## Abstract

We propose a systematic approach to evaluating and optimising the wavelength conversion bandwidth and gain ripple of four-wave mixing based fiber optical wavelength converters. Truly tunable wavelength conversion in these devices requires a highly tunable pump. For a given fiber dispersion slope, we find an optimum dispersion curvature that maximises the wavelength conversion bandwidth.

©2003 Optical Society of America

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### Equations (11)

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(1)
$$2{\omega}_{p}={\omega}_{s}+{\omega}_{c},$$
(2)
$$\Delta \beta =2{\beta}_{p}-{\beta}_{s}-{\beta}_{c}.$$
(3)
$$G={\left(\frac{\gamma {P}_{P}}{g}\mathrm{sinh}\left(gL\right)\right)}^{2},$$
(4)
$${g}^{2}=\frac{1}{4}\left[\Delta \beta \left(4\gamma {P}_{P}-\Delta \beta \right)\right].$$
(5)
$${G}_{max}={\mathrm{sinh}}^{2}\left(\gamma {P}_{P}L\right).$$
(6)
$${G}_{0}={\left(\gamma {P}_{P}L\right)}^{2}.$$
(7)
$$\Delta \beta =-\left({\beta}_{3}\left({\omega}_{p}-{\omega}_{0}\right)+\frac{{\beta}_{4}}{2}\left[{\left({\omega}_{p}-{\omega}_{0}\right)}^{2}+\frac{1}{6}{\left({\omega}_{p}-{\omega}_{s}\right)}^{2}\right]\right){\left({\omega}_{p}-{\omega}_{s}\right)}^{2}.$$
(8)
$$R=\frac{{G}_{max}}{{G}_{0}}={\left(\frac{\mathrm{sinh}\left(\gamma {P}_{P}L\right)}{\gamma {P}_{P}L}\right)}^{2}.$$
(9)
$${\omega}_{S}={\omega}_{p}\pm \sqrt{-\frac{12\Phi}{{\beta}_{4}}},{\omega}_{s}={\omega}_{p}\phantom{\rule{.2em}{0ex}}\mathrm{and}$$
(9)
$${\omega}_{s}={\omega}_{p}\pm \sqrt{6\frac{-\Phi \pm \sqrt{{\Phi}^{2}-\left(\frac{16}{3}\right){\beta}_{4}\gamma {P}_{p}}}{{\beta}_{4}}},$$
(10)
$$\Delta \omega =2{\left(\frac{48\gamma {P}_{p}}{{\beta}_{4}}\right)}^{\frac{1}{4}},\mathrm{and}\phantom{\rule{.2em}{0ex}}\mathrm{when}\phantom{\rule{.2em}{0ex}}{\beta}_{4}=0,\Delta \omega =2{\left(\frac{4\gamma {P}_{p}}{{\beta}_{3}}\right)}^{\frac{1}{3}}.$$