## Abstract

A parabolalike fiber end to couple the light from a high-power laser diode into a multimode fiber is presented. The formula for the coupling efficiency of such a system is given, and numerical evaluation shows that the theoretical coupling efficiency can be as high as 92% without an antireflection coating on the fiber’s end face. This beam-shaping system can be fabricated easily and has a large alignment tolerance.

© 2003 Optical Society of America

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### Equations (5)

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(1)
$$\mathrm{\gamma}=\mathrm{\alpha}\prime -2\mathrm{\beta},$$
(2)
$$\mathrm{\gamma}<\frac{\mathrm{\pi}}{2}-{sin}^{-1}\frac{{n}_{2}}{{n}_{1}},$$
(3)
$$I\left(x,0,z\right)=|A{|}^{2}\frac{1}{{z}^{2}}{\left(\frac{{\mathrm{\Gamma}}^{2}}{{\mathrm{\Gamma}}^{2}+{x}^{2}}\right)}^{2},$$
(4)
$$I\left(\mathrm{\theta},z\right)=\frac{|A{|}^{2}}{{z}^{2}}{\left(\frac{\mathrm{\Gamma}_{1}{}^{2}}{\mathrm{\Gamma}_{1}{}^{2}+tan\mathrm{\theta}}\right)}^{2},$$
(5)
$$\mathrm{\eta}=\frac{{\int}_{-{\mathrm{\theta}}_{1}}^{{\mathrm{\theta}}_{1}}I\left(\mathrm{\theta}\right)R\left(\mathrm{\theta}\right)T\left(\mathrm{\theta}\right)d\mathrm{\theta}+2{\int}_{{\mathrm{\theta}}_{1}}^{{\mathrm{\theta}}_{2}}I\left(\mathrm{\theta}\right)R\left(\mathrm{\theta}\right)T\left(\mathrm{\theta}\right)d\mathrm{\theta}}{{\int}_{-\mathrm{\pi}/2}^{\mathrm{\pi}/2}I\left(\mathrm{\theta}\right)d\mathrm{\theta}},$$