## Abstract

Self-collimations are found in one-dimensional (1D) photonic crystals consisting of two kinds of single-negative materials that effectively cancel each other out. Compared to the self-collimations in all-dielectric photonic crystals or 1D photonic crystals with negative-index materials, this kind of structure can amplify both far and near fields greatly during collimation.

© 2010 OSA

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### Equations (5)

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(1)
$${\mu}_{\text{1}}\text{=}{\mu}_{\text{a}}-\frac{{\alpha}^{\text{2}}}{{(2\pi f)}^{\text{2}}},\text{}{\epsilon}_{\text{1}}\text{=}{\epsilon}_{\text{a}},$$
(2)
$$\text{}{\mu}_{\text{2}}\text{=}{\mu}_{\text{b}},\text{}{\epsilon}_{\text{2}}\text{=}{\epsilon}_{\text{b}}-\frac{{\beta}^{\text{2}}}{{(2\pi f)}^{\text{2}}},$$
(3)
$$\mathrm{cos}({K}_{z}d)=\mathrm{cos}({\gamma}_{1}{d}_{1})\mathrm{cos}({\gamma}_{2}{d}_{2})-\frac{{\gamma}_{1}{}^{2}{\mu}_{2}{}^{2}+{\gamma}_{2}{}^{2}{\mu}_{1}{}^{2}}{2{\gamma}_{1}{\gamma}_{2}{\mu}_{1}{\mu}_{2}}\mathrm{sin}({\gamma}_{1}{d}_{1})\phantom{\rule{.2em}{0ex}}\mathrm{sin}({\gamma}_{2}{d}_{2}),$$
(4)
$${E}_{y}={\displaystyle \underset{-\infty}{\overset{\infty}{\int}}\mathrm{exp}i({k}_{x}x+{k}_{0z}z)\psi ({k}_{x})}d{k}_{x},$$
(5)
$$\psi ({k}_{x})=\frac{g}{2\sqrt{\pi}}\mathrm{exp}\{-[{g}^{2}{k}_{x}{}^{2}/4]\},$$