Instrumentation & Measurement Magazine 24-5 - 64
factors fj
entailed within the Lorentz dispersive model for the
macroscopic permittivity [15]:
2f
0 22
where ω is the angular frequency, ωp
and ε0
0 pj
,
j jj i
is the plasma frequency
is the free-space permittivity.
In this work, we explore theoretically the feasibility of applying
a SPR sensor based on a D-shaped PCF to monitor the
first-order dispersion of an optical medium. The proposed
sensing platform is projected to exhibit two distinct and independent
plasmonic resonance spectra in the optical domain.
This is obtained from a configuration that comprises two gold
slabs of different thicknesses deposited on the top of the core
region at the flat face of the D-shaped PCF. The sensing response
is taken as the changes in the distance between the
two resonance peaks in the spectral losses for linear dispersive
profiles. Upon a qualitative perspective, the numerical
computations show that the structure presents independent
responses for the average refractive index and for the dispersion,
with small crosstalk, allowing the spectral distances
between plasmonic resonances to be read as a linear function
of the first-order dispersion. Our final goal is to demonstrate
a principle suitable to characterize complex substances as fluidic
composites, whose optical properties are better modeled
in terms of dispersive relationships rather than an average refractive
index.
In the following sections, we detail the modelling of the
SPR sensor based on a D-shaped PCF and discuss the results
for dispersion sensing. A set of concluding remarks to highlight
the main properties of the sensor are also provided.
Designed Structure and Modeling
The proposed sensing
platform is schematically
depicted in Fig. 1. The PCF
is composed of a hexagonal
array of air holes embedded
in fused silica. The
cross-sectional area presents
four layers of air holes
around a core region of silica.
The fiber diameter is
D = 24 μm, the diameter of
each air hole is d = 1.76 μm
and the distance between
two adjacent air holes (also
named pitch) is Λ = 2 μm.
The PCF is side polished
to obtain a D-shaped crosssection,
and two gold slabs
of equal width but different
thicknesses (t1
t2
= 25 nm and
= 40 nm) are deposited on
the flat surface of the fiber.
64
(1)
A perfectly matched layer (PML) with thickness of 0.1D is used
in the numerical simulations for the truncation of the computational
domain.
The numerical modelling is carried out in the Finite Element
based software COMSOL Multiphysics [16]. More
specifically, the Wave Optics package in the frequency domain
is applied to compute the eigenvalues of the Helmholtz equation
in the angular frequency ω:
0.
2 22
In (2), k0
Er k,
n E r ,
eff
(2)
is the magnitude of the free-space wavenumber
and ε is the complex frequency-dependent relative permittivity.
The expression for ε also depends on the region at which (1)
is solved. E(
the position r perpendicular to the direction of light propagation.
The eigenvalue neff is the corresponding complex effective
index of the resulting modal fields that arise from the coupling
between the fundamental fiber mode and the plasmonic excitations
at the boundaries of the gold slabs. The real part of neff
refers to the mode phase. On the other hand, the imaginary
part is related to the losses experienced by the confined mode
as the fields are tunneled through the gold slabs.
An accurate modelling might consider the dispersive character
of all materials (dielectric and metallic components) that
compose the sensing structure. The air regions are modelled
by a constant refractive index nair
= 1. In turn, the refractive index
of silica is computed from the Sellmeier equation [17]. To
model the dispersive character of gold, we applied the DrudeLorentz
formalism [18], which is an improvement of the
original Drude model that provides a better approximation to
the corresponding experimental data:
Au
2
p
i
22
2
ΔΩL
ΩΓiLL
(3)
r ,ω) is the modal electric field distribution taken at
Fig. 1. Schematic design of the D-shaped photonic crystal fiber with two gold slabs. (a) Perspective view of the sensor
with fiber diameter D = 24 μm, diameter of air holes d = 1.76 μm and Λ = 2 μm. (b) The two gold slabs deposited on the top
of the flat face of the PCF are of equal width but different thicknesses: t1
corresponds to a 0.1D thick PML.
= 25 nm and t2
IEEE Instrumentation & Measurement Magazine
= 40 nm. The outermost blue layer
August 2021
Instrumentation & Measurement Magazine 24-5
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