## Abstract

Spatially resolved spectral interferometry is used to measure the mode content of a Yb-doped photonic-crystal fiber rod amplifier with a $2300\text{\hspace{0.17em}}{\mathrm{\mu m}}^{2}$ mode area. The technique, known as ${S}^{2}$ imaging, was adapted for the short fiber amplifier at full power and revealed a small amount of a copolarized ${\mathrm{LP}}_{11}$ mode. Simulations illustrate the potential for weak mode suppression in this fiber and agree qualitatively with the measurements of ${S}^{2}$ and ${M}^{2}$. Higher-order-mode content depends on the alignment of the input signal at injection and ranged from $-18\text{\hspace{0.17em}}\mathrm{dB}$ for optimized alignment to $-13\text{\hspace{0.17em}}\mathrm{dB}$ when the injection alignment was offset along the ${\mathrm{LP}}_{11}$ axis by 30% of the $55\text{\hspace{0.17em}}\mathrm{\mu m}$ mode-field diameter.

© 2011 Optical Society of America

Full Article |

PDF Article
### Equations (6)

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

(1)
$${E}_{2}(x,y,\omega )=\alpha (x,y,\omega ){E}_{1}(x,y,\omega ),$$
(2)
$${E}_{2}(x,y,\omega )=\alpha (x,y,\omega ){E}_{1}(x,y,\omega )\mathrm{exp}(-i\omega \mathrm{\Delta}{\tau}_{\mathrm{G}}).$$
(3)
$$I(x,y,\omega )=|{E}_{1}(x,y,\omega )+{E}_{2}(x,y,\omega ){|}^{2}={I}_{1}(x,y,\omega )[1+|\alpha {|}^{2}+2|\alpha |\mathrm{cos}(\omega \mathrm{\Delta}{\tau}_{\mathrm{G}}-{\varphi}_{\alpha})].$$
(4)
$$f(x,y)=\frac{2|\overline{\alpha}|\mathrm{exp}(-i{\varphi}_{\alpha})}{1+|\overline{\alpha}{|}^{2}},$$
(5)
$$\overline{\alpha}(x,y)=\frac{1-\sqrt{1-4|f(x,y){|}^{2}}}{2f(x,y)}.$$
(6)
$${P}_{2}/{P}_{1}=\iint {I}_{2}(x,y)\mathrm{d}x\mathrm{d}y/\iint {I}_{1}(x,y)\mathrm{d}x\mathrm{d}y\phantom{\rule{0ex}{0ex}}=\frac{\iint {I}_{T}|\overline{\alpha}{|}^{2}/(1+|\overline{\alpha}{|}^{2})\mathrm{d}x\mathrm{d}y}{\iint {I}_{T}/(1+|\overline{\alpha}{|}^{2})\mathrm{d}x\mathrm{d}y}.$$