We investigate the onset of vector solitons in a three level, cascade, atomic system. We present an existence curve in the model parameter space for bright vector solitons. Approximate analytical solutions are given and the stability of the solutions discussed. Numerical simulations confirm the analytical predictions. References M. Segev. Optical spatial solitons. Optical and Quantum Electronics, 30, 1998, 503--533. J. Li, J. Liu and X. Yang. Superluminal optical soliton via resonant tunneling in coupled quantum dots. Physica E, 40, 2008, 2916--2920. doi:10.1016/j.physe.2008.02.004 G. Huang, L. Deng and M. G. Payne. Dynamics of ultraslow optical solitons in a cold three-state atomic system. Phys. Rev. E, 72, 2005, 016617. doi:10.1103/PhysRevE.72.016617 N. A. Ansari, Z. Jovanoski, H. S. Sidhu and I. N. Towers. Non-linear interaction of two intense fields with a three-level atomic system. J. Nonlin. Opt. Phys. Mat., 15, 2006, 401--413. doi:10.1142/S0218863506003402 N. A. Ansari, I. N. Towers, Z. Jovanoski and H. S. Sidhu. A semi-classical approach to two-frequency solitons in a three-level cascade atomic system. Opt. Commun., 274, 2007, 66--73. doi:10.1016/j.optcom.2007.02.019 C. R. Menyuk, IEEE J. Quantum Electron., {QE-23}, 174 (1987). Y. S. Kivshar and G. P. Agrawal. Optical Solitons: From fibers to photonic crystals, Chapter 9, San Diego: Academic Press, 2003. N. N. Akhmediev and A. Ankiewicz. Solitons: Nonlinear pulses and beams, p.27, London : Chapman and Hall, 1997. S. Flugge. Practical quantum mechanics, Vol. 1, pg. 94--100, Berlin; New York : Springer-Verlag, 1971. A. W. Snyder and J. D. Love. Optical Waveguide Theory, pp. 264--8, London; New York : Chapman and Hall, 1983. F. W. J. Olver. Introduction to Asymptotics and Special Functions, p.169, New York; London: Academic Press, 1974. L. F. Shampine, P. H. Muir and H. Xu. A User-Friendly BVP solver. JNAIAM, 1, 2006, 201--17. http://cs.stmarys.ca/ muir/JNAIAM_Shampine_Muir_Xu2006.pdf O. V. Sinkin, R. Holzlohner, J. Zweck and C. R. Menyuk. Optimization of the Split-Step Fourier Method in Modeling Optical-Fiber Communications Systems. J. Lightw. Technol., 21, 2003, 61--8. doi:10.1109/JLT.2003.808628
We investigate the onset of vector solitons in a three level, cascade, atomic system. We present an existence curve in the model parameter space for bright vector solitons. Approximate analytical solutions are given and the stability of the solutions discussed. Numerical simulations confirm the analytical predictions. References M. Segev. Optical spatial solitons. Optical and Quantum Electronics, 30, 1998, 503--533. J. Li, J. Liu and X. Yang. Superluminal optical soliton via resonant tunneling in coupled quantum dots. Physica E, 40, 2008, 2916--2920. doi:10.1016/j.physe.2008.02.004 G. Huang, L. Deng and M. G. Payne. Dynamics of ultraslow optical solitons in a cold three-state atomic system. Phys. Rev. E, 72, 2005, 016617. doi:10.1103/PhysRevE.72.016617 N. A. Ansari, Z. Jovanoski, H. S. Sidhu and I. N. Towers. Non-linear interaction of two intense fields with a three-level atomic system. J. Nonlin. Opt. Phys. Mat., 15, 2006, 401--413. doi:10.1142/S0218863506003402 N. A. Ansari, I. N. Towers, Z. Jovanoski and H. S. Sidhu. A semi-classical approach to two-frequency solitons in a three-level cascade atomic system. Opt. Commun., 274, 2007, 66--73. doi:10.1016/j.optcom.2007.02.019 C. R. Menyuk, IEEE J. Quantum Electron., {QE-23}, 174 (1987). Y. S. Kivshar and G. P. Agrawal. Optical Solitons: From fibers to photonic crystals, Chapter 9, San Diego: Academic Press, 2003. N. N. Akhmediev and A. Ankiewicz. Solitons: Nonlinear pulses and beams, p.27, London : Chapman and Hall, 1997. S. Flugge. Practical quantum mechanics, Vol. 1, pg. 94--100, Berlin; New York : Springer-Verlag, 1971. A. W. Snyder and J. D. Love. Optical Waveguide Theory, pp. 264--8, London; New York : Chapman and Hall, 1983. F. W. J. Olver. Introduction to Asymptotics and Special Functions, p.169, New York; London: Academic Press, 1974. L. F. Shampine, P. H. Muir and H. Xu. A User-Friendly BVP solver. JNAIAM, 1, 2006, 201--17. http://cs.stmarys.ca/ muir/JNAIAM_Shampine_Muir_Xu2006.pdf O. V. Sinkin, R. Holzlohner, J. Zweck and C. R. Menyuk. Optimization of the Split-Step Fourier Method in Modeling Optical-Fiber Communications Systems. J. Lightw. Technol., 21, 2003, 61--8. doi:10.1109/JLT.2003.808628
We study the propagation dynamics of a single pair of probe and coupling laser pulses in a three-level cascade atomic medium by numerical solving the Maxwell-Bloch equations for atoms and fields. Influences of the pulse durations, intensity and pulse area of the coupling laser on the probe laser propagation are investigated. We found the conditions that the undistorted probe pulse in such i.e., the effect is established. Under conditions, the ground state population is trapped in a dark state. Full Text: PDF References A. Imamoglu, S.E. Harris, Lasers without inversion: interference of dressed lifetime-broadened states, Opt. Lett. 14 (1989) 1344. CrossRef K.J. Boller, A. Imamoglu, S.E. Harris, Observation of electromagnetically induced transparency, Phys. Rev. Lett. 66 (1991) 2593. CrossRef A.S. Zibrov, M.D. Lukin, D.E. Nikonov, L. Hollberg, M.O. Scully, V.L. Velichansky, and H.G. Robinson, Experimental Demonstration of Laser Oscillation without Population Inversion via Quantum Interference in Rb, Phys. Rev. Lett. 75 (1995) 1499. CrossRef L.V. Hau, S. E. Harris, Z. Dutton, C.H. Bejroozi, speed reduction to 17 metres per second in an ultracold atomic gas, Nature, 397 (1999) 594. CrossRef L.V. Doai, D.X. Khoa, and N.H. Bang, EIT enhanced self-Kerr nonlinearity in the three-level lambda system under Doppler broadening, Phys. Scr. 90 (2015)045502. CrossRef D.X. Khoa, L.V. Doai, D.H. Son, and N.H. Bang, Enhancement of self-Kerr nonlinearity via electromagnetically induced transparency in a five-level cascade system: an analytical approach, J. Opt. Soc. Am. B, 31, N6 (2014), pp. 1330. CrossRef F.T. Hioe and R. Grobe, Matched Optical Solitary Waves for Three- and Five-Level Systems, Phys. Rev. Lett. 73, (1994) 2559. CrossRef S.E. Harris and Z.F. Luo, Preparation energy for electromagnetically induced transparency, Phys. Rev. A. 52 (1995) R928. CrossRef V. G. Arkhipkin, I.V. Timofeev, Adiabatic propagation of short pulses under conditions of electromagnetically induced transparency, Quantum Electronics, 30 (2000) 180. CrossRef M. Kiffner, T. N. Dey, Dynamical control of pulse propagation in electromagnetically induced transparency, Phys. Rev. A. 79 (2009) 023829. CrossRef R. Yu, J. Li, P. Huang, A. Zheng, X. Yang, Dynamic control of light propagation and optical switching through an RF-driven cascade-type atomic medium, Phys. Lett. A. 373 (2009) 2992. CrossRef E. Paspalakis,N. J. Kylstra and P. L. Knight, Propagation and nonlinear generation dynamics in a coherently prepared four-level system, Phys. Rev. A 65 (2002) 053808. CrossRef E. Ignesti, R. Buffa, L. Fini, E. Sali, M. V. Tognetti, S. Cavalieri, Controlling the propagation of broadband light pulses by Induced Transparency, Opt. Commun, 285 (2012) 1185. CrossRef P. R. Bermanand C. H. Raymond Ooi, Pulse propagation in a medium of ?-type atoms, Phys. Rev. A 86 (2012), 053812. CrossRef G. Buica, T. Nakajima, Propagation of two short laser pulse trains in a ?-type three-level medium under conditions of electromagnetically induced transparency, Opt. Commun. 332 (2014) 59. CrossRef L. V. Doai, P. V. Trong, D. X. Khoa, and Ng. H. Bang, Electromagnetically induced transparency in five-level cascade scheme of 85Rb atoms: An analytical approach, Optik, 125 (2014) 3666?3669. CrossRef J.H. Eberly, Transmission of dressed fields in three-level media, Quantum Semiclass. Opt. 7 (1995) 373. CrossRef M.D. Crisp, Propagation of Small-Area Pulses of Coherent Light through a Resonant Medium, Phys. Rev. A 1 (1970) 1604. CrossRef
We study the propagation dynamics of a single pair of probe and coupling laser pulses in a three-level cascade atomic medium by numerical solving the Maxwell-Bloch equations for atoms and fields. Influences of the pulse durations, intensity and pulse area of the coupling laser on the probe laser propagation are investigated. We found the conditions that the undistorted probe pulse in such medium, i.e., the EIT effect is established. Under EIT conditions, the ground state population is trapped in a dark state. Full Text: PDF References A. Imamoglu, S.E. Harris, "Lasers without inversion: interference of dressed lifetime-broadened states", Opt. Lett. 14 (1989) 1344. CrossRef K.J. Boller, A. Imamoglu, S.E. Harris, "Observation of electromagnetically induced transparency", Phys. Rev. Lett. 66 (1991) 2593. CrossRef A.S. Zibrov, M.D. Lukin, D.E. Nikonov, L. Hollberg, M.O. Scully, V.L. Velichansky, and H.G. Robinson, "Experimental Demonstration of Laser Oscillation without Population Inversion via Quantum Interference in Rb", Phys. Rev. Lett. 75 (1995) 1499. CrossRef L.V. Hau, S. E. Harris, Z. Dutton, C.H. Bejroozi, "Light speed reduction to 17 metres per second in an ultracold atomic gas", Nature, 397 (1999) 594. CrossRef L.V. Doai, D.X. Khoa, and N.H. Bang, "EIT enhanced self-Kerr nonlinearity in the three-level lambda system under Doppler broadening", Phys. Scr. 90 (2015)045502. CrossRef D.X. Khoa, L.V. Doai, D.H. Son, and N.H. Bang, "Enhancement of self-Kerr nonlinearity via electromagnetically induced transparency in a five-level cascade system: an analytical approach", J. Opt. Soc. Am. B, 31, N6 (2014), pp. 1330. CrossRef F.T. Hioe and R. Grobe, "Matched Optical Solitary Waves for Three- and Five-Level Systems", Phys. Rev. Lett. 73, (1994) 2559. CrossRef S.E. Harris and Z.F. Luo, "Preparation energy for electromagnetically induced transparency", Phys. Rev. A. 52 (1995) R928. CrossRef V. G. Arkhipkin, I.V. Timofeev, "Adiabatic propagation of short pulses under conditions of electromagnetically induced transparency", Quantum Electronics, 30 (2000) 180. CrossRef M. Kiffner, T. N. Dey, "Dynamical control of pulse propagation in electromagnetically induced transparency", Phys. Rev. A. 79 (2009) 023829. CrossRef R. Yu, J. Li, P. Huang, A. Zheng, X. Yang, "Dynamic control of light propagation and optical switching through an RF-driven cascade-type atomic medium", Phys. Lett. A. 373 (2009) 2992. CrossRef E. Paspalakis,N. J. Kylstra and P. L. Knight, "Propagation and nonlinear generation dynamics in a coherently prepared four-level system", Phys. Rev. A 65 (2002) 053808. CrossRef E. Ignesti, R. Buffa, L. Fini, E. Sali, M. V. Tognetti, S. Cavalieri, "Controlling the propagation of broadband light pulses by Electromagnetically Induced Transparency", Opt. Commun, 285 (2012) 1185. CrossRef P. R. Bermanand C. H. Raymond Ooi, "Pulse propagation in a medium of ?-type atoms", Phys. Rev. A 86 (2012), 053812. CrossRef G. Buica, T. Nakajima, "Propagation of two short laser pulse trains in a ?-type three-level medium under conditions of electromagnetically induced transparency", Opt. Commun. 332 (2014) 59. CrossRef L. V. Doai, P. V. Trong, D. X. Khoa, and Ng. H. Bang, "Electromagnetically induced transparency in five-level cascade scheme of 85Rb atoms: An analytical approach", Optik, 125 (2014) 3666?3669. CrossRef J.H. Eberly, "Transmission of dressed fields in three-level media", Quantum Semiclass. Opt. 7 (1995) 373. CrossRef M.D. Crisp, "Propagation of Small-Area Pulses of Coherent Light through a Resonant Medium", Phys. Rev. A 1 (1970) 1604. CrossRef