## Abstract

We describe an alternative to fiber-gratings for converting higher-order ${\mathrm{L}\mathrm{P}}_{0m}\text{\hspace{0.17em}}(m>1)$ fiber modes into a nearly fundamental Gaussian shape at the output of a fiber. This schematic enables the use of light propagation in higher-order modes of a fiber, a fiber-platform that has recently shown great promise for achieving very large mode areas needed for future high-power lasers and amplifiers. The conversion will be done by using a binary phase plate in the near field of the fiber, which emits the ${\mathrm{L}\mathrm{P}}_{0m}$ mode. Since the binary phase plate alone cannot increase the quality factor ${M}^{2}$ of the laser beam because of some broad sidebands, a filtering of the sidebands is done in the Fourier plane of a telescope. Of course, this will cost some of the total light power, but on the other side the ${M}^{2}$ factor can be reduced to nearly the ideal value near 1.0, and it is shown that $\sim 76\%$ of the total light power can be conserved for all investigated modes $(2\le m\le 8)$. A tolerance analysis for the phase plate and its adjustment is made, and different optical imaging systems to form a magnified image of the fiber mode on the phase plate are discussed in order to have more tolerance for the adjustment of the phase plate.

© 2007 Optical Society of America

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### Equations (11)

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(1)
$${{M}_{x}}^{2}=\frac{4\pi}{\lambda}\text{\hspace{0.17em}}{\sigma}_{x}{\sigma}_{\theta x},$$
(2)
$${{\sigma}_{x}}^{2}=\frac{{\displaystyle {\int}_{-\infty}^{+\infty}{\displaystyle {\int}_{-\infty}^{+\infty}{x}^{2}I\left(x,y\right)\mathrm{d}x\mathrm{d}y}}}{{\displaystyle {\int}_{-\infty}^{+\infty}{\displaystyle {\int}_{-\infty}^{+\infty}I\left(x,y\right)\mathrm{d}x\mathrm{d}y}}}\text{,}$$
(3)
$${{\sigma}_{\theta x}}^{2}=\frac{{\displaystyle {\int}_{-\infty}^{+\infty}{\displaystyle {\int}_{-\infty}^{+\infty}{{\theta}_{x}}^{2}\tilde{I}\left({\theta}_{x},{\theta}_{y}\right)\mathrm{d}{\theta}_{x}\mathrm{d}{\theta}_{y}}}}{{\displaystyle {\int}_{-\infty}^{+\infty}{\displaystyle {\int}_{-\infty}^{+\infty}\tilde{I}\left({\theta}_{x},{\theta}_{y}\right)\mathrm{d}{\theta}_{x}\mathrm{d}{\theta}_{y}}}}\mathrm{.}$$
(4)
$${A}_{\text{eff}}=\frac{{\left(\int \int I\mathrm{d}A\right)}^{2}}{{\displaystyle \int \int {I}^{2}\mathrm{d}A}}.$$
(5)
$$\Delta \Phi =\frac{2\pi}{\lambda}\left(n-1\right)d.$$
(6)
$$\left(\begin{array}{c}x\prime \\ \phi \prime \end{array}\right)=M\left(\begin{array}{c}x\\ \phi \end{array}\right),$$
(7)
$$M=\left(\begin{array}{cc}A& B\\ C& D\end{array}\right)=\left(\begin{array}{cc}\mathrm{cos}\text{\hspace{0.17em}}\alpha & f\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}\alpha \\ -\frac{\mathrm{sin}\text{\hspace{0.17em}}\alpha}{f}& \mathrm{cos}\text{\hspace{0.17em}}\alpha \end{array}\right)\text{,}$$
(8)
$$\alpha =\sqrt{\frac{2{n}_{1}}{{n}_{0}}}\text{\hspace{0.17em}}z;\text{\hspace{0.17em}}f=\frac{1}{\sqrt{2{n}_{0}{n}_{1}}}.$$
(9)
$$n\left(r\right)={n}_{0}\text{\hspace{0.17em} sech}\left(gr\right)=\frac{{n}_{0}}{\mathrm{cosh}\left(gr\right)}=\frac{2{n}_{0}}{\mathrm{exp}\left(gr\right)+\mathrm{exp}\left(-gr\right)}\text{,}$$
(10)
$$g=\sqrt{\frac{2{n}_{1}}{{n}_{0}}},$$
(11)
$$M\prime =\left(\begin{array}{cc}A\prime & B\prime \\ C\prime & D\prime \end{array}\right)=\left(\begin{array}{cc}\mathrm{cos}\text{\hspace{0.17em}}\alpha -\frac{{d}_{2}}{f}\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}\alpha & {d}_{1}\text{\hspace{0.17em}}\mathrm{cos}\text{\hspace{0.17em}}\alpha +f\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}\alpha +{d}_{2}\text{\hspace{0.17em}}\mathrm{cos}\text{\hspace{0.17em}}\alpha -\frac{{d}_{1}{d}_{2}}{f}\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}\alpha \\ -\frac{1}{f}\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}\alpha & \mathrm{cos}\text{\hspace{0.17em}}\alpha -\frac{{d}_{1}}{f}\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}\alpha \end{array}\right).$$