Nonlinear Optics of Photons and Atoms
Cao Long V. 1, Khoa Dinh Xuan 2, Trippenbach Marek 3
1 Institute of Physics, University of Zielona Góra
ul. Prof. Szafrana 4a, 65-516 Zielona Góra, Poland
e-mail: vanlongcao@yahoo.com
2Vinh University, 182 Le Duan str., Vinh, Nghe An, Vietnam
3Department of Physics, Warsaw University
ul. Hoża 69, 00-681 Warsaw, Poland
Received:
Received: 29 June 2010; accepted: 13 September 2010
DOI: 10.12921/cmst.2010.SI.02.73-76
OAI: oai:lib.psnc.pl:705
Abstract:
In this presentation we intend to focus on the exchange of experience between nonlinear optics (optical pulse and beam propagation in nonlinear media) and atom optics (dynamics of coherent waves generated from Bose-Einstein condensates). A common ground here is the nonlinear Schrödinger equation, which with the proper substitution of variables describes both types of phenomena. In nonlinear optics it is a light propagation equation that relates the signal at the end of the nonlinear crystal to the signal at the input face of the medium. In Bose-Einstein condensate dynamics it is the called the Gross-Pitaevskii equation. We will discuss various types of phenomena which have realisations both in the nonlinear optics and atom optics. We will concentrate our consideration on soliton formation, which is a challenge to fundamental and applied research in these two domains of physics.
Key words:
atom optics; Gross-Pitaevskii equation, soliton; nonlinear optics
References:
[1] Cao Long Van, M. Trippenbach, New Optical Solitary waves in the higher order nonlinear Schrödinger Equation. Scientific Biuletin 126, Technical University of Zielona Gora, Poland 2001, p. 19 (Cao Long Van ed.).
[2] V. Cao Long, H. Nguyen Viet, M. Trippenbach, K. Dinh Xuan, Propagation Technique for Ultrashort Pulses I. Computational Methods in Science and Technology 14 (1), 5 (2008).
[3] V. Cao Long, H. Nguyen Viet, M. Trippenbach, K. Dinh Xuan, Propagation Technique for Ultrashort Pulses II. Computational Methods in Science and Technology 14 (1), 13 (2008).
[4] V. Cao Long, H. Nguyen Viet, M. Trippenbach, K. Dinh Xuan, Propagation Technique for Ultrashort Pulses III. Computational Methods in Science and Technology 14(1), 21 (2008).
[5] Cao Long Van, P.P. Goldstein, A concise Course in nonlinear Partial Differential Equations, University of Zielona Gora (2008).
[6] A.V. Buryak, Yu. S. Kivshar, Phys. Lett. A197, 407 (1995).
[7] M. Trippenbach, M. Matuszeski, E. Infreld, Cao Long Van, R.S. Tasgal, J.B. Band, Enhancement of third harmonic generation by wave vector mismatch to counter phasemodulation. Optics Communications 229, 391 (2004).
[8] M. Matuszewski, M. Trippenbach, B.A. Malomed, E. Infeld, A.A. Skorupki, Two dimensional dispersion managed light bullets in a Kerr medium. Phys. Rev. E70, 016603 (2004).
[9] Nguyen Viet Hung, Cao Long Van, M. Trippenbach, Stability of two dimensional dispersion managed light bullet in a Kerr medium. Communications in Physics 17, suppl. 51 (2007).
[10] Y. Silberberg, Collapse of optical pulses. Opt. Lett. 15, 1282 (1990).
[11] K. Hayata, M. Koshiba, Multidimensional solitons in quadratic nonlinear media. Phys. Rev. Lett. 71, 3275 (1993).
[12] X. Liu, L.J. Qian, F.W. Wise, Generation of Optical Spatiotemporal Solitons. Phys. Rev. Lett. 82, 4631 (1999).
[13] B.A. Malomed, D. Mihalache, F. Wise, L. Torner, Spatiotemporal optical solitons. J. Opt. B: Quant. Semicl. Opt. 7, R53 (2205).
[14] L. Berge’, Wave collapse in physics: principles and applications to light and plasma waves. Phys. Rev. 303, 259 (1998).
[15] D.E. Edmundson, R.H. Enns, Roust bistable light bullets. Opt. Lett. 17, 586 (1992).
[16] D. Mihalache at el., Stable spinning optical solitons in three dimensions. Phys. Rev. Lett. 88, 073902, 1-4 (2002).
[17] I. Towers, B.A Malomed, Stable (2+1)-dimensional solitons in a layered medium with sign-alternating Kerr nonlinearlity. J. Opt. Soc. Am. B19, 537 (2002).
[18] P. Di Trapani et al., Observation of Temporal Solitons in Second – Harmonic Generation with Tilted Pulses. Phys. Rev. Lett. 81, 570 (1998).
[19] M. Trippenbach et al., Two-and three-dimensional light bullets in a Kerr medium with dispersion management. (to be published in Phys. Rev. A).
[20] J.H.B. Nijhof, N.J. Doran, W. Forysiak, F.M. Knox, Stable soliton like propagation in dispersion managed systems with net anomalous, zero and normal dispersion. Electron. Lett. 33, 1726 (1997).
[21] Dinh Xuan Khoa, Cao Long Van, M. Trippenbach, Nonlinear Optics of Photons and Atoms. Proceeding of National Conference on Theoretical Physics, Hue, Vietnam, 15-18 August 2005.
[22] M. Trippenbach, Cao Long Van, Vu Ngoc Sau, Nguyen Huy Bang, Bragg scattering of Bose-Einstein Condensates an Imaginary Time Method. Proceeding of National
Conference on Theoretical Physics, Sam son, Vietnam, 12-14 August 2003.
[23] H. Staito, M. Ueda, Dynamically Stabilized Bright Solitons in a two Dimensional Bose Einstein. Phys. Rev. Lett. 90, 040403 (2003).
[24] F. Kh. Abdulaev, J.G. Caputo. R.A. Kraenkel, B.A. Malomed, Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length. Phys. Rev. A67, 013605 (2003).
[25] G.D. Montesinos. V.M. Perez-Grarcia, P.J. Torres, Stabilization of soliton of the multidimensional nonlinear Schrödinger equation: Matter-Wave breathers. Physic D191, 193 (2004).
[26] M. Trippenbach, M. Matuszewski, Cao Long Van, E. Infeld, B.A. Malomed, Fully three-dimensional breather solitons can be created using Feshbach resonance. Communications in Physics 17, suppl. 111 (2007).
In this presentation we intend to focus on the exchange of experience between nonlinear optics (optical pulse and beam propagation in nonlinear media) and atom optics (dynamics of coherent waves generated from Bose-Einstein condensates). A common ground here is the nonlinear Schrödinger equation, which with the proper substitution of variables describes both types of phenomena. In nonlinear optics it is a light propagation equation that relates the signal at the end of the nonlinear crystal to the signal at the input face of the medium. In Bose-Einstein condensate dynamics it is the called the Gross-Pitaevskii equation. We will discuss various types of phenomena which have realisations both in the nonlinear optics and atom optics. We will concentrate our consideration on soliton formation, which is a challenge to fundamental and applied research in these two domains of physics.
Key words:
atom optics; Gross-Pitaevskii equation, soliton; nonlinear optics
References:
[1] Cao Long Van, M. Trippenbach, New Optical Solitary waves in the higher order nonlinear Schrödinger Equation. Scientific Biuletin 126, Technical University of Zielona Gora, Poland 2001, p. 19 (Cao Long Van ed.).
[2] V. Cao Long, H. Nguyen Viet, M. Trippenbach, K. Dinh Xuan, Propagation Technique for Ultrashort Pulses I. Computational Methods in Science and Technology 14 (1), 5 (2008).
[3] V. Cao Long, H. Nguyen Viet, M. Trippenbach, K. Dinh Xuan, Propagation Technique for Ultrashort Pulses II. Computational Methods in Science and Technology 14 (1), 13 (2008).
[4] V. Cao Long, H. Nguyen Viet, M. Trippenbach, K. Dinh Xuan, Propagation Technique for Ultrashort Pulses III. Computational Methods in Science and Technology 14(1), 21 (2008).
[5] Cao Long Van, P.P. Goldstein, A concise Course in nonlinear Partial Differential Equations, University of Zielona Gora (2008).
[6] A.V. Buryak, Yu. S. Kivshar, Phys. Lett. A197, 407 (1995).
[7] M. Trippenbach, M. Matuszeski, E. Infreld, Cao Long Van, R.S. Tasgal, J.B. Band, Enhancement of third harmonic generation by wave vector mismatch to counter phasemodulation. Optics Communications 229, 391 (2004).
[8] M. Matuszewski, M. Trippenbach, B.A. Malomed, E. Infeld, A.A. Skorupki, Two dimensional dispersion managed light bullets in a Kerr medium. Phys. Rev. E70, 016603 (2004).
[9] Nguyen Viet Hung, Cao Long Van, M. Trippenbach, Stability of two dimensional dispersion managed light bullet in a Kerr medium. Communications in Physics 17, suppl. 51 (2007).
[10] Y. Silberberg, Collapse of optical pulses. Opt. Lett. 15, 1282 (1990).
[11] K. Hayata, M. Koshiba, Multidimensional solitons in quadratic nonlinear media. Phys. Rev. Lett. 71, 3275 (1993).
[12] X. Liu, L.J. Qian, F.W. Wise, Generation of Optical Spatiotemporal Solitons. Phys. Rev. Lett. 82, 4631 (1999).
[13] B.A. Malomed, D. Mihalache, F. Wise, L. Torner, Spatiotemporal optical solitons. J. Opt. B: Quant. Semicl. Opt. 7, R53 (2205).
[14] L. Berge’, Wave collapse in physics: principles and applications to light and plasma waves. Phys. Rev. 303, 259 (1998).
[15] D.E. Edmundson, R.H. Enns, Roust bistable light bullets. Opt. Lett. 17, 586 (1992).
[16] D. Mihalache at el., Stable spinning optical solitons in three dimensions. Phys. Rev. Lett. 88, 073902, 1-4 (2002).
[17] I. Towers, B.A Malomed, Stable (2+1)-dimensional solitons in a layered medium with sign-alternating Kerr nonlinearlity. J. Opt. Soc. Am. B19, 537 (2002).
[18] P. Di Trapani et al., Observation of Temporal Solitons in Second – Harmonic Generation with Tilted Pulses. Phys. Rev. Lett. 81, 570 (1998).
[19] M. Trippenbach et al., Two-and three-dimensional light bullets in a Kerr medium with dispersion management. (to be published in Phys. Rev. A).
[20] J.H.B. Nijhof, N.J. Doran, W. Forysiak, F.M. Knox, Stable soliton like propagation in dispersion managed systems with net anomalous, zero and normal dispersion. Electron. Lett. 33, 1726 (1997).
[21] Dinh Xuan Khoa, Cao Long Van, M. Trippenbach, Nonlinear Optics of Photons and Atoms. Proceeding of National Conference on Theoretical Physics, Hue, Vietnam, 15-18 August 2005.
[22] M. Trippenbach, Cao Long Van, Vu Ngoc Sau, Nguyen Huy Bang, Bragg scattering of Bose-Einstein Condensates an Imaginary Time Method. Proceeding of National
Conference on Theoretical Physics, Sam son, Vietnam, 12-14 August 2003.
[23] H. Staito, M. Ueda, Dynamically Stabilized Bright Solitons in a two Dimensional Bose Einstein. Phys. Rev. Lett. 90, 040403 (2003).
[24] F. Kh. Abdulaev, J.G. Caputo. R.A. Kraenkel, B.A. Malomed, Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length. Phys. Rev. A67, 013605 (2003).
[25] G.D. Montesinos. V.M. Perez-Grarcia, P.J. Torres, Stabilization of soliton of the multidimensional nonlinear Schrödinger equation: Matter-Wave breathers. Physic D191, 193 (2004).
[26] M. Trippenbach, M. Matuszewski, Cao Long Van, E. Infeld, B.A. Malomed, Fully three-dimensional breather solitons can be created using Feshbach resonance. Communications in Physics 17, suppl. 111 (2007).
