Theory of compression of optical pulses in a nonlinear fibre waveguide

A variational approach to an analysis of soliton evolution is used to generalise the equations of perturbation theory of solitons in the adiabatic approximation. The formalism developed in this way is used to discuss the propagation of a two-frequency short optical pulse in a nonlinear fibre. It is shown that when the energy of a pulse exceeds a certain critical threshold $W_c$, the pulse is self-compressed. The value of $W_c$ is governed not only by the nonlinear characteristics of the fibre waveguide, but also by the effective dispersion constants $\widetilde\sigma$ of the group velocities, in such a way that $W_c\sim\widetilde\sigma$. Selection of the frequencies and partial energies of the carrier waves in a given pulse makes it possible to vary the value of $\widetilde\sigma$ over a wide range and to alter the self-compression threshold $W_c$.