## Abstract

We demonstrate that a short pulse with spectrum in the range of normal group velocity dispersion can experience periodic reflections on a refractive index maximum created by a co-propagating with it soliton, providing the latter is continuously decelerated by the intrapulse Raman scattering. After each reflection the intensity profile and phase of the pulse are almost perfectly reconstructed, while its frequency is stepwise converted. This phenomenon has direct analogy with the effect of ’quantum bouncing’ known for cold atoms.

© 2007 Optical Society of America

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### Equations (8)

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(1)
$$i{\partial}_{z}{A}_{\mathrm{1,2}}+{d}_{\mathrm{1,2}}{\partial}_{x}^{2}{A}_{\mathrm{1,2}}=-\left[{\mid {A}_{\mathrm{1,2}}\mid}^{2}+2{\mid {A}_{\mathrm{2,1}}\mid}^{2}\right]{A}_{\mathrm{1,2}}+{\mathrm{TA}}_{\mathrm{1,2}}{\partial}_{x}\left[{\mid {A}_{1}\mid}^{2}+{\mid {A}_{2}\mid}^{2}\right],$$
(2)
$${A}_{1}^{\left(s\right)}={\psi}_{0}\left(\xi \right)\mathrm{exp}\left[i\frac{\mathrm{\xi gz}}{{2d}_{1}}-i\frac{{g}^{2}{z}^{3}}{{12d}_{1}}+\mathit{iqz}\right],$$
(3)
$${\psi}_{0}=\sqrt{2q}\mathrm{sech}\left(\sqrt{\frac{q}{{d}_{1}\xi}}\right),\xi =x-\frac{{\mathrm{gz}}^{2}}{2},g=\frac{{32\mathrm{Tq}}^{2}}{15}.$$
(4)
$${A}_{2}=\phi \left(z,\xi \right)\mathrm{exp}\left[i\frac{\mathrm{\xi gz}}{{2d}_{z}}-i\frac{{g}^{2}{z}^{2}}{{12d}_{2}}\right].$$
(5)
$$i{\partial}_{z}\phi -\mid {d}_{2}\mid {\partial}_{\xi}^{2}\phi +V\left(\xi \right)\phi =0,$$
(6)
$$V\left(\xi \right)={2\psi}_{0}^{2}-{T\partial}_{\xi}{\psi}_{0}^{2}+\frac{\mathrm{g\xi}}{2\mid {d}_{2}\mid}.$$
(7)
$$\phi \left(z,\xi \right)\approx \sum _{n}{c}_{n}{y}_{n}\left(\xi \right)\mathrm{exp}\left({\mathrm{i\lambda}}_{n}z\right).$$
(8)
$$\phi (\xi ,z=0)=a\phantom{\rule{.2em}{0ex}}\mathrm{exp}\left[-\frac{{\left(\xi -{\xi}_{0}-L\right)}^{2}}{{w}^{2}}\right].$$