## Abstract

An optical refraction prism consisting of metal and dielectric, subwavelength, periodic multilayered thin films has been proposed. The multilayered structure of metal and dielectric thin films has a cylindrical dispersion surface for TM polarized light. The light behaviors are very different from those of conventional glass prisms and photonic crystal superprisms. Refraction and diffraction of the light wave for the metal–dielectric multilayered prism has been investigated by numerical simulations and graphical representation based on the dispersion surface. A prism with $0.2\text{\hspace{0.17em}}\mu \mathrm{m}$ period had an angular dispersion of 0.20°/nm for $\sim 0.8\text{\hspace{0.17em}}\mu \mathrm{m}$ wavelength light. The finite thick metal–dielectric multilayered structure acted as a slab waveguide.

© 2008 Optical Society of America

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### Equations (12)

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(1)
$$\mathrm{cos}\left({\beta}_{x}\Lambda \right)=\mathrm{cos}\left({k}_{1x}a\right)\mathrm{cos}\left({k}_{2x}b\right)-\frac{1}{2}(\frac{{n}_{1}^{2}}{{n}_{2}^{2}}\frac{{k}_{2x}}{{k}_{1x}}+\frac{{n}_{2}^{2}}{{n}_{1}^{2}}\frac{{k}_{1x}}{{k}_{2x}})\mathrm{sin}\left({k}_{1x}a\right)\mathrm{sin}\left({k}_{2x}b\right),$$
(2)
$${k}_{1x}=\sqrt{{\left(\frac{{n}_{1}\omega}{c}\right)}^{2}-{\beta}_{y}^{2}},$$
(3)
$${k}_{2x}=\sqrt{{\left(\frac{{n}_{2}\omega}{c}\right)}^{2}-{\beta}_{y}^{2}},$$
(4)
$$\frac{{\beta}_{x}^{2}}{{n}_{\mathit{TE}}^{2}}+\frac{{\beta}_{y}^{2}}{{n}_{\mathit{TM}}^{2}}=\frac{{\omega}^{2}}{{c}^{2}},$$
(5)
$${n}_{\mathit{TE}}^{2}=f{n}_{1}^{2}+(1-f){n}_{2}^{2},$$
(6)
$$\frac{1}{{n}_{\mathit{TM}}^{2}}=\frac{f}{{n}_{1}^{2}}+\frac{1-f}{{n}_{2}^{2}}.$$
(7)
$${n}_{1}=\stackrel{\u0303}{n}(1-i)\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\stackrel{\u0303}{n}\to \infty ,$$
(8)
$${\beta}_{y}^{2}=\frac{{\omega}^{2}}{{c}^{2}}\frac{{n}_{2}^{2}}{1-f}.$$
(9)
$$({n}_{x},{n}_{y},{n}_{z})\equiv \frac{c}{\omega}({\beta}_{x},{\beta}_{y},{\beta}_{z}).$$
(10)
$$\mathrm{tan}\left(ht\right)=\frac{2hp}{{h}^{2}-{p}^{2}},$$
(11)
$$h=\sqrt{{n}_{2}^{2}\frac{{\omega}^{2}}{{c}^{2}}-{\beta}_{Sy}^{2}},\phantom{\rule{1em}{0ex}}p=\frac{n_{2}{}^{2}}{n_{1}{}^{2}}\sqrt{{\beta}_{Sy}^{2}-{n}_{1}^{2}\frac{{\omega}^{2}}{{c}^{2}}},$$
(12)
$$\mathrm{sin}({\theta}_{\mathit{out}}+\alpha )=2\frac{{n}_{\mathit{eff}}}{n}\phantom{\rule{0.2em}{0ex}}\mathrm{sin}\phantom{\rule{0.2em}{0ex}}\alpha +\mathrm{sin}({\theta}_{\mathit{in}}-\alpha )-\frac{\lambda}{\Lambda}\frac{\mathrm{cos}\phantom{\rule{0.2em}{0ex}}\alpha}{n},$$