tailieunhanh - Propagation of ultrashort pulses in nonlinear media

In this paper, a general propagation equation of ultrashort pulses in an arbitrary dispersive nonlinear medium has been used for the case of Kerr media. This equation which is called Generalized Nonlinear Schroedinger Equation usually has very complicated form and looking for its solutions is usually a very difficult task. Theoretical methods reviewed in this paper to solve this equation are effective only for some special cases. | Communications in Physics, Vol. 26, No. 4 (2016), pp. 301-323 DOI: Invited Paper PROPAGATION OF ULTRASHORT PULSES IN NONLINEAR MEDIA CAO LONG VAN † Institute of Physics, University of Zielona G´ora, ul. Prof. Szafrana 4a, 65-516 Zielona G´ora, Poland † E-mail: caolongvanuz@ Received 01 January 2017 Accepted for publication 24 February 2017 Abstract. In this paper, a general propagation equation of ultrashort pulses in an arbitrary dispersive nonlinear medium has been used for the case of Kerr media. This equation which is called Generalized Nonlinear Schroedinger Equation usually has very complicated form and looking for its solutions is usually a very difficult task. Theoretical methods reviewed in this paper to solve this equation are effective only for some special cases. As an example we describe the method of developed elliptic Jacobi function expansion and its expended form: F-expansion Method. Several numerical methods of finding approximate solutions are briefly discussed. We concentrate mainly on the methods: Split-Step, Runge-Kutta and Imaginary-time algorithms. Some numerical experiments are implemented for soliton propagation and interacting high order solitons. Keywords: ultrashort pulses, Kerr media, generalized nonlinear Schroedinger equation, solitons. Classification numbers: , , , . Hw. I. INTRODUCTION Propagation of ultrashort laser pulses (in fs) in a medium has been intensively considered both theoretically and experimentally during the last few decades [1–4] because of their potential applications in technology. Modern lasers can generate very short pulses with durations on the order of 10−15 seconds. This allows us to look at very fast events, such as molecules vibrating, or charge transfer in biological systems. By manipulating the shape of the pulse and using it to control precisely the quantum phenomena, one can observe the formation of molecules from cold atoms .