## Abstract

We demonstrate the existence of electromagnetic surface modes and surface plasma waves in the interface of a one-dimensional photonic crystal and a metal. These modes can exist in the region in which bandgaps of the photonic crystal overlap and in the region below the plasma frequency of a metal in the frequency wave-vector space. An analytic dispersion relation to determine the existence of these electromagnetic surface modes is obtained, and it is shown that these modes can be excited and observed without prism or grating configurations even under normal incidence from vacuum.

© 2003 Optical Society of America

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### Equations (18)

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(1)
$$m({\eta}_{j},{\delta}_{j})=\left[\begin{array}{cc}cos({\delta}_{j})& \frac{i}{{\eta}_{j}}sin({\delta}_{j})\\ i{\eta}_{j}sin({\delta}_{j})& cos({\delta}_{j})\end{array}\right].$$
(2)
$${\delta}_{j}=\frac{2\pi}{\mathrm{\Lambda}}{\overline{k}}_{\mathit{zj}}{d}_{j}$$
(3)
$${\eta}_{j}=\left\{\begin{array}{ll}y{\overline{k}}_{\mathit{zj}}/\overline{\omega}& \mathrm{TE}\hspace{0.5em}\mathrm{polarization}\\ {\mathit{yn}}_{j}^{2}\overline{\omega}/{\overline{k}}_{\mathit{zj}}& \mathrm{TM}\hspace{0.5em}\mathrm{polarization}\end{array}\right.$$
(4)
$${\overline{k}}_{\mathit{zj}}=({n}_{j}^{2}{\overline{\omega}}^{2}-{\overline{\beta}}^{2}{)}^{1/2}$$
(5)
$$M({\eta}_{e},{\delta}_{e})=\left[\begin{array}{cc}cos({\delta}_{e})& \frac{i}{{\eta}_{e}}sin({\delta}_{e})\\ i{\eta}_{e}sin({\delta}_{e})& cos({\delta}_{e})\end{array}\right],$$
(6)
$${M}_{11}=cos(2{\delta}_{p})cos({\delta}_{q})-{\rho}^{+}sin(2{\delta}_{p})sin({\delta}_{q}),$$
(7)
$${M}_{22}={M}_{11},$$
(8)
$${M}_{21}=i{\eta}_{p}[sin(2{\delta}_{p})cos({\delta}_{q})+{\rho}^{+}cos(2{\delta}_{p})sin({\delta}_{q})-{\rho}^{-}sin({\delta}_{q})],$$
(9)
$${M}_{12}=\frac{i}{{\eta}_{p}}[sin(2{\delta}_{p})cos({\delta}_{q})+{\rho}^{+}cos(2{\delta}_{p})sin({\delta}_{q})+{\rho}^{-}sin({\delta}_{q})],$$
(10)
$${\rho}^{+}=\frac{1}{2}\left(\frac{{\eta}_{p}}{{\eta}_{q}}+\frac{{\eta}_{q}}{{\eta}_{p}}\right),$$
(11)
$${\rho}^{-}=\frac{1}{2}\left(\frac{{\eta}_{p}}{{\eta}_{q}}-\frac{{\eta}_{q}}{{\eta}_{p}}\right).$$
(12)
$$cos({\delta}_{e})=cos(2{\delta}_{p})cos({\delta}_{q})-{\rho}^{+}sin(2{\delta}_{p})sin({\delta}_{q}),$$
(13)
$${\eta}_{e}=\frac{{\eta}_{p}}{sin({\delta}_{e})}[sin(2{\delta}_{p})cos({\delta}_{q})+{\rho}^{+}cos(2{\delta}_{p})sin({\delta}_{q})-{\rho}^{-}sin({\delta}_{q})].$$
(14)
$${\eta}_{0}+{\eta}_{e}+i\left(\frac{{\eta}_{0}{\eta}_{e}}{{\eta}_{m}}+{\eta}_{m}\right)tan({\delta}_{m})=0.$$
(15)
$${\eta}_{m}=-{\eta}_{0},$$
(16)
$${\eta}_{m}=-{\eta}_{e}.$$
(17)
$${\eta}_{0}+{\eta}_{m}+i\left(\frac{{\eta}_{0}{\eta}_{m}}{{\eta}_{e}}+{\eta}_{e}\right)tan(\sigma {\delta}_{e})=0.$$
(18)
$${\eta}_{e}=-{\eta}_{0}.$$