We investigate two types of nonlinear interaction between collinear femtosecond laser pulses with power slightly above the critical for self-focusing Pcr. In the first case we study energy exchange between filaments. The model describes this process through degenerate four-photon parametric mixing (FPPM) scheme and requests initial phase difference between the waves. When there are no initial phase difference between the pulses, the FPPM process does not work. In this case it is obtained the second type of interaction as merging between two, three or four filaments in a single filament with higher power. It is found that in the second case the interflow between the filaments has potential of interaction due to cross-phase modulation (CPM).
We investigate two types of nonlinear interaction between collinear femtosecond laser pulses with power slightly above the critical for self-focusing Pcr. In the first case we study energy exchange between filaments. The model describes this process through degenerate four-photon parametric mixing (FPPM) scheme and requests initial phase difference between the waves. When there are no initial phase difference between the pulses, the FPPM process does not work. In this case it is obtained the second type of interaction as merging between two, three or four filaments in a single filament with higher power. It is found that in the second case the interflow between the filaments has potential of interaction due to cross-phase modulation (CPM).
“…The one-dimensional scalar nonlinear amplitude equation which describes the propagation of optical pulses in isotropic waveguide with Kerr-type nonlinearity in Cartesian coordinate system is [2,7,8] :…”
Section: Solution Of the Nonlinear Amplitude Equationmentioning
It is known that the Nonlinear Schrödinger equation (NLSE) very well describes the evolution of nanosecond and picosecond pulses in isotropic nonlinear dispersive medium. For exploration the propagation of femtosecond and attosecond light pulses it is necessary to be used the more general nonlinear amplitude equation. Therefore it is important to clarify the difference between the solutions of these two equations.In the present paper are investigated the one-dimensional soliton solutions of the NLSE and the nonlinear amplitude equation describing the evolution of optical pulses in a single-mode fiber with negative dispersion of the group velocity. It is shown that for a fundamental soliton the main difference between the two solutions is in the phases of the pulses. It is also seen that the soliton obtained in our work is with the same width as this of the NLSE but with an amplitude 2 times greater.
The well-known (1+1D) nonlinear Schrödinger equation (NSE) governs the propagation of narrow-band pulses in optical fibers and others one-dimensional structures. For exploration the evolution of broad-band optical pulses (femtosecond and attosecond) it is necessary to use the more general nonlinear amplitude equation (GNAE) which differs from NSE with two additional non-paraxial terms. That is way, it is important to make clear the difference between the solutions of these two equations. We found a new analytical soliton solution of GNAE and compare it with the well-known NSE one. It is shown that for the fundamental soliton the main difference between the two solutions is in their phases. It appears that, this changes significantly the evolution of optical pulses in multisoliton regime of propagation and admits a behavior different from that of the higher-order NSE solitons.
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