Complete tunneling of light through a composite barrier consisting of multiple layers

Junghyun Park (박정현), Kyoung-Youm Kim (김경염), and Byoungho Lee (이병호)

Phys. Rev. A 79, 023820 – Published 18 February 2009

Abstract

The general conditions required for complete tunneling of light through surface impedance-matched barrier layers were investigated. By analogy with the effective barrier length defined by Kim [Phys. Rev. E 70, 047603 (2004)], we define the extended effective barrier length and show that complete tunneling occurs when the extended effective barrier length becomes zero. The surface mode plays an important role in complete tunneling that arises from balancing field enhancement and decay. We need at least one interface which supports a local surface mode, and it is not necessary that every interface between adjacent barrier layers support a surface mode. Complete tunneling can still occur under arbitrary permutations of the order of the barrier layers. The effect of total barrier length on the angular dependence is also discussed.

Received 19 May 2008

DOI:https://doi.org/10.1103/PhysRevA.79.023820

Authors & Affiliations

Junghyun Park (박정현)¹, Kyoung-Youm Kim (김경염)², and Byoungho Lee (이병호)^1,*

¹National Creative Research Center for Active Plasmonics Application Systems, Inter-University Semiconductor Research Center and School of Electrical Engineering, Seoul National University, Gwanak-Gu Sillim-Dong, Seoul 151-744, Korea
²Department of Optical Engineering, Sejong University, Gunja-Dong, Gwangjin-Gu, Seoul 143-747, Korea

^*Corresponding author: byoungho@snu.ac.kr

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Vol. 79, Iss. 2 — February 2009

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Figure 1
Schematic diagram of a composite barrier consisting of multiple layers. The incident angle is assumed to be sufficiently large that the fields inside the barrier are all evanescent.Reuse & Permissions
Figure 2
(a) $H_{y}$ distribution when the TM plane wave is incident on a composite barrier which is designed properly so that complete tunneling can occur. The permittivity and the permeability in each layer are $(ε_{l}, ε_{1}, ε_{2}, \dots, ε_{6}, ε_{r}) = (2.2 5, 1, - 3, - 1, - 4, 0.8, 1.2, 2.2 5)$ and $(μ_{l}, μ_{1}, \dots, μ_{6}, μ_{r}) = (1, 1, 1, - 1, 1.625, 1.475, 0.65, 1)$ , respectively. The length is determined by Eq. (22). The incident angle is chosen tomeet $\sqrt{ε_{l} μ_{l}} \sin θ_{inc} = \sqrt{ε_{1} ε_{2} (ε_{1} μ_{2} - ε_{2} μ_{1}) ∕ [(ε_{1} + ε_{2}) (ε_{1} - ε_{2})]}$ (about 54.74°). The dotted lines indicate the interfaces between the layers. (b) $\log_{10} ∣ H_{y} ∣$ distribution along $x = 0$ . Two local maxima are observed at $z = l_{1}$ and $l_{4}$ , where the surface modes exist due to changes in the signs of $ε_{1}$ , $ε_{2}$ and $ε_{4}$ , $ε_{5}$ . The dotted vertical lines indicate the interfaces between the layers. The ellipse with dashed line highlights the change of the signs of permittivity.Reuse & Permissions
Figure 3
$\log_{10} ∣ H_{y} ∣$ distributions for various permutations of the order of layers. (a) $A B C$ , (b) $A C B$ , and (c) $B A C$ . The layer $A$ has $(ε_{A}, μ_{A}, d_{A})$ of $(1, 1, p ∕ α_{A})$ . $(ε_{B}, μ_{B}, d_{B})$ is $(- 3, 1, 2 p ∕ α_{B})$ , and $(ε_{C}, μ_{C}, d_{C})$ is $(2.5, - 0.65, p ∕ α_{C})$ . $α_{i} (i = A, B, C)$ is obtained by Eq. (5). $p$ is chosen in such a way that the total barrier length $(l_{3})$ is $2 λ_{0}$ . The dotted vertical lines indicate the interfaces between the layers. The incident angle is set to satisfy $\sqrt{ε_{l} μ_{l}} \sin θ_{inc} = \sqrt{ε_{A} ε_{B} (ε_{A} μ_{B} - ε_{B} μ_{A}) ∕ [(ε_{A} + ε_{B}) (ε_{A} - ε_{B})]}$ (about 54.74°). Complete tunneling still occurs after arbitrary permutations on the order of the composite barrier layers.Reuse & Permissions
Figure 4
(a) Transmission coefficient as a function of incident angle for various total barrier lengths $(l_{N})$ : 0.4, 0.7, 1.0, 1.3, and 1.6 times $λ_{0}$ . The arrow indicates the decreasing direction of the total barrier length from $1.6 λ_{0}$ to $0.4 λ_{0}$ . The configuration is the same as that in Fig. 3a except for the total barrier length. (b) Extended effective barrier length as a function of incident angle for various total barrier lengths. (c) $∣ H_{y} ∣$ distribution when a Gaussian beam with beam width $10 λ_{0}$ and an incident angle of 54.74° is incident on the composite barrier with a total barrier length of $0.4 λ_{0}$ . (d) $∣ H_{y} ∣$ distribution for the total barrier length of $1.6 λ_{0}$ . All else are the same as in (c). It is seen that, as the total barrier length increases, the condition for complete tunneling becomes more stringent.Reuse & Permissions

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