Solitary waves in optical fibers governed by higher-order dispersion

An exact solitary wave solution is presented for the nonlinear Schrödinger equation governing the propagation of pulses in optical fibers including the effects of second-, third-, and fourth-order dispersions. The stability of this solitonlike solution with a ${\mathrm{sech}}^2$ shape is proven. The main criteria governing the existence of such stable localized pulses propagating in optical fibers are also formulated. A unique feature of these solitonlike optical pulses propagating in a fiber with higher-order dispersion is that their parameters satisfy efficient scaling relations. The main term of the perturbation theory describing ultrashort localized pulses is also presented when absorption or gain is included in the nonlinear Schrödinger equation. We anticipate that this type of stable localized pulses could find practical applications in communications, slow-light devices, and ultrafast lasers.

Figure 1

Shape $\left|U\right|=u_{\lambda }{\mathrm{sech}}^2\left(w_{\lambda }T\right)$ of the soliton for $\lambda ={\lambda }_n\text{:}{\lambda }_0=0,{\lambda }_1=\pm 0.6,{\lambda }_2=\pm 0.9,{\lambda }_3=\pm 1.2$, and ${\lambda }_4=\pm 1.5$. Peak of amplitude monotonically decreases for increasing $|{\lambda }_n|$.

Figure 2

Inverse velocity $v_{\lambda }^{-1}$ (solid line) and inverse temporal width $w_{\lambda }$ (dashed line) of the soliton for $-\sqrt{8/3}<\lambda <\sqrt{8/3}$.

Figure 3

Energy $E_{\lambda }$ (solid line) and momentum $M_{\lambda }$ (dashed line) of the soliton for interval $-\sqrt{8/3}<\lambda <\sqrt{8/3}$.