Instrumentation & Measurement Magazine 24-5 - 65

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. Neff
and SPP mode t2
and t2
of the intersections of the dispersion curves for the fundamental Y-polarized fiber mode and the plasmonic modes at the gold interfaces.
The parameters ωp
= 2155.6 THz and γ = 15.92 THz are
the plasma frequency and damping factor, respectively, and
ε∞
= 5.9673 stands for the residual polarization of gold at
high frequencies. The parameters in the correction factor are
 = 1.09, ΩL
= 650.07 THz and ΓL
= 104.86 THz.
Results and Discussion
An optimal coupling is achieved when the phase of the fundamental
fiber mode matches the phase of the surface plasmon
mode. As a result, the penetration of the fields into the gold
layers is maximized and a peak in the losses at the optical spectrum
can be visualized. It is illustrated in Fig. 2, where the
computed real and imaginary parts of the effective indexes
of the fundamental fiber mode and plasmonic modes are displayed
for an analyte with refractive index equal to 1.36.
Regarding the overall sensing structure as an insulatormetal-insulator
(IMI) configuration, then the refractive index
detection can be transduced in terms of the dependence of the
resonant wavelength at which the peak occurs upon the optical
properties of the analyte. Since the excited plasmonic
modes are strongly impacted by the structural parameters of
the metallic slabs, several resonant peaks are expected to be obtained
by adding metallic layers of different dimensions.
We also point out that the fiber mode must be guided in the
proper polarization for the coupling to be maximal. In fact, the
fundamental mode of the PCF is degenerate, presenting two
orthogonal polarizations. Solely, the polarization perpendicular
to the gold interfaces allows for the excitation of plasmonic
modes. Therefore, our numerical simulations are focused on
the optical modes with polarization normal to the gold slabs.
In the present work, we explore further the dependence of
plasmon resonances on the refractive index of the analyte to
August 2021
show that the structure can also provide information about
the dispersion profile. We carried out computations of the
SPR spectral losses for the dispersive characters: constant
refractive index, normal dispersion and anomalous dispersion.
Fig. 3 displays the spectral losses of the SPR D-shaped
PCF with two gold slabs for the three dispersion regimes. The
spectral losses for a constant refractive index equal to 1.36
(dotted red line) are represented by the dotted blue line and
show two distinct regions of maximum absorption due to the
nonuniformity of the gold slabs deposited on the flat face of
the PCF (the two gold slabs have different thicknesses). The
higher losses are located at shorter wavelengths and are associated
with the plasmonic modes excited at the interface of
the thinner gold slab.
Furthermore, we consider two arbitrary media with dispersion
curves of opposite slopes. As a first approximation,
the refractive index is supposed to be linearly dependent on
the wavelength. In Fig. 3, the solid blue line represents the
spectral losses due to the anomalous dispersion curve (solid
red line) whereas the dashed blue line comprises the losses
associated to the normal dispersion curve (dashed red line).
Analogous to the case of a constant refractive index, there
are two distinct resonance wavelengths for a dispersive refractive
index. It indicates that the wavelengths for the phase
matching between the fiber mode and the surface plasmon
mode remain clearly determined for spectral-varying refractive
indexes. Concerning the amplitude of the resonance
peaks, it is observed that larger losses are related to the thinner
gold layer for the three cases. On the other hand, the
distance between the resonance wavelengths is influenced
by the dispersion profile. Taking the case of constant refractive
index as reference, the distance between the two peaks
IEEE Instrumentation & Measurement Magazine
65
is the mode index and Ypol and Xpol designate the polarizations perpendicular and parallel to the gold slabs, respectively. SPP mode t1
are the dispersion curves of the plasmonic modes excited at the gold slabs of thicknesses t1
, respectively. The insets show a detailed view

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