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Journals >Photonics Research >Volume 7 >Issue 7 >Page 728 > Article

Photonics Research
Vol. 7, Issue 7, 728 (2019)

Controllability of surface plasmon polariton far-field radiation using a metasurface

Wanxia Huang^1、*, Xiyue Zhang², Qianjin Wang³, Maosheng Wang¹, Chaogang Li¹, Kuanguo Li¹, Xinyan Yang¹, and Jianping Shi¹

Author Affiliations

¹College of Physics and Electronic Information, Anhui Normal University, Wuhu 241000, China

²State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China

³National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China

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DOI: 10.1364/PRJ.7.000728 Cite this Article Set citation alerts

Wanxia Huang, Xiyue Zhang, Qianjin Wang, Maosheng Wang, Chaogang Li, Kuanguo Li, Xinyan Yang, Jianping Shi. Controllability of surface plasmon polariton far-field radiation using a metasurface[J]. Photonics Research, 2019, 7(7): 728 Copy Citation Text

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Abstract

In this study, a point-scattering approach to the plane-wave optical transmission of subwavelength metal nanoslit arrays with varying angles of rotation and that of subwavelength metal supercell arrays consisting of nanoslits capable of various angles of rotation is developed. It is demonstrated that the suggested theories show good agreement with the simulations and experiments. The results show that constructive and destructive interference at each nanoslit can respectively enhance and suppress the surface plasmon polariton (SPP) far-field radiation of a metasurface. The proposed theory can predict the quantity and resonant wavelength of SPPs and provide a design scheme for an SPP device.

\frac{2 π c}{ω_{r}} \sqrt{{(\frac{i_{x}}{p_{x}})}^{2} + {(\frac{i_{y}}{p_{y}})}^{2}} = \sqrt{\frac{Re [1 - ω_{p}^{2} / (ω_{r}^{2} + i ω_{r} γ)] ε_{d}}{Re (1 - \frac{ω_{p}^{2}}{ω_{r}^{2} + i ω_{r} γ}) + ε_{d}},}

(1)

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{\overset{⇀}{r}}_{j} = n p_{x} \hat{x} + m p_{y} \hat{y},

(2)

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{\hat{u}}_{j} \otimes {\hat{u}}_{j} = \frac{n p_{x} n p_{x} \hat{x} \hat{x} + n p_{x} m p_{y} \hat{x} \hat{y} + m p_{y} n p_{x} \hat{y} \hat{x} + m p_{y} m p_{y} \hat{y} \hat{y}}{{(n p_{x})}^{2} + {(m p_{y})}^{2}} .

(3)

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t_{scatt} \cdot {\hat{u}}_{SPP} = \sum_{(n, m) \neq (0, 0)} S (k_{SPP}) e^{- \frac{i π}{4}} {[Re (k_{SPP}) / (2 π)]}^{\frac{1}{2}} \frac{e^{i k_{SPP} | {\overset{⇀}{r}}_{j} |}}{\sqrt{| {\overset{⇀}{r}}_{j} |}} \cdot e^{i {\overset{⇀}{k}}_{in} \cdot {\overset{⇀}{r}}_{j}} {\hat{u}}_{j} \otimes {\hat{u}}_{j} \cdot {\hat{u}}_{SPP},

(4)

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\hat{v} = \hat{y} \cos α - \hat{x} \sin α .

(5)

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{\hat{u}}_{SPP} = (\hat{v} \cdot {\overset{⇀}{E}}_{in}) \cdot \hat{v} = \hat{y} \cos^{2} α - \hat{x} \sin α \cdot \cos α .

(6)

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t_{scatt} \cdot {\hat{u}}_{SPP} = \sum_{(n, m) \neq (0, 0)} S (k_{SPP}) e^{- \frac{i π}{4}} {[Re (k_{SPP}) / (2 π)]}^{\frac{1}{2}} \cdot \frac{e^{i k_{SPP} \sqrt{(n p_{x})^{2} + (m p_{y})^{2}}}}{{[(n p_{x})^{2} + (m p_{y})^{2}]}^{\frac{5}{4}}} \cdot [- \cos α \cdot \sin α (n p_{x} n p_{x} \hat{x} + m p_{y} n p_{x} \hat{y}) + \cos^{2} α (n p_{x} m p_{y} \hat{x} + m p_{y} m p_{y} \hat{y})] .

(7)

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T = \frac{{| t_{scatt} \cdot {\hat{u}}_{SPP} |}^{2}}{T_{0}} .

(8)

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T = \frac{1}{T_{0}} | \sum_{(n, m) \neq (0, 0)} \sum_{l} S (k_{SPP}) e^{- \frac{i π}{4}} {[Re (k_{SPP}) / (2 π)]}^{\frac{1}{2}} \cdot \frac{e^{i k_{SPP} \sqrt{{(n p_{x} + x_{l}^{'})}^{2} + {(m p_{y} + y_{l}^{'})}^{2}}}}{{[{(n p_{x} + x_{l}^{'})}^{2} + {(m p_{y} + y_{l}^{'})}^{2}]}^{\frac{5}{4}}} \cdot {- \cos α_{l} \cdot \sin α_{l} [{(n p_{x} + x_{l}^{'})}^{2} \hat{x} + (n p_{x} + x_{l}^{'}) (m p_{y} + y_{l}^{'}) \hat{y}]} {+ \cos^{2} α_{l} [{(m p_{y} + y_{l}^{'})}^{2} \hat{y} + (n p_{x} + x_{l}^{'}) (m p_{y} + y_{l}^{'}) \hat{x}] |}^{2},

(9)

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Wanxia Huang, Xiyue Zhang, Qianjin Wang, Maosheng Wang, Chaogang Li, Kuanguo Li, Xinyan Yang, Jianping Shi. Controllability of surface plasmon polariton far-field radiation using a metasurface[J]. Photonics Research, 2019, 7(7): 728

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