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

Abstract 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.


I. INTRODUCTION
Surface plasmon-polaritons (SPPs) are electromagnetic modes that arise from the coupling between light and free electrons at conducting surfaces.Surface plasmons allow to surpass many limits in optical technologies, from near field enhancement to subwavelength optical confinement.Along the A Multi-Plasmonic Approach for Simultaneous Measurements based on a D-Shaped Photonic Crystal Fiber Sensor: from Temperature to Optical Dispersion last two decades, the effort into providing feasible techniques to excite and manipulate surface plasmon modes has been crucial to attain a broad variety of innovative technological applications.
In optical sensing, plasmonic resonances represent a noticeable milestone into achieving quite refined levels of sensitivity and resolution, which are direct results of the large amount of optical power confined at subwavelength scale [8].The sort of applications includes biochemical sensing, medical diagnosis, monitoring of pipeline integrity in the oil and natural gas industry, among others.
Based on the concepts of Krestchmann method to excite SPPs [9], the SPR sensors have evolved from bulky prism configuration to conducting layers fully integrated to optical fibers [10]- [11].The SPR condition occurs when the guided fiber mode phase matches the phase of the SPP at the interface between the fiber and the conducting layer.Some reported setups comprise the deposition of metallic nanoparticles over the tapered region of an optical fiber [12], grating-based fibers coated by metallic layers [13] or D-shaped fibers covered by conducting slabs on the flat face [14].Photonic crystal fibers (PCF) are particularly useful to excite plasmonic resonances due to the high mode confinement within a large mode area [15].SPR sensors based on D-shaped PCFs can be found in several designs [16]- [17].
In previous works, we extensively characterized a SPR sensor composed by a D-shaped PCF coated by gold layers of different thicknesses [18]- [19].This sensing platform yields multiple SPR channels able to not only detect average constitutive parameters such as refractive indexes but also to accurately describe the optical dispersion of a medium.In this article, we explore further the spectral characteristics of the SPR sensor based on a D-shaped PCF coated by two gold layers aiming at the simultaneous detection of optical dispersion regimes and temperature.Based on numerical results, we discuss how excited plasmonic resonances can offer independent sensing responses suitable for multiparameter readout.

II. THE DESIGNED STRUCTURE
The perspective view of the proposed sensor is depicted in Fig. 1 (a).The sensing configuration consists of a D-shaped PCF with diameter D = 24 µm composed by a hexagonal arrangement of air holes incrusted in fused silica.The region with absence of air holes has a diameter of 5 µm.The distance between two consecutive air holes (pitch) is Λ = 2 µm and the diameter of each air hole is d = 1.76 µm.This type of fiber can be fabricated from a stack-and-draw process [20] accompanied by a side-polishing or controlled etching technique [21] to obtain the D-shape of the fiber cross-section.In (1), k0 is the magnitude of the free-space wavevector and ε is the complex dispersive relative permittivity.E(r⊥,ω) is the modal electric field distribution at the position r⊥ perpendicular to the direction of light propagation.The effective index neff is associated to the resultant mode that arises from the coupling between the fundamental fiber mode and the SPP excited at the conducting interface.The real part of neff is related to the mode phase and the imaginary part corresponds to the losses of the confined mode due to the penetration of the evanescent fields into the gold layers.
An accurate solution of (1) at the optical domain must regard the dispersive characteristics of all materials involved in the design of the sensor.To model the dispersive character of gold, we applied the corrected Drude-Lorentz formalism [24], an improvement of the original analytical Drude model better adjusted to the corresponding experimental data: Where ε∞ = 5.9673 stands for the residual polarization of gold at high frequencies and the correction factors are given by Δϵ = 1.09,ΩL = 650.07THz and ΓL = 104.86THz.
The influence of the temperature T on ( 2) is included in the plasma frequency ωp (T) and in the damping factor γt (T) according to the Alabastri model [25]: (3) In ( 3) and ( 4), T0 is the room temperature and ωp and γ (T0) are the corresponding plasma and collision frequencies at T0, respectively.The constant γe =14.2x10 -6 K -1 is the expansion coefficient of gold and γ0 = 8.04x10 13 rad/s is the intraband damping coefficient.The γ (T) depends on two factors: phonon-electron scattering and electron-electron scattering.The temperature-dependent collision frequency γcp(T) is due to phonon-electron scattering and can be obtained from the Holstein model [26]: Where TD =170K is the Debye temperature.
The contribution γce due to electron-electron scattering can be modeled by using the Lawrence model [26]: Where Γ=0.55 is the average scattering probability over the Fermi surface, Δ=0.77 is the fractional Umklapp scattering, EF = 5.53 eV is the Fermi energy, h is the Plank constant and kB is the Boltzmanm constant.
The effect of the temperature in the fiber is included in the Sellmeier expression for the refractive index of silica [27].

III. MODELLING AND RESULTS
The surface plasmon resonance arises from the phase-matching between the fundamental fiber mode and the surface plasmon mode at the gold interface.At this point, field penetration into the gold layers is maximum and a peak in the losses can be observed.Fig. 2 displays the real and imaginary components of the effective index of the fundamental fiber mode and SPP dispersion curves for a sample with refractive index equal to 1.36 and for room temperature.The imaginary part of neff is depicted in terms of the confinement losses α [28]: where λ represents the wavelength and Imneff is the imaginary part of the effective mode index.
Although the fundamental mode of the PCF is degenerate for two orthogonal polarizations, only the polarization perpendicular to the gold interfaces can match the phase of the surface plasmon mode [18]- [19].Considering the orientation axes shown in Fig. 1, only the Y-polarized fundamental fiber mode is therefore capable of contributing to the SPR condition.Fig. 3. shows the distribution of the electric field intensity at the different wavelengths over the spectral range shown in Fig. 2, including the resonance wavelengths.Such field distributions correspond to the electric field perpendicular to the surface of the metallic slabs and therefore capable of exciting plasmonic resonances.The fundamental aspect is that the coupling between the fundamental fiber mode and the SPP at the gold interface is maximized when the phase-matching is reached.At λ = 582 nm (Fig. 3(b)), the major of optical power carried by the fiber mode is transferred to the surface plasmon mode at the thinner gold layer.There is another mode coupling at λ = 650 nm (Fig. 3(e)) that provides an additional SPR at the thicker gold layer.In this case, however, the coupling is not strong as it is seen for 582 nm.This difference in coupling is the reason of the smaller SPR peak amplitude at 650 nm shown in Fig. 2. On the other hand, Fig. 3(a), (c), (d) and (f) taken at off-resonance wavelengths show that both modes are excited separately, preventing a sharp increase in confinement losses at these wavelengths.The wave-coupling restricted by electric fields perpendicular to the conducting interface yields a low crosstalk between SPR spectral channels.As consequence, the SPR sensing platform shown in In the present work, we deal with the perspective of the multichannel SPR sensor being applied to also interrogate temperature.
On the contrary to the sensitivity of the optical dispersion, only the SPR channel excited at the thinner gold layer allows to obtain a linear sensing response to temperature variations.Hence, by considering the first resonance amplitude (which is associated to the SPP mode 1 in Fig. 2) we can estimate the temperature sensitivity of the sensor as: (9) Where Δαpeak is the amplitude resonance displacement and ΔT is defined as the changes in temperature.Since the variations in the temperature are estimated from the amplitude of the SPR peak excited at the thinner gold slab whereas the characterization of the dispersion regime is taken from the distance between resonance wavelengths, we infer that the proposed SPR sensor enables to monitor simultaneously dispersion and temperature.Moreover, the sensing response is obtained at one location of the sensor structure.This is a very attractive feature that reduces the complexity in interrogating several outputs provided by multiparameter optical sensors [29][30][31][32].By allowing simultaneous measurements of multiple quantities at the same place of the fiber, rather than placing specialized sensors sequentially along the fiber, this approach extends the notion of distributed sensing.Indeed, instead of having each quantity measured at a specific location, it is possible to obtain the set of variations of different monitored quantities at separated places of the fiber by distributing several multiple parameter sensors along it.
We can even consider adding the interrogation of refractive indexes to the multichannel SPR sensor.
The shifts in the resonance wavelength at the SPR peak excited at the thicker gold slab can be linearly related to changes in the refractive index of the analyte.Nonetheless, we remark that the entire SPR sensing structure is optimized to characterize the dispersive profile of the analyte and thus only a small average sensitivity of 375 nm/RIU for the two SPR spectra can be achieved for refractive

Fig. 1 .
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 .
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 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. 1 Fig. 4 .
Fig. 1 can respond unambiguously to the dispersion regime of the external medium.The characterization of the optical dispersion is based on the changes in the spectral distance between the two resonance peaks as illustrated in Fig. 4. (a) Regarding the difference in resonance wavelengths for a constant refractive index as reference, the distance between the two peaks decreases for the anomalous dispersion whereas the normal dispersion leads to a larger difference [18].Fig. 4. (b)

Fig. 5 (
Fig. 5 (a) shows the variation in the confinement losses with the temperature for an analyte with refractive index kept fixed at 1.36 for the first peak in Fig. 2. The losses decrease with increasing temperatures at an average sensitivity of -0.86 dB/cmK as displayed in Fig. 5(b).

Fig. 5 .
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.
indexes in the range[1.3,1.39].IV.CONCLUSIONSThis paper addressed the potential of a multichannel SPR sensor based on a D-shaped PCF to be applied as a multiparameter sensing platform.The flat surface of the D-shaped PCF is coated by two gold layers of different thicknesses that enable the excitation of two SPR spectral channels based on the waveguide coupling technique.It has already been demonstrated that these two channels present low crosstalk and are sensitive to both normal and anomalous dispersion regimes when analyzed in combination.This work introduced an additional sensing functionality by which the temperature of the analyte is linearly related to the variations in amplitude of the sharper SPR peak.In particular, the proposed SPR sensor comprises two distinct sensing principles that can be applied for a simultaneous measurement of temperature and optical dispersion.These sensing properties are quite appropriate for a better characterization of complex composites as fluidic media with time-varying constituents.Upon a general framework, we summarize that the applicability of the SPR sensor configuration for multiparameter sensing purpose benefits from two independent responses taken at a single location on a D-shaped PCF.ACKNOWLEDGMENT This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior -Brazil (CAPES) -Finance code 001.During the period of elaboration of this work, the authors have Journal of Microwaves, Optoelectronics and Electromagnetic Applications, Vol.22,No. 1, March 2023 Brazilian Microwave and Optoelectronics Society-SBMO received 4 Apr 2022; for review 11 Apr 2022; accepted 5 Dec 2022 Brazilian Society of Electromagnetism-SBMag © 2023 SBMO/SBMag ISSN 2179-1074