Surface modes at the interfaces between isotropic media and indefinite media

Wei Yan; Linfang Shen; Lixin Ran; Jin Au Kong

doi:10.1364/JOSAA.24.000530

Journal of the Optical Society of America A
Vol. 24,
Issue 2,
pp. 530-535
(2007)
•https://doi.org/10.1364/JOSAA.24.000530

Surface modes at the interfaces between isotropic media and indefinite media

Wei Yan, Linfang Shen, Lixin Ran, and Jin Au Kong

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Wei Yan, Linfang Shen, Lixin Ran, and Jin Au Kong, "Surface modes at the interfaces between isotropic media and indefinite media," J. Opt. Soc. Am. A 24, 530-535 (2007)

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Abstract

Characteristics of surface modes at the interface between an isotropic medium and an indefinite medium that has a dispersion relation of hyperbolic form are studied. Four cases for the isotropic medium, including normal, left-handed, magnetic (with negative permeability), and metallic media, are considered. The conditions for the existence of surface modes in each case are analyzed in detail, and the results are expressed explicitly, indicating that the existence of surface modes is determined by the nature of the indefinite medium as well as the orientation of the boundary surface of this anisotropic medium. The energy flows associated with the surface modes are also discussed.

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Equations (27)

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Case	$μ_{y}$	θ	Necessary Condition
(i)	$μ_{y} > 0$	$∣ θ ∣ < θ_{c 1}^{T M}$	$ϵ_{ξ 1} μ_{y 1} > 1$
(ii)	$μ_{y} < 0$	$θ_{c 1}^{T M} < ∣ θ ∣ ⩽ π ∕ 2$	$ϵ_{η 1} μ_{y 1} > 1$
(iii)	$μ_{y} > 0$	$∣ θ ∣ < θ_{c 2}^{T M}$	$ϵ_{η 1} ∕ μ_{y 1} < 1$
(iv)	$μ_{y} < 0$	$θ_{c 2}^{T M} < ∣ θ ∣ ⩽ π ∕ 2$	$ϵ_{ξ 1} ∕ μ_{y 1} < 1$

Case	$ϵ_{y}$	θ	Necessary Condition
(i)	$ϵ_{y} > 0$	$∣ θ ∣ < θ_{c 1}^{T E}$	$μ_{ξ 1} ϵ_{y 1} > 1$
(ii)	$ϵ_{y} < 0$	$θ_{c 1}^{T E} < ∣ θ ∣ ⩽ π ∕ 2$	$μ_{η 1} ϵ_{y 1} > 1$
(iii)	$ϵ_{y} < 0$	$θ_{c 2}^{T E} < ∣ θ ∣ ⩽ π ∕ 2$	$μ_{x i 1} ∕ ϵ_{y 1} < 1$
(iv)	$ϵ_{y} > 0$	$∣ θ ∣ < θ_{c 2}^{T E}$	$μ_{η 1} ∕ ϵ_{y 1} < 1$

Case	$μ_{y}$	θ	Necessary Condition
(i)	$μ_{y} > 0$	$∣ θ ∣ < θ_{c 1}^{T M}$	$ϵ_{ξ 1} μ_{y 1} > 1$
(ii)	$μ_{y} < 0$	$θ_{c 1}^{T M} < ∣ θ ∣ ⩽ π ∕ 2$	$ϵ_{η 1} μ_{y 1} > 1$
(iii)	$μ_{y} > 0$	$∣ θ ∣ < θ_{c 2}^{T M}$	$ϵ_{η 1} ∕ μ_{y 1} < 1$
(iv)	$μ_{y} < 0$	$θ_{c 2}^{T M} < ∣ θ ∣ ⩽ π ∕ 2$	$ϵ_{ξ 1} ∕ μ_{y 1} < 1$

Case	$ϵ_{y}$	θ	Necessary Condition
(i)	$ϵ_{y} > 0$	$∣ θ ∣ < θ_{c 1}^{T E}$	$μ_{ξ 1} ϵ_{y 1} > 1$
(ii)	$ϵ_{y} < 0$	$θ_{c 1}^{T E} < ∣ θ ∣ ⩽ π ∕ 2$	$μ_{η 1} ϵ_{y 1} > 1$
(iii)	$ϵ_{y} < 0$	$θ_{c 2}^{T E} < ∣ θ ∣ ⩽ π ∕ 2$	$μ_{x i 1} ∕ ϵ_{y 1} < 1$
(iv)	$ϵ_{y} > 0$	$∣ θ ∣ < θ_{c 2}^{T E}$	$μ_{η 1} ∕ ϵ_{y 1} < 1$

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Equations (27)

Journal of the Optical Society of America A