Theoretical study on negative permittivity of the material producing sharp surface plasmon resonance dips

Dejing Gong; Yinquan Yuan; Lei Liang; Minghong Yang

doi:10.3788/COL201917.042801

Journals >Chinese Optics Letters >Volume 17 >Issue 4 >Page 042801 > Article

Chinese Optics Letters
Vol. 17, Issue 4, 042801 (2019)

Theoretical study on negative permittivity of the material producing sharp surface plasmon resonance dips

Dejing Gong^1,2, Yinquan Yuan^1,*, Lei Liang^1,2, and Minghong Yang^1,**

Author Affiliations

¹National Engineering Laboratory for Fiber Optic Sensing Technology, Wuhan University of Technology, Wuhan 430070, China

²School of Information Engineering, Wuhan University of Technology, Wuhan 430070, China

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DOI: 10.3788/COL201917.042801 Cite this Article Set citation alerts

Dejing Gong, Yinquan Yuan, Lei Liang, Minghong Yang, "Theoretical study on negative permittivity of the material producing sharp surface plasmon resonance dips," Chin. Opt. Lett. 17, 042801 (2019) Copy Citation Text

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Abstract

Using theoretical simulations for optical fiber surface plasmon resonance (SPR) sensors and prism-based SPR sensors coated with negative permittivity material (NPM), we investigated the effect of the permittivity of NPM on the transmitted spectrum of optical fiber SPR sensors and the reflected spectrum of prism-based SPR sensors and then obtained optimum permittivity of the NPM, which can excite the sharpest SPR spectrum in the white light region (400–900 nm).

ε_{m} (ω) = 1 - \frac{f_{0} ω_{p}^{2}}{ω (ω + i Γ_{0})} + \sum_{j = 1}^{k} \frac{f_{j} ω_{p}^{2}}{ω_{j}^{2} - ω^{2} + i ω Γ_{j}},

(1)

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d P \propto \frac{n_{1}^{2} \sin θ \cos θ}{{(1 - n_{1}^{2} \cos^{2} θ)}^{2}} d θ,

(2)

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P_{trans} = \frac{\int_{θ_{cr}}^{π / 2} R_{p}^{N_{ref} (θ)} P (θ) d θ}{\int_{θ_{cr}}^{π / 2} P (θ) d θ},

(3)

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N_{ref} (θ) = \frac{L}{D \tan θ}, θ_{cr} = \arcsin (\frac{n_{cl}}{n_{1}}) .

(4)

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ε_{NPM} (λ) = (ε_{re 0} - k λ) + i ε_{im} (λ),

(5)

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λ_{res} (n_{f}) = λ_{res} (n_{f 0}) + ξ_{1} (n_{f} - n_{f 0}) + ξ_{2} {(n_{f} - n_{f 0})}^{2},

(6)

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Δ θ_{res} = γ_{1} \cdot Δ n_{sam},

(7)

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Dejing Gong, Yinquan Yuan, Lei Liang, Minghong Yang, "Theoretical study on negative permittivity of the material producing sharp surface plasmon resonance dips," Chin. Opt. Lett. 17, 042801 (2019)

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