A Multi-Plasmonic Approach for Simultaneous Measurements based on a D-Shaped Photonic Crystal Fiber Sensor: from Temperature to Optical Dispersion

The growing demand for multiparameter sensors includes compact devices accompanied by simple calibration processes to distinguish the outputs from each other. This paper evaluates a scheme to determine multiple parameters of a medium using localized surface plasmon resonances (SPR) excited on a Dshaped photonic crystal fiber (PCF) partially covered by two gold layers of different thicknesses. We demonstrate that the proposed sensing platform, once customized to characterize the possible dispersive profiles of the refractive index of the analyte, also allows interrogating the temperature of a sample from a linear relationship. Since the plasmonic resonances are excited at separated and low crosstalk spectral channels, different sensing responses can be obtained simultaneously in the same location of the D-shaped PCF. These features turn out the SPR sensor a suitable tool for simultaneous monitoring of optical dispersion and temperature.

Index Terms
surface plasmon resonance; Photonic crystal fiber; multiparameter sensing; optical sensors; optical dispersion

Authorship

Amanda F. Romeiro

Federal University of Pará, Applied Eletromagnetism Laboratory, Belém Pará, Brazil – romeiro.amanda@gmail.com, markosdenardi@gmail.com, jweyl@ufpa.br.Federal University of ParáBrazilBelém Pará, BrazilFederal University of Pará, Applied Eletromagnetism Laboratory, Belém Pará, Brazil – romeiro.amanda@gmail.com, markosdenardi@gmail.com, jweyl@ufpa.br.

https://orcid.org/0000-0001-8728-7224

Markos P. Cardoso

https://orcid.org/0000-0002-0688-8093

Anderson O. Silva

Federal Center for Technological Education Celso Suckow da Fonseca, Rio de Janeiro, Brazil – anderson.osilva@gmail.comFederal Center for Technological Education Celso Suckow da FonsecaBrazilRio de Janeiro, BrazilFederal Center for Technological Education Celso Suckow da Fonseca, Rio de Janeiro, Brazil – anderson.osilva@gmail.com

https://orcid.org/0000-0002-2103-4213

João C. W. A. Costa

https://orcid.org/0000-0003-4482-6886

M. Thereza R. Giraldi

Military Institute of Engineering, Rio de Janeiro, Brazil – mtmrocco@gmail.comMilitary Institute of EngineeringBrazilRio de Janeiro, BrazilMilitary Institute of Engineering, Rio de Janeiro, Brazil – mtmrocco@gmail.com

https://orcid.org/0000-0001-8066-6395

José L. Santos

INESC TEC, Porto, Portugal, asguerre@fc.up.pt, josantos@fc.up.pt, jmb@staff.uma.ptINESC TECPortugalPorto, PortugalINESC TEC, Porto, Portugal, asguerre@fc.up.pt, josantos@fc.up.pt, jmb@staff.uma.pt

Faculty of Sciences, University of Porto, Porto, PortugalUniversity of PortoPortugalPorto, PortugalFaculty of Sciences, University of Porto, Porto, Portugal

https://orcid.org/0000-0002-0818-4268

José M. Baptista

INESC TEC, Porto, Portugal, asguerre@fc.up.pt, josantos@fc.up.pt, jmb@staff.uma.ptINESC TECPortugalPorto, PortugalINESC TEC, Porto, Portugal, asguerre@fc.up.pt, josantos@fc.up.pt, jmb@staff.uma.pt

Faculty of Exact Sciences and Engineering, University of Madeira, Funchal, PortugalUniversity of MadeiraPortugalFunchal, PortugalFaculty of Exact Sciences and Engineering, University of Madeira, Funchal, Portugal

https://orcid.org/0000-0002-4111-1095

Ariel Guerreiro

INESC TEC, Porto, Portugal, asguerre@fc.up.pt, josantos@fc.up.pt, jmb@staff.uma.ptINESC TECPortugalPorto, PortugalINESC TEC, Porto, Portugal, asguerre@fc.up.pt, josantos@fc.up.pt, jmb@staff.uma.pt

Faculty of Sciences, University of Porto, Porto, PortugalUniversity of PortoPortugalPorto, PortugalFaculty of Sciences, University of Porto, Porto, Portugal

https://orcid.org/0000-0002-4542-7417

SCIMAGO INSTITUTIONS RANKINGS

INESC TEC, Porto, Portugal, asguerre@fc.up.pt, josantos@fc.up.pt, jmb@staff.uma.ptINESC TECPortugalPorto, PortugalINESC TEC, Porto, Portugal, asguerre@fc.up.pt, josantos@fc.up.pt, jmb@staff.uma.pt

Faculty of Sciences, University of Porto, Porto, PortugalUniversity of PortoPortugalPorto, PortugalFaculty of Sciences, University of Porto, Porto, Portugal

Figures | Formulas

Figures (5)
Formulas (9)

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Fig. 1
D-shaped photonic crystal fiber coated by gold slabs sensing platform. (a) Perspective view of the sensor. The entire fiber diameter is D = 24 μm, the diameter of each air hole is d = 1.76 μm and the pitch is Λ = 2 μm. The outermost layer that encloses the entire domain corresponds to a 0.1D thick PML. (b) Highlight of the two gold slabs deposited on the top of the flat face of the PCF. They present equal width W = 4 μm but different thicknesses: t₁ = 25 nm and t₂ = 40 nm.

Thumbnail

Fig. 2
Effective indexes of the confined modes in the SPR sensor based on a D-shaped PCF with two gold slabs of different thicknesses for an analyte with refractive index of 1.36. N_eff is the mode index and Y-pol designate the perpendicular polarization to the gold slabs. SPP mode 1 and SPP mode 2 are the dispersion curves of the plasmonic modes excited at the gold slabs of thicknesses t₁ and t₂, respectively. The insets show a detailed view of the intersections of the dispersion curves for the fundamental Y-polarized fiber mode and the plasmonic modes at the gold interfaces.

Thumbnail

Fig. 3
Distribution of the Y-polarized electric field intensity at the different wavelengths λ: (a) 570 nm, (b) 582 nm, (c) 600 nm, (d) 630 nm, (e) 650 nm and (f) 660 nm.

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Fig. 4
(a) Spectral losses of the SPR D-shaped PCF with two gold slabs for different dispersive profiles. (b) Distance Δλ_peak between SPR wavelengths as function of the dispersion slope dn/dλ. The green straight line represents the fitting curve for the computed values.

Thumbnail

Fig. 5
(a) Amplitude from the first resonance peak for different temperatures with a refractive index kept fixed at 1.36. (b) Computed data for the amplitude of first peak for different values of temperature and a linear fitting.

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

Fig. 1 D-shaped photonic crystal fiber coated by gold slabs sensing platform. (a) Perspective view of the sensor. The entire fiber diameter is D = 24 μm, the diameter of each air hole is d = 1.76 μm and the pitch is Λ = 2 μm. The outermost layer that encloses the entire domain corresponds to a 0.1D thick PML. (b) Highlight of the two gold slabs deposited on the top of the flat face of the PCF. They present equal width W = 4 μm but different thicknesses: t₁ = 25 nm and t₂ = 40 nm.

Fig. 2 Effective indexes of the confined modes in the SPR sensor based on a D-shaped PCF with two gold slabs of different thicknesses for an analyte with refractive index of 1.36. N_eff is the mode index and Y-pol designate the perpendicular polarization to the gold slabs. SPP mode 1 and SPP mode 2 are the dispersion curves of the plasmonic modes excited at the gold slabs of thicknesses t₁ and t₂, respectively. The insets show a detailed view of the intersections of the dispersion curves for the fundamental Y-polarized fiber mode and the plasmonic modes at the gold interfaces.

Fig. 3 Distribution of the Y-polarized electric field intensity at the different wavelengths λ: (a) 570 nm, (b) 582 nm, (c) 600 nm, (d) 630 nm, (e) 650 nm and (f) 660 nm.

Fig. 4 (a) Spectral losses of the SPR D-shaped PCF with two gold slabs for different dispersive profiles. (b) Distance Δλ_peak between SPR wavelengths as function of the dispersion slope dn/dλ. The green straight line represents the fitting curve for the computed values.

Fig. 5 (a) Amplitude from the first resonance peak for different temperatures with a refractive index kept fixed at 1.36. (b) Computed data for the amplitude of first peak for different values of temperature and a linear fitting.

(1)

\nabla_{⊥}^{2} E (r_{⊥}, ω) + k_{0}^{2} (ε (ω) - n_{e f f}^{2}) E (r_{⊥}, ω) = 0

(2)

ε_{A u} (ω) = ε_{\infty} - \frac{ω_{p}^{2} (T)}{ω (ω + i γ_{t} (T))} - \frac{Δ ϵ Ω_{L}^{2}}{(ω^{2} - Ω_{L}^{2}) + i ω Γ_{L}}

(3)

ω_{p} (T) = ω_{p} {[1 + γ_{e} (T - T_{0})]}^{- 1 / 2}

(4)

γ_{t} (T) = γ_{0} + γ (T) - γ (T_{0})

(5)

γ_{c p} (T) = γ_{0} [\frac{2}{5} + 4 {(\frac{T}{T_{D}})}^{5} \int_{0}^{T_{D} / T} \frac{z^{4} d z}{e^{z} - 1}]

(6)

γ_{c e} (T) = \frac{1}{6} π^{4} \frac{Γ Δ}{h E_{f}} [{(k_{B} T)}^{2} + {(\frac{h ω}{4 π^{2}})}^{2}]

(7)

n (λ, T) = \sqrt{A + \frac{B}{(1 - C / λ^{2})} + \frac{D}{(1 - E / λ^{2})}}

(8)

α = 8, 686 \times \frac{2 π}{λ} \times I m_{n e f f} \times 10^{4} (\frac{d B}{c m}),

(9)

S_{T} = Δ α_{peak} / Δ_{T} (dB / cmK)

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A Multi-Plasmonic Approach for Simultaneous Measurements based on a D-Shaped Photonic Crystal Fiber Sensor: from Temperature to Optical Dispersion

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