Ported from Self-Similar Analytic Solutions of Ginzburg--Landau Equation with Varying Coefficients
FENG Jie1, XU Wen-Cheng2, LI Shu-Xian2, LIU Wei-Ci2, LIU Song-Hao2
1School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 5100062Lab of Photonic information Technology, School of Information and Optoelectronic Science and Engineering, South China Normal University, Guangzhou 510006
Ported from Self-Similar Analytic Solutions of Ginzburg--Landau Equation with Varying Coefficients
1School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 5100062Lab of Photonic information Technology, School of Information and Optoelectronic Science and Engineering, South China Normal University, Guangzhou 510006
摘要Employing the technique of symmetry reduction of analytic method, we solve the Ginzburg--Landau equation with varying nonlinear, dispersion, gain coefficients, and gain dispersion which originates from the limiting effect of transition bandwidth in the realistic doped fibres. The parabolic asymptotic self-similar analytical solutions in gain medium of the normal GVD is found for the first time to our best knowledge. The evolution of pulse amplitude, strict linear phase chirp and effective temporal width are given with self-similarity results in longitudinal nonlinearity distribution and longitudinal gain fibre. These analytical solutions are in good agreement with the numerical simulations. Furthermore, we theoretically prove that pulse evolution has the characteristics of parabolic asymptotic self-similarity in doped ions dipole gain fibres.
Abstract：Employing the technique of symmetry reduction of analytic method, we solve the Ginzburg--Landau equation with varying nonlinear, dispersion, gain coefficients, and gain dispersion which originates from the limiting effect of transition bandwidth in the realistic doped fibres. The parabolic asymptotic self-similar analytical solutions in gain medium of the normal GVD is found for the first time to our best knowledge. The evolution of pulse amplitude, strict linear phase chirp and effective temporal width are given with self-similarity results in longitudinal nonlinearity distribution and longitudinal gain fibre. These analytical solutions are in good agreement with the numerical simulations. Furthermore, we theoretically prove that pulse evolution has the characteristics of parabolic asymptotic self-similarity in doped ions dipole gain fibres.
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2008, Vol. 25 
