Abstract
We consider the problem of propagation of large-intensity monochromatic radiation in a solid with the three-dimensional superlattice of quantum dots interlinked by strong tunneling along one axis. Electrons are treated in a classical way in the formalism of the Boltzmann kinetic equation for the distribution function. Analysis of the Maxwell equations for this case yields a (2+1)-dimensional equation, which has a form similar to the Schrödinger nonlinear equation. Various regimes of the electromagnetic-field propagation were numerically analyzed. The super-Gaussian light beam was found to undergo a waist stage, and the interaction of light beams led to their merging.
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References
Zh. I. Alferov, Usp. Fiz. Nauk, 172, 1068 (2002).
Yu. V. Gulyaev, Usp. Fiz. Nauk, 175, 887 (2005).
F. G. Bass, A. A. Bulgakov, and A. P. Tetervov, High-Frequency Properties of Semiconductors with Superlattices [in Russian], Nauka, Moscow (1989).
M. Herman, Semiconductor Superlattices, Akademie Verlag, Berlin (1986).
A. A. Ignatov and Yu. A. Romanov, Fiz. Tverd. Tela, 17, 3388 (1975).
E. M. Epshtein, Fiz. Tverd. Tela, 19, 3456 (1977).
M. B. Belonenko, Pis’ma Zh. Éksp. Teor. Fiz., 35, 40 (2009).
M. J. Ablowitz and H. Sigur, Solitons and the Inverse Scattering Transform, SIAM, Philadelphia (1981).
Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals, Academic Press, San Diego (2003).
V. E. Zakharov, S. V. Manakov, and S. P. Novikov, Soliton Theory: The Inverse Scattering Method [in Russian], Nauka, Moscow (1980).
L. D. Landau and E. M. Lifshitz, Field Theory [in Russian], Nauka, Moscow (1988).
M. B. Belonenko, E. V. Demushkina, and N. G. Lebedev, J. Russ. Laser Res., 27, 457 (2006).
V. L. Bonch-Bruevich and S. G. Kalashnikov, Semiconductor Physics [in Russian], Nauka, Moscow (1990).
M. B. Belonenko, N. G. Lebedev, and O. Yu. Tuzalina, J. Russ. Laser Res., 30, 102 (2009).
R. Bullough and P. Caudrey (eds.), Solitons, Springer, Berlin (1980).
R. K. Dodd, J. C. Eilenbeck, J. D. Gibbon, and Y. C. Morris, Solitons and Nonlinear Wave Equations, Academic Press, New York (1984).
M. Delfour, J. Comput. Phys., 44, 277 (1981).
V. E. Lobanov, A. K. Sukhorukova, and A. P. Sukhorukov, Kvant. Élektron., 38, 951 (2008).
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Translated from a manuscript submitted first on January 25, 2010 and in final form on February 24, 2010.
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Belonenko, M.B. Nonlinear diffraction in a system of quantum dots. J Russ Laser Res 31, 249–255 (2010). https://doi.org/10.1007/s10946-010-9142-6
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DOI: https://doi.org/10.1007/s10946-010-9142-6