell and R. Corbalán, “Enhancement of second harmonic generation in a periodic structure with a defect,” Opt. Commun. 108, 319–323 (1994). [CrossRef]
  8. 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]
  9. J. Trull, R. Vilaseca, J. Martorell, and R. Corbalán, “Second-harmonic generation in local modes of a truncated periodic structure,” Opt. Lett. 20, 1746–1748 (1995). [CrossRef] [PubMed]
  10. J. Martorell, R. Vilaseca, and R. Corbalán, “Scattering of second harmonic light from small spherical particles,” in Quantum Electronics and Laser Science Conference (Optical Society of America, Washington, D.C., 1995) Vol. 16, p. 32.
  11. J. Martorell, “Second-harmonic scattering from sites of a crystalline lattice,” in Photonic Band Gap Materials, C. M. Soukoulis, ed. (Kluwer Academic, Dordrecht, The Netherlands, 1996), p. 529–534.
  12. K. Sakoda and K. Ohtaka, “Optical response of three-dimensional photonic lattices: solutions of inhomogeneous Maxwell’s equations and their applications,” Phys. Rev. B 54, 5732–5741 (1996). [CrossRef]
  13. K. Sakoda and K. Ohtaka, “Sum-frequency generation in two-dimensional photonic lattices,” Phys. Rev. B 54, 5722–5749 (1996). [CrossRef]
  14. R. J. Gehr, G. L. Fischer, R. W. Boyd, and J. E. Sipe, “Nonlinear response of layered composite materials,” Phys. Rev. A 53, 2792–2798 (1996). [CrossRef] [PubMed]
  15. J. Martorell, R. Vilaseca, and R. Corbalán, “Second harmonic generation in a photonic crystal,” Appl. Phys. Lett. 70, 702–704 (1997). [CrossRef]
  16. J. Martorell, R. Vilaseca, and R. Corbalán, “Scattering of second harmonic light from small spherical particles ordered in a crystalline lattice,” Phys. Rev. A 55, 4520–4525 (1997). [CrossRef]
  17. J. Martorell, R. Vilaseca, J. Trull, and R. Corbalán, “Second harmonic generation in a photonic crystal,” Opt. Photon. News 8, 34 (1997). [CrossRef]
  18. M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second harmonic generation in nonlinear, one-dimensional periodic structures,” Phys. Rev. A 56, 3166–3174 (1997). [CrossRef]
  19. H.-B. Lin, R. J. Tonucci, and A. J. Campillo, “Two-dimensional photonic bandgap optical limiter in the visible,” Opt. Lett. 23, 94–96 (1998). [CrossRef]
  20. J. Trull, J. Martorell, and R. Vilaseca, “Angular dependence of phase-matched second-harmonic generation in a photonic crystal,” J. Opt. Soc. Am. B 15, 2581–2585 (1998). [CrossRef]
  21. L. A. Golovan, A. M. Zheltikov, P. K. Kashkarov, N. I. Koroteev, M. G. Lisachenki, A. N. Naumov, D. A. Sidorov-Biryukov, V. Yu Timoshenko, and A. B. Fedotov, “Generation of second optical harmonic in porous silicon-based structures with a photonic band gap,” JETP Lett. 69, 300–305 (1999). [CrossRef]
  22. Y. Xu, Reginald K. Lee, and A. Yariv, “Propagation and second-harmonic generation of electromagnetic waves in a coupled-resonator optical waveguide,” J. Opt. Soc. Am. B 17, 387–400 (2000). [CrossRef]
  23. A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, A. P. Shkurinov, P. Masselin, and G. Mouret, “Enhancement of sum frequency generation near the photonic band edge under quasi phase matching conditions,” Phys. Rev. E 63, 046609 (1–11) (2001). [CrossRef]
  24. Y. Dumeige, P. Vidakovic, S. Sauvage, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001). [CrossRef]
  25. M. de Sterke, S. M. Saltiel, and Y. Kivshar, “Efficient collinear fourth-harmonic generation by two-channel multistep cascading in a single two-dimensional nonlinear photonic crystal,” Opt. Lett. 26, 539–541 (2001). [CrossRef]
  26. J. Martorell, “Quadratic nonlinear interactions in three-dimensional photonic crystals” in Photonic Crystals and Light Localization in the 21st Century, C. M. Soukoulis, ed. (Kluwer Academic, Dordrecht, The Netherlands, 2001), pp. 589–599.
  27. K. Sakoda, “Enhanced light amplification due to group-velocity anomaly peculiar to two- and three-dimensional photonic crystals,” Opt. Express 4, 167–176 (1999), http://www.osa.org/opticsexpress. [CrossRef] [PubMed]
  28. As is well known, bound states in 3-D lattices are obtained only when the strength of the defect exceeds a critical threshold value, see, for instance, P. Sheng, Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena (Academic, San Diego, Calif., 1995).
  29. See, for instance, E. Butkov, Mathematical Physics (Addison-Wesley, Reading, Mass., 1968).
  30. P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–119 (1961). [CrossRef]
  31. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962). [CrossRef]
  32. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Bayer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992). [CrossRef]
  33. N. Bloembergen and A. J. Sievers, “Nonlinear optical properties of periodic laminar structures,” Appl. Phys. Lett. 17, 483 (1970). [CrossRef]
  34. Amnon Yariv and Pochi Yeh, “Electromagnetic propagation in periodic stratified media. II. Birefringence, phase matching, and x-ray lasers,” J. Opt. Soc. Am. B 67, 438–448 (1977). [CrossRef]
  35. J. P. Van der Ziel and M. Ilegems, “Optical second harmonic generation in periodic multilayer GaAs-Al0.3Ga0.7As structures,” Appl. Phys. Lett. 28, 437–439 (1976). [CrossRef]
  36. J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, “Second-harmonic Rayleigh scattering from a sphere of centrosymmetric material,” Phys. Rev. Lett. 83, 4045–4048 (1999). [CrossRef]
  37. N. Yang, W. E. Angerer, and A. G. Yodh, “Angle-resolved second-harmonic light scattering from colloidal particles,” Phys. Rev. Lett. 87(10), 103902 (1–4) (2001). [CrossRef] [PubMed]

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