## Abstract

We present a technique for measuring the modal filtering ability of single mode fibers. The ideal modal filter rejects all input field components that have no overlap with the fundamental mode of the filter and does not attenuate the fundamental mode. We define the quality of a nonideal modal filter
{Q}_{f} as the ratio of transmittance for the fundamental mode to the transmittance for an input field that has no overlap with the fundamental mode. We demonstrate the technique on a 20 cm long mid-infrared fiber that was produced by the U.S. Naval Research Laboratory. The filter quality
{Q}_{f} for this fiber at
10.5\text{\hspace{0.17em} \mu m} wavelength is
\text{1000}\pm \text{300}.
The absorption and scattering losses in the fundamental mode are approximately
\text{8 \hspace{0.17em}}\text{dB}/\text{m}.
The total transmittance for the fundamental mode, including Fresnel reflections, is
0.428\pm 0.002. The application of interest is the search for extrasolar Earthlike planets using nulling interferometry. It requires high rejection ratios to suppress the light of a bright star, so that the faint planet becomes visible. The use of modal filters increases the rejection ratio (or, equivalently, relaxes requirements on the wavefront quality) by reducing the sensitivity to small wavefront errors. We show theoretically that, exclusive of coupling losses, the use of a modal filter leads to the improvement of the rejection ratio in a two-beam interferometer by a factor of {Q}_{f}.

© 2007 Optical Society of America

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### Equations (98)

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(3)
10.5\text{\hspace{0.17em} \mu m}
(4)
\text{1000}\pm \text{300}
(5)
\text{8 \hspace{0.17em}}\text{dB}/\text{m}
(10)
{Q}_{f}={T}_{F}/{T}_{A}
(11)
2\text{\hspace{0.17em} nm}
(12)
\text{10 \hspace{0.17em} \mu m}
(20)
{T}_{A}={P}_{L}/{P}_{I}
(21)
10.5\text{\hspace{0.17em} \mu m}
(26)
{\text{CO}}_{\text{2}}
(27)
\sim 10.6\text{\hspace{0.17em} \mu m}
(28)
{\text{CO}}_{\text{2}}
(29)
$$\alpha l=\mathrm{ln}\text{\hspace{0.17em}}R+\mathrm{ln}\left({{I}_{+}}^{1/2}+{{I}_{-}}^{1/2}\right)-\mathrm{ln}\left({{I}_{+}}^{1/2}-{{I}_{-}}^{1/2}\right)\text{,}$$
(32)
$${T}_{F}={\left(1-R\right)}^{2}{e}^{-\alpha l}/\left(1-{R}^{2}{e}^{-2\alpha l}\right).$$
(33)
10.5\text{\hspace{0.17em} \mu m}
(37)
\left(41\pm 12\right)
(39)
{P}_{I}=\left(1.05\pm 0.05\right)\times {10}^{5}
(40)
{T}_{A}={P}_{L}/{P}_{I}=\left(4\pm 1\right)\times {10}^{-4}
(42)
10.6\text{\hspace{0.17em} \mu m}
(43)
\text{2 .725}\pm \text{0 .005}
(44)
\text{0 .2144}\pm \text{0 .002}
(48)
20\text{\hspace{0.17em} cm}
(49)
\text{8 \hspace{0.17em}}\text{dB}/\text{m}
(57)
{Q}_{f}={T}_{F}/{T}_{A}
(59)
10\text{\hspace{0.17em} \mu m}
(61)
\text{8 \hspace{0.17em}}\text{dB}/\text{m}
(63)
10.5\text{\hspace{0.17em} \mu m}
(64)
\text{1000}\pm \text{300}
(69)
{E}_{i}\left(x,y\right)
(71)
{E}_{1}\left(x,y\right)
(72)
{E}_{2}\left(x,y\right)
(73)
\xi ={\displaystyle {\int}_{{A}_{\infty}}{e}_{1}\left(x,y\right){e}_{2}*\left(x,y\right)\mathrm{d}x\mathrm{d}y}
(78)
{\displaystyle {\int}_{{A}_{\infty}}{e}_{1}\left(x,y\right){e}_{1}*\left(x,y\right)\mathrm{d}x\mathrm{d}y=1}
(79)
{E}_{1}\left(x,y\right)\approx {E}_{2}\left(x,y\right)
(80)
\epsilon =1-\left|\xi \right|
(81)
{P}_{C}\approx 4{P}_{1}
(82)
{P}_{D}\approx 2\epsilon {P}_{1}
(84)
$${R}_{0}\approx \left(2/\epsilon \right)\text{.}$$
(85)
{P}_{in}\approx 2\epsilon {P}_{1}
(87)
{P}_{C}\approx 4{T}_{F}\eta {P}_{1}
(89)
{P}_{D}={T}_{A}{P}_{in}\approx 2{T}_{A}\epsilon {P}_{1}
(91)
$${R}_{f}\equiv {P}_{C}/{P}_{D}\simeq \left(2/\epsilon \right)\left({T}_{F}\eta /{T}_{A}\right)=\left({T}_{F}\eta /{T}_{A}\right){R}_{0}\text{.}$$
(92)
\left(\eta {T}_{F}/{T}_{A}\right)
(96)
{Q}_{f}={T}_{F}/{T}_{A}