Abstract
The bidirectional propagation and collision of counter-propagating optical solitons in a two-level resonant medium is analyzed. For sufficiently short duration of the pulses and sufficiently high power levels, self-induced transparency allows the pulses to propagate without losses at anomalously low velocities. Here, we use an extended semiclassical approach, called Maxwell–Bloch model. The quantization of the electromagnetic field is neglected, however, a full quantum mechanical formulation is used to describe the behavior of the matter. The numerical simulations are performed by using the method of lines. For improved accuracy, spline interpolation of the fields is introduced. Results are presented to demonstrate the use of soliton collision for all-optical switching, in particular, as OR- and XOR-gates.
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References
Afanasev, A., Volkov, V., Dritz, V., Samson, B.: Interaction of counterpropagating self-induced transparency solitons. J. Mod. Opt. 37, 165–170 (1990)
Agrawal, G.P.: Nonlinear Fiber Optics, 4th edn. Academic Press, Boston (2007)
Alcock, C.B., Itkin, V.P., Horrigan, M.K.: Vapor pressure equations for the metallic elements: 298–2500 K. Can. Metall. Q. 23, 309–313 (1984)
Beeker, W., Lee, C., Can, E., Boller, K.: Storage by trapping and spatial staggering of multiple interacting solitons in \(\varLambda\)-type media. Phys. Rev. Lett. A 82, 053839 (2010)
Curtiss, C.F., Hirschfelder, J.O.: Integration of Stiff equations. Proc. Nat. Acad. Sci. U.S.A. 38, 235–243 (1952)
Frantzeskakis, D.J., Leblond, H., Mihalache, D.: Nonlinear optics of intense few-cycle pulses: an overview of recent theoretical and experimental developments. Rom. J. Phys. 59 (no.7–8), 767–784 (2014)
Hamdi, S., Schiesser, W.E., Griffiths, G.W.: Method of lines. Scholarpedia 2(7), 2859 (2007). https://doi.org/10.4249/scholarpedia.2859
Hildebrand, F.B.: Introduction to Numerical Analysis, 2nd edn. Dover, New York (1987)
Hutzler, M.: Collisions of optical solitons in two-level media. M.Sc. Thesis, FernUniversität in Hagen (2014)
Islam, M., Soccolich, C., Gordon, J.: Ultrafast digital soliton logic gates. Opt. Quantum Electron. 24, 1215–1235 (1992)
Lide, D.R. (ed.): CRC Handbook of Chemistry and Physics, 82nd edn. CRC Press, Boca Raton (2001)
Malomed, B., Mihalache, D., Wise, F., Torner, L.: Spatiotemporal optical solitons. J. Opt. B 7, 53–72 (2005)
McCall, S.L., Hahn, E.: Self-induced transparency. Phys. Rev. Lett. 183, 457–489 (1969)
Miller, D.A.B.: Quantum Mechanics for Scientists and Engineers. Cambridge University Press, Cambridge (2008)
Milonni, W., Eberly, J.: Laser Physics, Chap. 9, Coherence in Atom-Field Interactions. Wiley, New York (2010)
Mohr, P.J., Taylor, B.N., Newell, D.B.: The 2006 CODATA Recommended Values of the Fundamental Physical Constants, Web Version 5.1. available at http://physics.nist.gov/constants (National Institute of Standards and Technology, Gaithersburg, MD 20899, 31 December 2007 (2007). Accessed 1 Aug 2018
Novitsky, D.: Femtosecond pulses in a dense two-level medium: spectral transformations, transient processes, and collisional dynamics. Phys. Rev. Lett. A 84, 013817 (2011)
Novitsky, D.: Controlled absorption and all-optical diode action due to collisions of self-induced-transparency solitons. Phys. Rev. Lett. A 85, 043813 (2012)
Novitsky, D.: Ultrashort pulses in an inhomogeneously broadened two-level medium: soliton formation and inelastic collisions. J. Phys. B Atomic Mol. Opt. Phys. 47, 095401 (2014)
Pregla, R.: Analysis of Electromagnetic Fields and Waves—The Method of Lines. Wiley, Chichester (2008)
Pusch, A., Hamm, J.M., Hess, O.: Controllable interaction of counterpropagating solitons in three-level media. Phys. Rev. A 82, 023805 (2010)
Saleh, B., Teich, M.: Fundamentals of Photonics. Wiley, New York (2007)
Schiesser, W.E., Griffiths, G.W.: A Compendium of Partial Differential Equation Models: Method of Lines Analysis with Matlab. Cambridge University Press, Cambridge (2009)
Shaw, M., Shore, B.: Collisions of counterpropagating optical solitons. J. Opt. Soc. Am. B 8, 1127–1134 (1991)
Slusher, R., Gibbs, H.: Self-induced transparency in atomic rubidium. Phys. Rev. A 5, 1634–1659 (1972)
Steck, D.: Rubidium 87 D Line Data. http://steck.us/alkalidata, vol. revision 2.0.1 (2008)
Valcarcel, G., Roldan, E.: Semiclassical theory of amplification and lasing. Revista Mexicana de Fisica E 52, 198–214 (2006)
Acknowledgements
The analysis presented here was based on earlier work by Hutzler (2014). The advice by Klaus Boller (University of Twente) in this context is greatly appreciated. Furthermore, we thank Marina Haase and Nikolas Henry for reading the manuscript.
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This article is part of the Topical Collection on Optical Wave and Waveguide Theory and Numerical Modelling, OQTNM 2018.
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Spiller, W., Helfert, S.F. & Jahns, J. The numerical investigation of colliding optical solitons as an all-optical-gate using the method of Lines. Opt Quant Electron 51, 131 (2019). https://doi.org/10.1007/s11082-019-1785-0
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DOI: https://doi.org/10.1007/s11082-019-1785-0