## Abstract

We study semianalytically soliton dynamics in a soliton-based communication line for which the amplifier spacing is larger than the soliton period (referred to as the quasi-adiabatic regime). This regime allows us to overcome the limit on the soliton duration (*T*_{FWHM} ~ 15 ps) imposed by the average-soliton regime. Our calculations show that periodically stable propagation of short solitons (*T*_{FWHM} = 1–5 ps) is possible for an amplifier spacing ranging from 5 to 20 km. We discuss the dynamical features associated with the propagation of short solitons in the quasi-adiabatic regime and present a simple model capable of predicting the width and the mean frequency of the steady-state soliton. We compare the model with appropriate numerical simulations. Our analysis may also be applied to fiber lasers that produce ultrashort solitons (*T*_{FWHM} < 1 ps) in a relatively long-cavity configuration.

© 1995 Optical Society of America

Full Article |

PDF Article
### Equations (11)

Equations on this page are rendered with MathJax. Learn more.

(1)
$$G({\nu}_{0},{u}_{0})\hspace{0.17em}L=1,$$
(2)
$$\mathrm{\Delta}{\nu}_{\text{amp}}({\nu}_{0},{u}_{0})+\mathrm{\Delta}{\nu}_{\text{SSFS}}({u}_{0})=0,$$
(3)
$$G({\nu}_{0},{u}_{0})=\frac{{\int}_{-\infty}^{\infty}{G}_{L}(\nu )\mid v(\nu ){\mid}^{2}\hspace{0.17em}\text{d}\nu}{{\int}_{-\infty}^{\infty}\mid v(\nu ){\mid}^{2}\text{d}\nu},$$
(4)
$${G}_{L}(\nu )={L}_{I}\hspace{0.17em}\text{exp}\{{g}_{0}/[1+{(\nu /\mathrm{\Delta}{\nu}_{G})}^{2}]\},$$
(5)
$$L=\text{exp}(-\alpha {z}_{a})(1-{L}_{\text{FSA}}),$$
(6)
$$\mathrm{\Delta}{\nu}_{\text{amp}}({\nu}_{0},{u}_{0})=\frac{{\int}_{-\infty}^{\infty}\nu \hspace{0.17em}{G}_{L}(\nu )\mid v(\nu ){\mid}^{2}\text{d}\nu}{{\int}_{-\infty}^{\infty}{G}_{L}(\nu )\mid v(\nu ){\mid}^{2}\text{d}\nu}.$$
(7)
$$\frac{\partial {\nu}_{0}(z)}{\partial z}=-\frac{4}{15\pi}\frac{{T}_{R}}{{T}_{0}}\frac{1}{{{\tau}_{p}}^{4}(z)},$$
(8)
$${\tau}_{p}(z)={\tau}_{p}(0)\text{exp}(\alpha z).$$
(9)
$$\mathrm{\Delta}{\nu}_{\text{SSFS}}({u}_{0})=\frac{{T}_{R}[1-\text{exp}(4\alpha {z}_{a})}{15\pi \alpha {T}_{0}}{{u}_{0}}^{4},$$
(10)
$${G}_{0}({z}_{a})=\frac{{E}_{G}\hspace{0.17em}\text{exp}(\alpha {z}_{a})}{1-{L}_{\text{FSA}}},$$
(11)
$$\frac{\partial u}{\partial z}+\frac{i}{2}{\beta}_{2}\frac{{\partial}^{2}u}{\partial {t}^{2}}-i\mid u{\mid}^{2}u=-\frac{\alpha}{2}u-{T}_{R}u\frac{\partial \mid u{\mid}^{2}}{\partial t}+\frac{{\beta}_{3}}{6}\frac{{\partial}^{3}u}{\partial {t}^{3}},$$