## Abstract

Random nonuniformities in the photonic crystal lattice are shown to reduce the coupling length and the coupling efficiency of two-core photonic crystal fibers. These coupling properties are extremely sensitive to imperfections when the air holes are large; variations in the lattice of less than 1% are sufficient to cause essentially independent core propagation due to a drastic reduction in the efficiency of the core coupling. The observed sensitivity of two-core fibers to lattice imperfections is explained through a comparison with coupled mode theory.

© 2005 Optical Society of America

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### Equations (11)

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(1)
$$\overrightarrow{E}(x,y,z)=\sum _{j}{a}_{j}{\overrightarrow{e}}_{j}(x,y)\mathrm{exp}\left(i{\beta}_{j}z\right),$$
(2)
$${a}_{j}=\frac{1}{2{N}_{j}}\underset{\infty}{\int \int}\overrightarrow{E}(x,y,0)\times {\overrightarrow{h}}_{j}^{*}(x,y)\bullet \hat{z}\mathit{dxdy},$$
(3)
$$\frac{1}{2}\underset{\infty}{\int \int}{\overrightarrow{e}}_{j}(x,y)\times {\overrightarrow{h}}_{j}^{*}(x,y)\bullet \hat{z}\mathit{dxdy}=\frac{1}{2}\underset{\infty}{\int \int}\overrightarrow{e}(x,y)\times {\overrightarrow{h}}_{j}^{*}(x,y)\bullet \hat{z}\mathit{dxdy}={N}_{j}$$
(4)
$${P}_{\mathit{core}}\left(z\right)=\frac{1}{2}\mathrm{Re}\underset{\underset{\mathit{area}}{\mathit{core}}}{\int \int}\overrightarrow{E}(x,y,z)\times {\overrightarrow{H}}^{*}(x,y,z)\bullet \hat{z}\mathit{dxdy},$$
(5)
$$\overrightarrow{E}(x,y,z)=a(z){\overrightarrow{e}}^{a}(x,y)+b(z){\overrightarrow{e}}^{b}(x,y)$$
(6)
$$\overrightarrow{H}(x,y,z)=a(z){\overrightarrow{h}}^{a}(x,y)+b(z){\overrightarrow{h}}^{b}(x,y)$$
(7)
$$\frac{d}{dz}a\left(z\right)=i{\beta}_{a}a\left(z\right)+i{K}_{\mathit{ab}}b\left(z\right)$$
(8)
$$\frac{d}{dz}b\left(z\right)=i{K}_{\mathit{ba}}a\left(z\right)+i{\beta}_{b}b\left(z\right),$$
(9)
$${p}_{b}\left(z\right)={\mid b\left(z\right)\mid}^{2}={\mid \frac{{K}_{\mathit{ab}}}{\psi}\mid}^{2}{\mathrm{sin}}^{2}\psi z,$$
(10)
$$\mathit{where}:\psi =\sqrt{\frac{{\left({\beta}_{b}-{\beta}_{a}\right)}^{2}}{4}+{K}_{ab}{K}_{ba}},$$
(11)
$$\mathit{Efficiency}=\frac{4{\mid {K}_{ab}\mid}^{2}}{{\pi}^{2}}{L}_{c}^{2}$$