najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2015-6-6-779-785najo-897Research ArticlePAPERS, PRESENTED AT THE CONFERENCEPAPERS, PRESENTED AT THE CONFERENCEOn theory of second harmonic generation in 2D nonlinear photonic crystals with arbitrary structuresEshniyazovV. E.

100095, Tashkent

EshchanovB. Kh.

100095, Tashkent

YusupovD. B.

Universitetskya ul. 2, 100095, Tashkent

ErgashevQ. Ya.

Universitetskya ul. 2, 100095, Tashkent

SapaevU. K.

100095, Tashkent

usapaev@gmail.comDepartment of Physics, National University of Uzbekistan, named after Mirzo UlugbekUzbekistanTashkent State Technical University, named after Abu Raikhan BeruniUzbekistan20151508202566779785Copyright © Eshniyazov V.E., Eshchanov B.K., Yusupov D.B., Ergashev Q.Y., Sapaev U.K., 20252025Eshniyazov V.E., Eshchanov B.K., Yusupov D.B., Ergashev Q.Y., Sapaev U.K.Eshniyazov V.E., Eshchanov B.K., Yusupov D.B., Ergashev Q.Y., Sapaev U.K.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/897

Second harmonic generation in 2D nonlinear photonic crystals based on rectangular symmetry with rectangular motifs has been analyzed theoretically. An approximate solution of the spectral response for the second harmonic generation in any designed 2D nonlinear photonic crystal is obtained within the un-depleted pump approximation. Rapid calculation of the temporal profile of multidirectional second harmonic pulse in such nonlinear lattices has been also shown.

2D nonlinear photonic crystalssecond harmonic generationfrequency conversionquasi-phase matchingarbitrary domain structureslinearly chirped domain structuresrandomly sized domain structuresReferencesJ.A. Armstrong, N. Bloembergen, D. Ducing, P.S. Pershan. Interaction between light waves in a nonlinear dielectric. Phys. Rev., 1962, 127, P. 1918.J.A. Armstrong, N. Bloembergen, D. Ducing, P.S. Pershan. Interaction between light waves in a nonlinear dielectric. Phys. Rev., 1962, 127, P. 1918.V. Berger. Nonlinear photonic crystals. Phys. Rev. Lett., 1998, 81, P. 4136.V. Berger. Nonlinear photonic crystals. Phys. Rev. Lett., 1998, 81, P. 4136.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, 2002, 19, P. 2263.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, 2002, 19, P. 2263.S. Saltiel, Y. S. Kivshar. Phase matching in nonlinear photonic crystals, Opt. Lett., 2000, 25, P. 1204.S. Saltiel, Y. S. Kivshar. Phase matching in nonlinear photonic crystals, Opt. Lett., 2000, 25, P. 1204.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., 2000, 84, P. 4345.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., 2000, 84, P. 4345.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., 2001, 26, P. 1353.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., 2001, 26, P. 1353.S.M. Saltiel, Y.S. Kivshar: All { optical deflection and splitting by second { order cascading. Opt. Lett., 2002, 27, P. 921.S.M. Saltiel, Y.S. Kivshar: All { optical deflection and splitting by second { order cascading. Opt. Lett., 2002, 27, P. 921.K.Gallo, A.Pasquazi, S.Stivala, G.Assanto. Parametric Solitons in Two-Dimensional Lattices of Purely Nonlinear Origin. Phys. Rev. Lett., 2008, 100, P. 053901.K.Gallo, A.Pasquazi, S.Stivala, G.Assanto. Parametric Solitons in Two-Dimensional Lattices of Purely Nonlinear Origin. Phys. Rev. Lett., 2008, 100, P. 053901.A.Arie, N.Voloch. Periodic, quasi-periodic, and random quadratic nonlinear photonic crystals. Laser & Photon. Rev., 2010, 4, P. 355.A.Arie, N.Voloch. Periodic, quasi-periodic, and random quadratic nonlinear photonic crystals. Laser & Photon. Rev., 2010, 4, P. 355.A.M.Vyunishev, A.S.Chirkin. Multiple quasi-phase-matching in nonlinear Raman-Nath diffraction. Opt. Lett., 2015, 40, P. 1314.A.M.Vyunishev, A.S.Chirkin. Multiple quasi-phase-matching in nonlinear Raman-Nath diffraction. Opt. Lett., 2015, 40, P. 1314.D. T. Reid. Engineered quasi { phase { matching for second { harmoni cgeneration. Journal of optics A - pure and applied optics, 2003, 5(4), P. 97.D. T. Reid. Engineered quasi { phase { matching for second { harmoni cgeneration. Journal of optics A - pure and applied optics, 2003, 5(4), P. 97.U. K. Sapaev, D. T. Reid. General second { harmonic pulse shaping in grating { engineered quasi { phase { matched nonlinear crystals. Optics Express, 2005, 13, P. 3264.U. K. Sapaev, D. T. Reid. General second { harmonic pulse shaping in grating { engineered quasi { phase { matched nonlinear crystals. Optics Express, 2005, 13, P. 3264.U. K. Sapaev, G. Assanto. Femtosecond pulse synthesis by efficient second { harmonic generation in engineered quasi phase matching gratings. Optics Express, 2007, 15, P. 7448.U. K. Sapaev, G. Assanto. Femtosecond pulse synthesis by efficient second { harmonic generation in engineered quasi phase matching gratings. Optics Express, 2007, 15, P. 7448.U. K. Sapaev. Optimum Formation of the Response of Aperiodic Nonlinear Crystals in the Process of Second Harmonic Generation. Opt. and Spect., 2007, 102, P. 939.U. K. Sapaev. Optimum Formation of the Response of Aperiodic Nonlinear Crystals in the Process of Second Harmonic Generation. Opt. and Spect., 2007, 102, P. 939.D.B.Yusupov, U. K. Sapaev. Nonlinear Optics in Photonic Crystals. Tashkent, FAN, 2012, p. 128.D.B.Yusupov, U. K. Sapaev. Nonlinear Optics in Photonic Crystals. Tashkent, FAN, 2012, p. 128.U.K.Sapaev, D.B. Yusupov, A.A. Sherniyzov, A.A. Uzakov. Theory of backward second-harmonic generation of short laser pulses in periodically and a periodically poled nonlinear crystals. Journal of Russian Laser Research, 2012, 33, P. 103.U.K.Sapaev, D.B. Yusupov, A.A. Sherniyzov, A.A. Uzakov. Theory of backward second-harmonic generation of short laser pulses in periodically and a periodically poled nonlinear crystals. Journal of Russian Laser Research, 2012, 33, P. 103.S.M. Russel, P.E. Powers, M.J. Missey, K.L. Schepler. Broadband mid { infrared generation with two dimensional quasi-phase-matched structures. IEEE J. Quant. Electron, 2001, 37, P. 877.S.M. Russel, P.E. Powers, M.J. Missey, K.L. Schepler. Broadband mid { infrared generation with two dimensional quasi-phase-matched structures. IEEE J. Quant. Electron, 2001, 37, P. 877.M.A. Arbore, O. Marco, M.M. Fejer. Pulse compression during second { harmonic generation in a periodic quasi-phase { matching gratings. Opt. Lett., 1997, 22, P. 438.M.A. Arbore, O. Marco, M.M. Fejer. Pulse compression during second { harmonic generation in a periodic quasi-phase { matching gratings. Opt. Lett., 1997, 22, P. 438.

The authors declare that there are no conflicts of interest present.