Abstract
Nonlinear photonic crystals (NLPC) are materials in which the second order susceptibility χ (2) is modulated in an ordered fashion, usually in one or two dimensions, while the linear susceptibility remains constant. This modulation can be done, for example, by periodic electric field poling of ferroelectric crystals such as LiNbO3 or KTiOPO4, or by orientation pattering of semiconductors such as GaAs. NLPC are significantly different than the more common photonic crystals, in which the linear susceptibility is modulated, bringing forth optical processes involving several frequencies. For example, one dimensional (1D) modulation of the nonlinear susceptibility is widely used nowadays for quasi-phase-matched nonlinear frequency conversion. The extension to two-dimensional (2D) modulation allows further design flexibility, and is useful for non-collinear second harmonic generation (SHG), for simultaneous wavelength interchange, for third and fourth harmonic generation, and proposed for realization of all optical effects, e.g. all optical deflection and splitting. Note that other types of nonlinear interactions are possible in photonic crystals, including third-order (χ (3)) nonlinearities in “standard” photonic crystals, as well as photonic crystals in which both the linear and the second-order nonlinear susceptibilities are modulated. These interactions will not be considered in this chapter.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
V. Berger, Phys. Rev. Lett. 81(19), 4136–4139 (1998)
L.A. Eyres, P.J. Tourreau, T.J. Pinguet, C.B. Ebert, J.S. Harris, M.M. Fejer, L. Becouarn, B. Gerard, E. Lallier, Appl. Phys. Lett. 79, 904–906 (2001)
R.T. Bratfalean, A.C. Peacock, N.G.R. Broderick, K. Gallo, R. Lewen, Opt. Lett. 30, 424–426 (2005)
N.G.R. Broderick, G.W. Ross, H.L. Offerhaus, D.J. Richardson, D.C. Hanna, Phys. Rev. Lett. 84(19), 4345–4348 (2000)
N.G.R. Broderick, R.T. Bratfalean, T.M. Monro, D.J. Richardson, C.M. de Sterke, J. Opt. Soc. Am. B 19, 2263 (2002)
A. Chowdhury, C. Staus, B.F. Boland, T.F. Kuech, L. McCaughan, Opt. Lett. 26, 1353 (2001)
S. Saltiel, Y.S. Kivshar, Opt. Lett. 25, 1204–1206 (2000)
S.M. Saltiel, Y.S. Kivshar, Opt. Lett. 27, 921 (2002)
S.F. Mingaleev, Y.S. Kivshar, Phys. Rev. Lett. 86, 5474 (1996)
M. Bertolotti, J. Opt. A Pure Appl. Opt. 8, S9–S32 (2006)
C. Kittel, Introduction to Solid State Physics, 7th edn. (Wiley, New York, 1995)
T. Ellenbogen, A. Arie, S.M. Saltiel, Opt. Lett. 32, 262–264 (2007)
K. Fradkin-Kashi, A. Arie, P. Urenski, G. Rosenman, Phys. Rev. Lett. 88(2), 023903 (2001)
S.N. Zhu, Y.Y. Zhu, N.B. Ming, Science 278, 843 (1997)
H. Liu, S.N. Zhu, Y.Y. Zhu, N.B. Ming, X.C. Lin, W.J. Ling, A.Y. Yao, Z.Y. Xu, Appl. Phys. Lett. 81, 3326–3328 (2002)
J. Liao, J.L. He, H. Liu, J. Du, F. Xu, H.T. Wang, S.N. Zhu, Y.Y. Zhu, N.B. Ming, Appl. Phys. B Lasers Opt. 78, 265–267 (2004)
M.H. Chou, K.R. Parameswaran, M.M. Fejer, I. Brener, Opt. Lett. 24, 1157–1159 (1999)
M.M. Fejer, G.A. Magel, D.H. Jundt, R.L. Byer, IEEE J. Quantum Electron. 28, 2631–2654 (1992)
R.W. Boyd, Nonlinear Optics, 2th edn. (Academic Press, San Diego, 2003)
S.M. Russell, P.E. Powers, M.J. Missey, K.L. Schepler, IEEE J. Quantum Electron. 37, 877 (2001)
C. Giacovazzo, H.L. Monaco, G. Artioli, D. Viterbo, G. Ferraris, G. Gilli, G. Zanotti, M. Catti, Fundamentals of Crytallography, 2nd edn. (University Press, Oxford, 2002)
A. Arie, N. Habshoosh, A. Bahabad, Opt. Quantum Electron. 39, 361–375 (2007)
D. Shechtman, I. Blech, D. Gratias, J.W. Cahn, Phys. Rev. Lett. 53(20), 1951–1953 (1984)
V. Elser, Phys. Rev. B 32(8), 4892–4898 (1985)
N. de Bruijn, Proc. K. Ned. Akad. Wet. Ser. A 84, 39–66 (1981)
D.A. Rabson, T.L. Ho, N.D. Mermin, Acta Crystallogr. Sect. A 44(5), 678–688 (1988)
D.A. Rabson, T.L. Ho, N.D. Mermin, Acta Crystallogr. Sect. A 45(8), 538–547 (1989)
F. Gahler, J. Rhyner, J. Phys. A Math. Gen. 19, 267–277 (1986)
R. Lifshitz, A. Arie, A. Bahabad, Phys. Rev. Lett. 95(13), 133–901 (2005)
T.L. Ho, Phys. Rev. Lett. 56(5), 468–471 (1986)
A.H. Norton, C.M. de Sterke, Opt. Lett. 28, 188–190 (2003)
K. Fradkin, A. Arie, A. Skliar, G. Rosenman, Appl. Phys. Lett. 74, 914–916 (1999)
S. Emanueli, A. Arie, Appl. Opt. 42, 6661–6665 (2003)
K. Fradkin-Kashi, A. Arie, IEEE J. Quantum Electron. 35, 1649–1656 (1999)
A. Bahabad, N. Voloch, A. Arie, R. Lifshitz, J. Opt. Soc. Am. B 24, 1916–1921 (2007)
G.D. Boyd, D.A. Kleinman, J. Appl. Phys. 39, 3596–3639 (1968)
D. Kasimov, A. Arie, E. Winebrand, G. Rosenman, A. Bruner, P. Shaier, D. Eger, Opt. Express 14, 9371–9376 (2006)
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Arie, A., Bahabad, A., Habshoosh, N. (2009). Nonlinear Interactions in Periodic and Quasi-Periodic Nonlinear Photonic Crystals. In: Ferraro, P., Grilli, S., De Natale, P. (eds) Ferroelectric Crystals for Photonic Applications. Springer Series in Materials Science, vol 91. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77965-0_10
Download citation
DOI: https://doi.org/10.1007/978-3-540-77965-0_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77963-6
Online ISBN: 978-3-540-77965-0
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)