Abstract
Nonlinear photonic crystals are materials in which the second order susceptibility is modulated in an ordered fashion, usually in one or two dimensions, while the linear susceptibility remains constant. Here, a general analysis of quasi-phase-matched interactions in a nonlinear photonic crystal is derived for the cases of periodic and quasiperiodic structures. The effects of the lattice, motif and interaction area on the generated electric field and intensity are analyzed in a periodic nonlinear photonic crystal. For the case of a quasiperiodic frequency converter, a systematic procedure is described, enabling to phase match any set of interacting waves. Nonlinear photonic crystals with radial symmetry are introduced. These structures have continuous rotation symmetry, but no translation symmetry, in contrary to the lattice based structures. Finally, several applications of quasiperiodic nonlinear frequency converters are reviewed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
A. Arie, N. Voloch, Periodic, quasi-periodic, and random quadratic nonlinear photonic crystals. Laser Photonics Rev. 4(3), 355–373 (2010)
V. Berger, Nonlinear photonic crystals. 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, All-epitaxial fabrication of thick, orientation-patterned GaAs films for nonlinear optical frequency conversion. Appl. Phys. Lett. 79, 904–906 (2001)
R.T. Bratfalean, A.C. Peacock, N.G.R. Broderick, K. Gallo, R. Lewen, Harmonic generation in a two-dimensional nonlinear quasi-crystal. Opt. Lett. 30, 424–426 (2005)
N.G.R. Broderick, G.W. Ross, H.L. Offerhaus, D.J. Richardson, D.C. Hanna, Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal. Phys. Rev. Lett. 84(19), 4345–4348 (2000)
N.G.R. Broderick, R.T. Brafalean, T.M. Monro, D.J. Richardson, C.M. de Sterke, 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 (2002)
A. Chowdhury, C. Staus, B.F. Boland, T.F. Kuech, L. McCaughan, Experimental demonstration of 1535 1555-nm simultaneous optical wavelength interchange with a nonlinear photonic crystal. Opt. Lett. 26, 1353 (2001)
S.M. Saltiel, Y.S. Kivshar, Phase matching in nonlinear χ (2) photonic crystals. Opt. Lett. 25, 1204–1206 (2000)
S.M. Saltiel, Y.S. Kivshar, All-optical deflection and splitting by second-order cascading. Opt. Lett. 27, 921 (2002)
S.F. Mingaleev, Y.S. Kivshar, Self-trapping and stable localized modes in nonlinear photonic crystals. Phys. Rev. Lett. 86, 5474 (1996)
M. Bertolotti, Wave interactions in photonic band structures: an overview. 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, Noncollinear double quasi phase matching in one-dimensional poled crystals. Opt. Lett. 32, 262–264 (2007)
K. Fradkin-Kashi, A. Arie, P. Urenski, G. Rosenman, Multiple nonlinear optical interactions with arbitrary wave vector differences. Phys. Rev. Lett. 88(2), 023903 (2001)
S.N. Zhu, Y.Y. Zhu, N.B. Ming, Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice. 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, Multiple-wavelength second-harmonic generation in aperiodic optical superlattices. 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, Red, yellow, green and blue—four-color light from a single, aperiodically poled LiTaO3 crystal. Appl. Phys. B, Lasers Opt. 78, 265–267 (2004)
M.H. Chou, K.R. Parameswaran, M.M. Fejer, I. Brener, Multiple-channel wavelength conversion by use of engineered quasi-phase-matching structures in LiNbO3 waveguides. Opt. Lett. 24, 1157–1159 (1999)
M.M. Fejer, G.A. Magel, D.H. Jundt, R.L. Byer, Quasi-phase-matched second harmonic generation—tuning and tolerances. IEEE J. Quantum Electron. 28, 2631–2654 (1992)
R.W. Boyd, Nonlinear Optics, 2nd edn. (Academic Press, San Diego 2003)
S.M. Russell, P.E. Powers, M.J. Missey, K.L. Schepler, Broadband mid-infrared generation with two-dimensional quasi-phase-matched structures. 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 Crystallography, 2nd edn. (University Press, Oxford, 2002)
A. Arie, N. Habshoosh, A. Bahabad, Quasi phase matching in two-dimensional nonlinear photonic crystals. Opt. Quantum Electron. 39, 361–375 (2007)
D. Kasimov, A. Arie, E. Winebrand, G. Rosenman, A. Bruner, P. Shaier, D. Eger, Annular symmetry nonlinear frequency converters. Opt. Express 14, 9371–9376 (2006)
N. Voloch, T. Ellenbogen, A. Arie, Radially symmetric nonlinear photonic crystals. J. Opt. Soc. Am. B 26(1), 42–49 (2009)
D. Shechtman, I. Blech, D. Gratias, J.W. Cahn, Metallic phase with long-range orientational order and no translational symmetry. Phys. Rev. Lett. 53(20), 1951–1953 (1984)
V. Elser, Indexing problems in quasicrystal diffraction. Phys. Rev. B 32(8), 4892–4898 (1985)
N.G. de Bruijn, Algebraic theory of Penrose’s non-periodic tilings of the plane. Proc. K. Ned. Akad. Wet., Ser. A, Indag. Math. 84, 39–66 (1981)
D.A. Rabson, T.L. Ho, N.D. Mermin, Aperiodic tilings with non-symmorphic space groups p2j gm. Acta Crystallogr., Sect. A 44(5), 678–688 (1988)
D.A. Rabson, T.L. Ho, N.D. Mermin, Space groups of quasicrystallographic tilings. Acta Crystallogr., Sect. A 45(8), 538–547 (1989)
F. Gahler, J. Rhyner, Equivalence of the generalised grid and projection methods for the construction of quasiperiodic tilings. J. Phys. A, Math. Gen. 19, 267–277 (1986)
R. Lifshitz, A. Arie, A. Bahabad, Photonic quasicrystals for nonlinear optical frequency conversion. Phys. Rev. Lett. 95(13), 133901 (2005)
T.L. Ho, Periodic quasicrystal. Phys. Rev. Lett. 56(5), 468–471 (1986)
A.H. Norton, C.M. de Sterke, Optimal poling of nonlinear photonic crystals for frequency conversion. Opt. Lett. 28, 188–190 (2003)
K. Fradkin, A. Arie, A. Skliar, G. Rosenman, Tunable midinfrared source by difference frequency generation in bulk periodically poled KTiOPO4. Appl. Phys. Lett. 74, 914–916 (1999)
S. Emanueli, A. Arie, Temperature-dependent dispersion equations for KTiOPO4 and KTiOAsO4. Appl. Opt. 42, 6661–6665 (2003)
K. Fradkin-Kashi, A. Arie, Multiple-wavelength quasi-phase-matched nonlinear interactions. IEEE J. Quantum Electron. 35, 1649–1656 (1999)
A. Bahabad, N. Voloch, A. Arie, R. Lifshitz, Experimental confirmation of the general solution to the multiple phase matching problem. J. Opt. Soc. Am. B 24, 1916–1921 (2007)
S. Saltiel, Y. Deyanova, Polarization switching as a result of cascading of two simultaneously phase-matched quadratic processes. Opt. Lett. 24(18), 1296–1298 (1999)
A. Ganany-Padowicz, I. Juwiler, O. Gayer, A. Bahabad, A. Arie, All-optical polarization switch in a quadratic nonlinear photonic quasicrystal. Appl. Phys. Lett. 94(9), 091108 (2009)
G. Porat, O. Gayer, A. Arie, Simultaneous parametric oscillation and signal-to-idler conversion for efficient downconversion. Opt. Lett. 35(9), 1401–1403 (2010)
S.T. Flammia, N.C. Menicucci, O. Pfister, One-way quantum computing in the optical frequency comb. Phys. Rev. Lett. 101, 130501 (2008)
M. Pysher, A. Bahabad, P. Peng, A. Arie, O. Pfister, Quasi-phase-matched concurrent nonlinearities in periodically poled KTiOPO4 for quantum computing over the optical frequency comb. Opt. Lett. 35(4), 565–567 (2010)
A. Bahabad, A. Ganany-Padowicz, A. Arie, Engineering two-dimensional nonlinear photonic quasi-crystals. Opt. Lett. 33(12), 1386–1388 (2008)
N. Voloch-Bloch, T. Davidovich, T. Ellenbogen, A. Ganany-Padowicz, A. Arie, Omnidirectional phase matching of arbitrary processes by radial quasi-periodic nonlinear photonic crystal. Opt. Lett. 35(14), 2499–2501 (2010)
A. Bahabad, O. Cohen, M.M. Murnane, H.C. Kapteyn, Quasi-periodic and random quasi-phase matching of high harmonic generation. Opt. Lett. 33(17), 1936–1938 (2008)
I. Dolev, M. Volodarsky, G. Porat, A. Arie, Multiple coupling of surface plasmons in quasiperiodic gratings. Opt. Lett. 36(9), 1584–1586 (2011)
G.D. Boyd, D.A. Kleinman, Parametric interaction of focused Gaussian light beams. J. Appl. Phys. 39, 3596–3639 (1968)
T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, A. Arie, Nonlinear generation and manipulation of airy beams. Nat. Photonics 3, 395–398 (2009)
N. Voloch-Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, A. Arie, Twisting light by nonlinear photonic crystals. Phys. Rev. Lett. 108, 233902 (2012)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Arie, A., Bahabad, A., Habshoosh, N. (2014). 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/10.1007/978-3-642-41086-4_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-41086-4_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-41085-7
Online ISBN: 978-3-642-41086-4
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)