## Abstract

The simulated annealing method is used for retrieving the amplitude and phase from cross-phase modulation spectrograms. The method allows us to take into account the birefringence of the measurement fiber and resolution of the optical spectrum analyzer. The influence of the birefringence and analyzer resolution are discussed.

©2004 Optical Society of America

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### Equations (11)

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(1)
$$i{\partial}_{z}{E}_{x,y}+\frac{{\beta}_{2}}{2}{\partial}_{\mathit{tt}}{E}_{x,y}\pm i\sigma {\partial}_{t}{E}_{x,y}\pm \kappa {E}_{x,y}+\gamma [(\mid {E}_{x,y}{\mid}^{2}+\frac{2}{3}\mid {{E}_{y,x}\mid}^{2}){E}_{x,y}+\frac{1}{3}{E}_{y,x}^{2}{E}_{x,y}^{*}]=0,$$
(2)
$${\tilde{E}}_{x}={E}_{x}{e}^{i\kappa z},{\phantom{\rule{.9em}{0ex}}\tilde{E}}_{y}={E}_{y}{e}^{-i\kappa z},$$
(3)
$$i{\partial}_{z}{\tilde{E}}_{x,y}+\frac{{\beta}_{2}}{2}{\partial}_{\mathit{tt}}{\tilde{E}}_{x,y}\pm i\sigma {\partial}_{t}{\tilde{E}}_{x,y}+\gamma (\mid {\tilde{E}}_{x,y}{|}^{2}+\frac{2}{3}\mid {\tilde{E}}_{y,x}{|}^{2}){\tilde{E}}_{x,y}+\frac{\gamma}{3}{\tilde{E}}_{y,x}^{2}{\tilde{E}}_{x,y}^{*}{e}^{\mp 4i\kappa z}=0,$$
(4)
$$i{\partial}_{z}{\tilde{E}}_{x,y}\pm i\sigma {\partial}_{t}{\tilde{E}}_{x,y}+\gamma (\mid {\tilde{E}}_{x,y}{\mid}^{2}+\frac{2}{3}\mid {\tilde{E}}_{y,x}{|}^{2}){\tilde{E}}_{x,y}=0.$$
(5)
$${E}_{x,y}(z,t)={E}_{x,y}(0,t\mp \sigma z)\mathrm{exp}[i\gamma \mid {E}_{x,y}(0,t\mp \sigma z){|}^{2}z+\frac{i\gamma}{3}{\int}_{-z}^{z}\mid {E}_{y,x}(0,t\mp \sigma \xi ){|}^{2}d\xi ].$$
(6)
$${E}_{\mathit{SIG}}(t,\tau )=rE(0,t-\sigma L)\mathrm{exp}[i\gamma {r}^{2}{\mid E(0,t-\sigma L)\mid}^{2}z+\frac{i\gamma \left(1-{r}^{2}\right)}{3}{\int}_{-L}^{L}{\mid E(0,t-\tau +\sigma \xi )\mid}^{2}d\xi ],$$
(7)
$$S(\omega ,\tau )={\mid {\int}_{-\infty}^{\infty}{E}_{\mathit{SIG}}(t,\tau )\mathrm{exp}\left[i\omega t\right]dt\mid}^{2}.$$
(8)
$$S\prime (\omega ,\tau )={\int}_{-\infty}^{\infty}S(\Omega ,\tau )K\left(\omega -\Omega \right)d\Omega .$$
(9)
$${E}^{\prime}\left(t\right)\mathrm{exp}\left[i\mathit{\psi}\left(t\right)\right]\sum _{i=1}^{{n}_{p}}\sqrt{{S}_{i}}\mathrm{exp}\left[-2ln\left(2\right){\left(\frac{t-{t}_{i}/2}{T}\right)}^{2}\right],$$
(10)
$$\psi \left(t\right)=\mathit{a}{\left(\frac{t}{T}\right)}^{2}+b{\left(\frac{t}{T}\right)}^{3}+c{\left(\frac{t}{T}\right)}^{4}+q{\mid E\left(t\right)\mid}^{2},$$
(11)
$$E\left(t\right)={\U0001d4d5}^{-1}\left\{\mathrm{exp}\left[i\xi \left(\nu \right)\right]\U0001d4d5\left[E\prime \left(t\right)\right]\left(\nu \right)\right\}\left(t\right),\phantom{\rule{.2em}{0ex}}\xi \left(\nu \right)=u{\left(\nu T\right)}^{3}+v{\left(\nu T\right)}^{4}+x{\left(\nu T\right)}^{5}.$$