## Abstract

We propose a novel all-optical tunable delay line based on soliton self-frequency shift and filtering broadened spectrum due to self-phase modulation to compensate for the frequency shift. We experimentally demonstrate the proposed all-optical tunable delay line and achieve a continuous temporal shift up to 19.2 ps for 0.5 ps pulse, corresponding to a delay-to-pulse-width ratio of 38.4.

©2006 Optical Society of America

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### Equations (9)

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(1)
$$i\frac{\partial E}{\partial z}-\frac{{\beta}_{2}}{2}\frac{{\partial}^{2}E}{\partial {t}^{2}}\text{}+\gamma {\mid E\mid}^{2}E=-igE+i\frac{{\beta}_{3}}{6}\frac{{\partial}^{3}E}{\partial {t}^{3}}\text{}+\gamma {T}_{R}E\frac{\partial {\mid E\mid}^{2}}{\partial t}.$$
(2)
$$q=\frac{E\left[\sqrt{\mathrm{mW}}\right]}{\sqrt{{P}_{0}\left[\mathrm{mW}\right]}},\phantom{\rule{.2em}{0ex}}T=1.763\frac{t\left[\mathrm{ps}\right]}{{t}_{s}\left[\mathrm{ps}\right]},\phantom{\rule{.2em}{0ex}}Z=\frac{z\left[\mathrm{km}\right]}{{z}_{d}\left[\mathrm{km}\right]},$$
(3)
$$i\frac{\partial q}{\partial Z}+\frac{1}{2}\frac{{\partial}^{2}q}{\partial {T}^{2}}+{\mid q\mid}^{2}q={\tau}_{R}q\frac{\partial {\mid q\mid}^{2}}{\partial T},$$
(4)
$$\{\begin{array}{c}{P}_{0}=262.5\frac{{\left(\lambda \left[\mu m\right]\right)}^{3}D\left[\frac{\frac{\mathrm{ps}}{\mathrm{nm}}}{\mathrm{km}}\right]}{\frac{{n}_{2}}{{A}_{\mathrm{eff}}}[\text{}\times \frac{{10}^{-9}}{W}]{\left({t}_{s}\left[\mathrm{ps}\right]\right)}^{2}},\\ {z}_{d}=0.6062\frac{{\left({t}_{s}\left[\mathrm{ps}\right]\right)}^{2}}{{\left(\lambda \left[\mu m\right]\right)}^{2}D\left[\frac{\frac{\mathrm{ps}}{\mathrm{nm}}}{\mathrm{km}}\right]},\phantom{\rule{1.2em}{0ex}}\\ {\tau}_{R}=1.763\frac{{T}_{R}\left[\mathrm{ps}\right]}{{t}_{s}\left[\mathrm{ps}\right]}.\phantom{\rule{5.2em}{0ex}}\end{array}$$
(4)
$$q\left(Z,T\right)=\eta \left(Z\right)\mathrm{sech}\left[\eta \left(Z\right)\left\{T-{T}_{0}\left(Z\right)\right\}\right]\mathrm{exp}\left\{-i\kappa \left(Z\right)T+i\theta \left(Z\right)\right\},$$
(5)
$$\frac{d\eta}{dZ}=0,\phantom{\rule{.2em}{0ex}}\frac{d\kappa}{dZ}=-\frac{8}{15}{\tau}_{R}{\eta}^{4},\phantom{\rule{.2em}{0ex}}\frac{d{T}_{0}}{dZ}\text{}=-\kappa .$$
(6)
$$\eta \left(Z\right)={\eta}_{0},\kappa \left(Z\right)=-\frac{8}{15}{\tau}_{R}{\eta}_{0}^{4}Z,\phantom{\rule{.2em}{0ex}}{T}_{0}\left(Z\right)=\frac{4}{15}{\tau}_{R}{\eta}_{0}^{4}{Z}^{2},$$
(7)
$$q\left(Z=0,T\right)=A\mathrm{sech}\left(T\right).$$
(8)
$$\eta =2A-1,\phantom{\rule{.2em}{0ex}}\left(0.5\le A\text{}<1.5\right).$$