## Abstract

Soliton formation during dispersive compression of chirped few-picosecond pulses at the microjoule level in a hollow-core photonic bandgap (HC-PBG) fiber is studied by numerical simulations. Long-pass filtering of the emerging frequency-shifted solitons is investigated with the objective of obtaining pedestal-free output pulses. Particular emphasis is placed on the influence of the air pressure in the HC-PBG fiber. It is found that a reduction in air pressure enables an increase in the fraction of power going into the most redshifted soliton and also improves the quality of the filtered pulse at high powers. This allows a scaling of the output pulse energy toward the microjoule level.

© 2009 Optical Society of America

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### Equations (7)

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(1)
$$\frac{\partial A\left(z,\omega \right)}{\partial z}=i\frac{\omega}{c}\text{exp}\left(-i\beta \left(\omega \right)z\right)\sum _{\nu =1}^{2}\frac{{n}_{2}^{\left(\nu \right)}}{{\left[{A}_{eff}^{\left(\nu \right)}\left(\omega \right)\right]}^{1/4}}\frac{1}{{\left(2\pi \right)}^{2}}\times \int \mathrm{d}{\omega}_{1-2}\text{\hspace{0.17em}}{\widehat{A}}_{\left(\nu \right)}\left(z,{\omega}_{1}\right){\widehat{A}}_{\left(\nu \right)}\left(z,{\omega}_{2}\right){\widehat{A}}_{\left(\nu \right)}^{\ast}\left(z,{\omega}_{1}+{\omega}_{2}-\omega \right){R}_{\nu}\left(\omega -{\omega}_{1}\right),$$
(2)
$${\widehat{A}}_{\left(\nu \right)}\left(z,\omega \right)=\frac{A\left(z,\omega \right)\text{exp}\left(i\beta \left(\omega \right)z\right)}{{\left[{A}_{eff}^{\left(\nu \right)}\left(\omega \right)\right]}^{1/4}},$$
(3)
$${A}_{eff}^{\left(\nu \right)}=\frac{{\mu}_{0}{\left[\text{Re \hspace{0.17em}}\int \text{d}{\mathbf{r}}_{\perp}\mathbf{e}\times {\mathbf{h}}^{\ast}\cdot \hat{\mathbf{z}}\right]}^{2}}{{\epsilon}_{0}{n}_{\nu}^{2}{\int}_{\nu}\text{d}{\mathbf{r}}_{\perp}{\left|\mathbf{e}\left({\mathbf{r}}_{\perp}\right)\right|}^{4}}.$$
(4)
$$\mathbf{E}\left(\mathbf{r},t\right)=\frac{1}{2\pi}\int \text{d}\omega \text{\hspace{0.17em}}A\left(z,\omega \right)\mathbf{e}\left({\mathbf{r}}_{\perp},\omega \right)\text{exp}\left(i\left(\beta \left(\omega \right)z-\omega t\right)\right),$$
(5)
$${R}_{\nu}\left(t\right)=\delta \left(t\right)+{f}_{\nu}\frac{{\tau}_{1\nu}^{2}+{\tau}_{2\nu}^{2}}{{\tau}_{1\nu}{\tau}_{2\nu}^{2}}\text{sin}\left(t/{\tau}_{1\nu}\right)\text{exp}\left(-t/{\tau}_{2\nu}\right),$$
(6)
$$F\left(\lambda \right)=\frac{1}{\text{exp}\left[\left({\lambda}_{f}-\lambda \right)/\Delta \lambda \right]+1}.$$
(7)
$${\gamma}_{K}^{\left(\nu \right)}=\frac{\omega {n}_{2}^{\left(\nu \right)}}{c{A}_{eff}^{\left(\nu \right)}},\text{\hspace{0.5em} \hspace{0.5em}}{\gamma}_{R}^{\left(\nu \right)}={f}_{\nu}{\gamma}_{K}^{\left(\nu \right)}.$$