najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2017-8-3-334-338najo-605Research ArticlePHYSICSФИЗИКАInteraction of fast and slow varying electromagnetic waves propagating in paraelectric or ferroelectric materialMaimistovA. I.

Kashirskoe sh. 31, Moscow, 115409; Dolgoprudny, Moscow region, 141700

aimaimistov@gmail.comNational Nuclear Research University; Moscow Engineering Physics Institute; Moscow Institute of Physics and TechnologyRussian Federation20171108202583334338Copyright © Maimistov A.I., 20252025Maimistov A.I.Maimistov A.I.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/605

Once, a referee asked how one can write an oscillator model for a ferroelectric and the total Maxwell equation for a rapidly varying electric field. From what is known about polarization, it is a slow function of time and coordinates, but the optical wave is a fast function. However, there are examples for the interaction of high frequency and low frequency waves in nonlinear wave theory. This means that similar equations can be written for ferroelectric polarization and electromagnetic waves.

Maxwell equationelectromagnetic wavesDuffing oscillator modelferroelectricI am grateful to Dr. J. G. Caputo and Dr. E. V. Kazantseva for enlightening discussions. This investigation was supported by the Russian Foundation for Basic Research (Grant No. 15-02-02764) and by the Russian Science Foundation (Project 14-22-00098)ReferencesNesterov S.V., Sazonov S.V. On self-focusing and defocusing of few-cycle pulses in hydrogen-containing ferroelectrics. Quantum Electron., 2004, 34 (2), P. 151–155.Nesterov S.V., Sazonov S.V. On self-focusing and defocusing of few-cycle pulses in hydrogen-containing ferroelectrics. Quantum Electron., 2004, 34 (2), P. 151–155.Kazantseva E.V., Maimistov A.I. Nonlinear Waves in Para- and Ferroelectrics Described by the LandauKhalatnikov Equation. Opt. Spectr., 2005, 99 (1), P. 91-97.Kazantseva E.V., Maimistov A.I. Nonlinear Waves in Para- and Ferroelectrics Described by the LandauKhalatnikov Equation. Opt. Spectr., 2005, 99 (1), P. 91-97.Caputo J.-G., Kazantseva E.V., Maimistov A.I. Electromagnetically induced switching of ferroelectric thin films. Phys. Rev. B, 2007, 75 (1), 014113 (9 pp.).Caputo J.-G., Kazantseva E.V., Maimistov A.I. Electromagnetically induced switching of ferroelectric thin films. Phys. Rev. B, 2007, 75 (1), 014113 (9 pp.).Caputo J.G. , Kazantseva E.V., Loukitch V, Maimistov A.I. Cavity with an embedded polarized film: an adapted spectral approach. J. Phys. A, 2009, 42 (16), 165204 (18 pp.).Caputo J.G. , Kazantseva E.V., Loukitch V, Maimistov A.I. Cavity with an embedded polarized film: an adapted spectral approach. J. Phys. A, 2009, 42 (16), 165204 (18 pp.).Caputo J.-G., Maimistov A.I., et al. High frequency polarization switching dynamics of a thin ferroelectric film. Phys. Rev. B, 2010, 82, 094113 (8 pp.).Caputo J.-G., Maimistov A.I., et al. High frequency polarization switching dynamics of a thin ferroelectric film. Phys. Rev. B, 2010, 82, 094113 (8 pp.).Ozhenko S.S., Kazantseva E.V., Maimistov A.I. proagation of the ultrashort pulses in segnetoelectroc described by the Duffung model of fifth order. Nanosystems: Physics, Chemistry, Mathematics, 2012, 3 (1), P. 117–124.Ozhenko S.S., Kazantseva E.V., Maimistov A.I. proagation of the ultrashort pulses in segnetoelectroc described by the Duffung model of fifth order. Nanosystems: Physics, Chemistry, Mathematics, 2012, 3 (1), P. 117–124.Subedi A. Proposal for ultrafast switching of ferroelectrics using midinfrared pulses. Phys. Rev. B, 2015, 92 (21), 214303.Subedi A. Proposal for ultrafast switching of ferroelectrics using midinfrared pulses. Phys. Rev. B, 2015, 92 (21), 214303.Kazantseva E.V., Maimistov A.I. On the passage of an extremely short electromagnetic pulse through a ferroelectric layer embedded in a paraelectric. Opt. Spectr., 2012, 113 (5), P. 550–555.Kazantseva E.V., Maimistov A.I. On the passage of an extremely short electromagnetic pulse through a ferroelectric layer embedded in a paraelectric. Opt. Spectr., 2012, 113 (5), P. 550–555.Sazonov S.V. Electromagnetic vide solitons and brithers in the ferroelectric materials of KDP type. FTT, 1995, 37 (6), P. 1612–1622 (in Russian).Sazonov S.V. Electromagnetic vide solitons and brithers in the ferroelectric materials of KDP type. FTT, 1995, 37 (6), P. 1612–1622 (in Russian).Khomeriki R., Chotorlishvili L., Malomed B. A., Berakdar J. Creation and amplification of electromagnon solitons by electric field in nanostructured multiferroics. Phys. Rev. B, 2015, 91, 041408(R).Khomeriki R., Chotorlishvili L., Malomed B. A., Berakdar J. Creation and amplification of electromagnon solitons by electric field in nanostructured multiferroics. Phys. Rev. B, 2015, 91, 041408(R).Bandyopadhyay A.K., Ray P.C., Gopalan V. Solitons and critical breakup fields in lithium niobate type uniaxial ferroelectrics. Europ. Phys. Journal B, 2008, 65 (4), P. 525–531.Bandyopadhyay A.K., Ray P.C., Gopalan V. Solitons and critical breakup fields in lithium niobate type uniaxial ferroelectrics. Europ. Phys. Journal B, 2008, 65 (4), P. 525–531.Hoogeboom C., Kevrekidis P.G., Saxena A., Bishop A.R. Discrete breathers in a nonlinear polarizability model of ferroelectrics. Phys. Rev. E, 2012, 86 (6), 066601 (8 pp.).Hoogeboom C., Kevrekidis P.G., Saxena A., Bishop A.R. Discrete breathers in a nonlinear polarizability model of ferroelectrics. Phys. Rev. E, 2012, 86 (6), 066601 (8 pp.).Burgel V., Kleemann W., Bianchi U. Optical second-harmonic generation at interfaces of ferroelectric nanoregions in SrSiO3:Ca. Phys. Rev. B, 1996, 53 (9), P. 5222–5230.Burgel V., Kleemann W., Bianchi U. Optical second-harmonic generation at interfaces of ferroelectric nanoregions in SrSiO3:Ca. Phys. Rev. B, 1996, 53 (9), P. 5222–5230.Yan Sheng, Qian Kong, et al. Theoretical study of Cherenkov-type second-harmonic generation in periodically poled ferroelectric crystals. J. Opt. Soc. Amer. B, 2012, 29 (3), P. 312–318.Yan Sheng, Qian Kong, et al. Theoretical study of Cherenkov-type second-harmonic generation in periodically poled ferroelectric crystals. J. Opt. Soc. Amer. B, 2012, 29 (3), P. 312–318.Mishina E.D., Sherstyuk N.E., et al. Nonlinear-optical probing of nanosecond ferroelectric switching. Appl. Phys. Lett., 2003, 83 (12), P. 2402–2404.Mishina E.D., Sherstyuk N.E., et al. Nonlinear-optical probing of nanosecond ferroelectric switching. Appl. Phys. Lett., 2003, 83 (12), P. 2402–2404.Landau L.D., Pitaevskii L.P., Lifshitz E.M. Electrodynamics of Continuous Media. Elsevier Butterworth- Heinemann, Oxford, 2000.Landau L.D., Pitaevskii L.P., Lifshitz E.M. Electrodynamics of Continuous Media. Elsevier Butterworth- Heinemann, Oxford, 2000.Ginzburg V.L. On a dielectric properties of a segnetoelectrics and barium titanate. JETP, 1945, 15, P. 739–742 (in Russian).Ginzburg V.L. On a dielectric properties of a segnetoelectrics and barium titanate. JETP, 1945, 15, P. 739–742 (in Russian).Ginzburg V.L. Theory of segnetoelectric phenomena. Usp. Fiz. Nauk, 1949, 38 (8), P. 490–525 (in Russian).Ginzburg V.L. Theory of segnetoelectric phenomena. Usp. Fiz. Nauk, 1949, 38 (8), P. 490–525 (in Russian).Devonshire A.F. Theory of barium titanate. I. Philos. Mag., 1949, 40, P. 1040.Devonshire A.F. Theory of barium titanate. I. Philos. Mag., 1949, 40, P. 1040.Ginzburg V.L. Phase transitions in ferroelectrics: some historical remarks. Phys. Usp., 2001, 44 (10), P. 1037–1043.Ginzburg V.L. Phase transitions in ferroelectrics: some historical remarks. Phys. Usp., 2001, 44 (10), P. 1037–1043.Born M., Wolf E. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light. Seventh (expanded) ed., Cambridge Univ. Press, Cambridge, UK, 2003.Born M., Wolf E. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light. Seventh (expanded) ed., Cambridge Univ. Press, Cambridge, UK, 2003.Portengen T., Ostreich Th., Sham L.J. Theory of electronic ferroelectricity. Phys. Rev. B, 1996, 54 (24), P. 17452–17463.Portengen T., Ostreich Th., Sham L.J. Theory of electronic ferroelectricity. Phys. Rev. B, 1996, 54 (24), P. 17452–17463.Batista C.D., Gubernatis J.E., Wei-Guo Yin. Electronic mechanism for the coexistence of ferroelectricity and ferromagnetism. Phys. Rev. B, 2007, 75 (1), 014423 (5 pp.).Batista C.D., Gubernatis J.E., Wei-Guo Yin. Electronic mechanism for the coexistence of ferroelectricity and ferromagnetism. Phys. Rev. B, 2007, 75 (1), 014423 (5 pp.).Ishihara S. Electronic Ferroelectricity and Frustration. J. Phys. Soc. Jpn., 2010, 79 (01), 011010 (11 pp.).Ishihara S. Electronic Ferroelectricity and Frustration. J. Phys. Soc. Jpn., 2010, 79 (01), 011010 (11 pp.).Jie Wang, Tong-Yi Zhang. Size effects in epitaxial ferroelectric islands and thin films. Phys. Rev. B, 2006, 73 (14), 144107 (11 pp.).Jie Wang, Tong-Yi Zhang. Size effects in epitaxial ferroelectric islands and thin films. Phys. Rev. B, 2006, 73 (14), 144107 (11 pp.).Val’kov A.Yu., Kuzmin V.L., et al. Boundary effect on multiple scattering of elastic waves in a half-space. Nanosystems: Physics, Chemistry, Mathematics, 2015, 6 (4), P. 524–536.Val’kov A.Yu., Kuzmin V.L., et al. Boundary effect on multiple scattering of elastic waves in a half-space. Nanosystems: Physics, Chemistry, Mathematics, 2015, 6 (4), P. 524–536.

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