## Abstract

The frequency comb from a mode-locked fiber laser can be stabilized through feedback to the pump power. An understanding of the mechanisms and bandwidth governing this feedback is of practical importance for frequency comb design and of basic interest since it provides insight into the rich nonlinear laser dynamics. We compare experimental measurements of the response of a fiber-laser frequency comb to theory. The laser response to a pump-power change follows that of a simple low-pass filter with a time constant set by the gain relaxation time and the system-dependent nonlinear loss. Five different effects contribute to the magnitude of the response of the frequency comb spacing and offset frequency but the dominant effects are from the resonant contribution to the group velocity and intensity-dependent spectral shifts. The origins of the intensity-dependent spectral shifts are explained in terms of the laser parameters.

© 2005 Optical Society of America

Full Article |

PDF Article
### Equations (7)

Equations on this page are rendered with MathJax. Learn more.

(1)
$${\partial}_{T}\Delta w=\frac{1}{{T}_{r}}\left[\eta \Delta w\phantom{\rule{.2em}{0ex}}-2\phantom{\rule{.2em}{0ex}}\Delta g\phantom{\rule{.2em}{0ex}}w\right],$$
(2)
$${\partial}_{T}\Delta g=-\frac{1}{{T}_{g}}\left[\Delta g+{g}_{w}\frac{\Delta w}{w}-{g}_{P}\frac{\Delta P}{P}\right]$$
(3)
$$\frac{{\mathit{df}}_{\mathit{CEO}}}{\mathit{dP}}=\frac{{\beta}_{0}}{2\pi}\left(\frac{{\mathit{df}}_{r}}{\mathit{dP}}\right)+\frac{{f}_{r}}{2\pi}\left(\frac{{\mathit{d\phi}}_{\mathit{spm}}}{\mathit{dP}}\right)$$
(4)
$${T}_{r}=\frac{1}{{f}_{r}}={\beta}_{1}+{\omega}_{\Delta}{\beta}_{2}+\frac{1}{2}{\omega}_{\mathit{rms}}^{2}{\beta}_{3}+\frac{g}{{\Omega}_{g}}+\frac{\mu {A}^{2}\delta}{{\omega}_{0}}$$
(5)
$$\frac{d{f}_{r}}{\mathit{dP}}=-{f}_{r}^{2}\left\{\stackrel{\mathrm{Spectral}\phantom{\rule{.2em}{0ex}}\mathrm{Shift}}{\stackrel{\u0346}{{\beta}_{2}\frac{d{\omega}_{\Delta}}{\mathit{dP}}}}+\frac{\stackrel{\mathrm{TOD}}{\stackrel{\u0346}{{\omega}_{\mathit{rms}}^{2}{\beta}_{3}}}}{2P}+\frac{\stackrel{\mathrm{Gain}}{\stackrel{\u0346}{{\nu}_{3\mathrm{dB}}^{\mathit{Er}}}}}{2P{\nu}_{3\mathrm{dB}}{\Omega}_{g}}+\frac{\stackrel{\mathrm{SS}}{\stackrel{\u0346}{3\mu {A}^{2}\delta}}}{2P{\omega}_{0}}\right\},$$
(6)
$${\omega}_{\Delta ,\mathit{NL}}=\frac{-2{A}^{2}\delta}{5{D}_{g}\left(1+{C}^{2}\right)}\left({\tau}_{R}+\mu {\omega}_{0}^{-1}C\right)\phantom{\rule{.2em}{0ex}}\mathrm{and}\phantom{\rule{.2em}{0ex}}{\omega}_{\Delta ,L}=-\frac{{l}_{\omega}}{2{D}_{g}},$$
(7)
$$\frac{d{\omega}_{\Delta}}{\mathit{dP}}=\left({\omega}_{\Delta ,\mathit{NL}}+{\omega}_{\Delta ,L}\right)\frac{1}{P}+\frac{3{\omega}_{\Delta ,\mathit{NL}}}{2w}\frac{\mathit{dw}}{\mathit{dP}}.$$