Optical and Quantum Electronics

, Volume 39, Issue 4–6, pp 361–375 | Cite as

Quasi phase matching in two-dimensional nonlinear photonic crystals

Article

Abstract

We analyze quasi-phase-matched (QPM) conversion efficiency of the five possible types of periodic two-dimensional nonlinear structures: Hexagonal, square, rectangular, centered-rectangular, and oblique. The frequency conversion efficiency, as a function of the two-dimensional quasi-phase-matching order, is determined for the general case. Furthermore, it is demonstrated for two basic feasible motifs, a circular motif and a rectangular motif. This enables to determine the optimal motif dimensions for achieving the highest conversion efficiency. We find that a rectangular motif is more efficient than a circular motif for quasi-phase-matched processes that rely on a single reciprocal lattice vector (RLV), and that under optimal choice of motif dimensions, it converges into a one-dimensional periodic structure. In addition, in a few specific cases we found that higher order QPM can be significantly more efficient than lower order QPM.

Keywords

Quasi phase matching Nonlinear photonic crystals Nonlinear frequency conversion Second harmonic generation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Berger V. (1998) Nonlinear photonic crystals. Phys. Rev. Lett. 81: 4136–4139CrossRefADSGoogle Scholar
  2. Bratfalean R.T., Peacock A.C., Broderick N.G.R., Gallo K., Lewen R. (2005) Harmonic generation in a twodimensional nonlinear quasi-crystal. Opt. Lett. 30: 424–426CrossRefADSGoogle Scholar
  3. Broderick N.G.R., Ross G.W., Offerhaus H.L., Richardson D.J., Hanna D.C. (2000) Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal. Phys. Rev. Lett. 84: 4345–4348CrossRefADSGoogle Scholar
  4. Broderick N.G.R., Bratfalean R.T., Monro T.M., Richardson D.J., de Sterke C.M. (2002) Temperature and wavelength tuning of second-, third-, and fourth-harmonic generation in a two-dimensional hexagonally poled nonlinear crystal. J. Opt. Soc. Am. B 19: 2263–2272ADSCrossRefGoogle Scholar
  5. Chowdhury A., Staus C., Boland B.F., Kuech T.F., McCaughan L. (2001) Experimental demonstration of 1535–1555-nm simultaneous optical wavelength interchange with a nonlinear photonic crystal. Opt. Lett. 26: 1353–1355ADSGoogle Scholar
  6. Fejer M.M., Magel G.A., Jundt D.H., Byer R.L. (1992) Quasi-phase-matched second harmonic generation - tuning and tolerances. IEEE J. Quant. Electron. 28: 2631–2654CrossRefADSGoogle Scholar
  7. Giacovazzo C., Monaco H.L., Artioli G., Viterbo D., Ferraris G., Gilli G., Zanotti G., Catti M. (2002) Fundamentals of crystallography. 2nd edn., University Press, OxfordGoogle Scholar
  8. Glickman Y., Winebrand E., Arie A., Rosenman G. (2006) Electron-beam-induced domain poling in LiNb03 for twodimensional nonlinear frequency conversion. Appl. Phys. Lett. 88: 011103CrossRefADSGoogle Scholar
  9. Jankovic L., Kim H., Stegeman G., Carrasco S., Torner L., Katz M. (2003) Quadratic soliton self-reflection at a quadratically nonlinear interface. Opt. Lett. 28: 2103–2105ADSGoogle Scholar
  10. Kittel C. (1995) Introduction to solid state physics. 7th edn., Wiley, New YorkGoogle Scholar
  11. Lifshitz R., Arie A., Bahabad A. (2005) Photonic quasicrystals for nonlinear optical frequency conversion. Phys. Rev. Lett. 95: 133901CrossRefADSGoogle Scholar
  12. Myers R.A., Mukherjee N., Brueck S.R.J. (1991) Large second-order nonlinearity in poled fused silica. Opt. Lett. 16: 1732–1734ADSCrossRefGoogle Scholar
  13. Norton A.H., de Sterke C.M. (2003) Optimal poling of nonlinear photonic crystals for frequency conversion. Opt. Lett. 28: 188–190ADSGoogle Scholar
  14. Ni P., Ma B., Wang X., Cheng B., Zhang D. (2003) Second-harmonic generation in two-dimensional periodically poled lithium niobate using second-order quasiphase matching. Appl. Phys. Lett. 82: 4230–4232CrossRefADSGoogle Scholar
  15. Peng L.H., Hsu C.C., Shih Y.C. (2003) Second-harmonic green generation from two-dimensional χ(2) nonlinear photonic crystal with orthorhombic lattice structure. Appl. Phys. Lett. 83: 3447–3449CrossRefADSGoogle Scholar
  16. Russel S.M., Powers P.E., Missey M.J., Schepler K.L. (2001) Broadband mid-infrared generation with twodimensional quasi- phase-matched structures. IEEE J. Quant. Electron. 37: 877–887CrossRefADSGoogle Scholar
  17. Saltiel S., Kivshar Y.S. (2000) Phase matching in nonlinear χ(2) photonic crystals. Opt. Lett. 25: 1204–1206ADSGoogle Scholar
  18. Saltiel S.M., Kivshar Y.S. (2002) All-optical deflection and splitting by second-order cascading. Opt. Lett. 27: 921–923ADSGoogle Scholar
  19. Wang X.H., Gu B.Y. (2001) Nonlinear frequency conversion in 2D χ(2) photonic crystals and novel nonlinear doublecircle construction. Eur. Phys. J. B. 24: 323–326CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Physical Electronics, School of Electrical EngineeringTel-Aviv UniversityTel-AvivIsrael

Personalised recommendations