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Highly sensitive dual-function sensor for refractive index and temperature using D-shaped microchannel photonic crystal fiber

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Abstract

An innovative ultra-sensitive, dual-functional sensor employing a D-shaped microchannel photonic crystal fiber (PCF) for refractive index (RI) and temperature measurements is proposed and comprehensively investigated. Its high-sensitivity is achieved through the incorporation of gold (Au) and magnesium fluoride (MgF2) as plasmonic materials in the micro-rectangular channel. This configuration significantly enhances the interaction between the surface plasmon polaritons (SPPs) field and y-polarized evanescent field on external surfaces. Additionally, the integration of a temperature-sensitive fluid within the sensor allows for precise detection of temperature changes. Our simulations demonstrate a broad detection spectrum, covering RI values from 1.27 to 1.43 and temperatures ranging from 45°C to 100°C. The sensor achieves peak sensitivities of 31800nm/RIU for RI and 49 nm/°C for temperature. Besides, the sensor only has a cladding consisting of three air holes to enhance coupling and reduce the difficulty of preparation. Importantly, the sensor's performance remains robust against minor structural alterations in the PCF, indicating high fault tolerance. Given its high sensitivity, extensive detection range, and strong fabrication stability, this PCF-SPR sensor offers significant potential for applications in biochemical sensing and environmental monitoring.

© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Optical fiber sensors, due to their compact size, anti-electromagnetic interference and corrosion resistance, have been widely used in people's life and production [13]. Recent advancements in surface plasmon resonance (SPR) technology have further expanded the scope of optical fiber-based SPR sensors [4]. These sensors are now extensively used in refractive index (RI) sensing, bioimaging, and early disease diagnosis [58].

Traditional optical fiber-based SPR sensors, often employing gold (Au) film on photonic crystal fibers (PCF), faced limitations in sensitivity due to the weak coupling of core mode energy to the fiber surface [9,10]. The emergence of microstructured optical fibers (MOFs) provides an opportunity to solve this problem [11]. The structural adaptability of MOFs allows for the rectification of phase-matching issues between core and plasma modes, enhancing the SPR effect. For example, Bing et al. demonstrated enhanced wavelength sensitivity (4028 nm/RIU) by directly plating Au film inside the PCF air holes [12]. Similarly, Luan et al. introduced a hollow-core PCF-SPR sensor, featuring analyte-filled core holes and silver plating in the cladding holes, which achieves a broad refractive index detection range [13].

Despite these advancements, challenges persisted in metal coating and analyte introduction within micro-sized air holes. Innovations such as open-structure fibers with side-polished and side-open designs emerged, simplifying these processes [1416]. For instance, Chen et al.'s open-loop D-type PCF significantly improved sensor sensitivity [17]. However, the increasing complexity of detection demands necessitated sensors capable of multiple parameter measurements.

Addressing this need, dual-parameter PCF-SPR sensors have been developed. Luan et al. proposed a design featuring two orthogonal sensing channels – one for RI and the other for temperature [18]. These channels, coated with silver and filled with a thermo-sensitive polymer, achieved maximum sensitivities of 0.618 nm/°C and 12500 nm/RIU, respectively. Zhang et al. developed a unique D-type photonic crystal fiber (PCF) featuring dual polished surfaces. They employed polydimethylsiloxane (PDMS) and titanium dioxide (TiO2) as the respective sensing materials for refractive index (RI) and temperature. The sensitivities up to 1.25 × 104 nm/RIU for RI and 0.7 nm/°C for temperature were obtained [19]. While these design considerably improved RI sensitivity, the temperature sensitivity remained relatively low. Yin et al. further advanced this design with a dual-channel structure, one surface polished and coated in gold and the other filled with a temperature-sensitive medium [20]. The structure has a peak sensitivity of 8400 nm/RIU and a temperature sensitivity of 10.2 nm/°C. Tian et al. designed a dual-channel PCF-SPR sensor by coating TiO2/silver film on left side (for refractive index detection) and PDMS/TiO2/silver film on the right side (for temperature detection), ultimately achieving the highest sensitivities for refractive index and temperature of respectively 6700 nm/RIU and -21 nm/°C [21]. Thereby, this shows that they increase temperature sensitivity but at the expense of RI sensitivity.

To simultaneously enhance sensitivity and facilitate crosstalk-free temperature and RI detection, a dual-core structure with simultaneous polishing on both the top and bottom sides of the fiber was shown by Yin et al. [22]. Each core featured a polished surface coated with Au film, one of which was also embedded with a temperature-sensing medium. This design achieved substantial sensitivity improvements, reaching up to 20,000 nm/RIU for RI and 9.2 nm/°C for temperature. Wang et al. presented a three-core microstructured fiber consisting of an arrangement of 61 air holes, one of which was permeated with a temperature-sensitive material (chloroform), and simulations yielded temperature and wavelength sensitivities as high as 14.1 nm/°C and 26771.7 nm/RIU [23]. However, the complexity of these design, which included multiple polishing planes and a large number of air holes, made them impractical and costly for mass production.

Our research addresses these manufacturing challenges by introducing a novel micro-rectangular channel D-shaped PCF-SPR sensor for RI and temperature. This design, featuring a micro-rectangular opening near the PCF core, significantly enhances the coupling between the evanescent and plasma waves, thus markedly improving the sensor's dual-parameter detection capabilities. Finite Element Method (FEM) calculations indicate a peak sensitivity of 31800nm/RIU for RI (range between 1.27 to 1.43) and 49 nm/°C for temperature (from 45°C to 100°C). Furthermore, our analysis suggests that the sensor's sensitivity is largely unaffected by variations in the PCF's structural parameters, indicating a robust fabrication tolerance.

2. Structural design and modelling

The cross-sectional structure of the sensor is demonstrated in Fig. 1(a), illustrating a PCF structure with three air holes and a rectangular groove. This design not only prevents escape of energy from the core to the cladding, but also adjusts the dimensions of the core to help enhance the coupling strength between the two modes (core and SPP modes), particularly on the surface of polished rectangular groove. The air holes, each with a radius of , are uniformly spaced, with an inter-hole distance of ${\wedge}$. The width and depth of the rectangular groove structure are w and h, respectively. An Au film with thickness t and MgF2 film with thickness ${t_1}$ are deposited on the rectangular groove as sensing material.

Figure 1(b) presents the 3D structure of the complete D-typed PCF-SPR sensor. The structure of PCF can be manufactured by using the stack-and-draw method [24], where it consists mainly of solid rods and capillaries stacked up. The size of the air holes can be adjusted by changing the thick and thin capillaries. Following the stacking process, a flat D-type PCF is produced through a polishing technique. The micro-rectangular grooved structure on flat surface is manufactured using focused ion-beam milling [25]. Finally, Au and MgF2 were plated on the D-shaped PCF's slotted structures using magnetron sputtering [26]. Figure 2 shows the measurement system setup for the feasibility of the proposed D-type PCF-SPR sensor. The light source (broader spectrum) (DH-2000-BAL, Ocean Optics Inc.) is transmitted through the SMF to the D-shaped PCF SPR sensor region to excite the SPR effect. A second SMF couples the sensing head to a miniature spectrometer (USB 4000, Ocean Optics Inc.), which records information on the change in the loss spectrum affected by changes in the RI and temperature of the external analyte. The measurement data is then collected and processed by a computer for further analysis.

 figure: Fig. 1.

Fig. 1. Structural schematic of (a) 2D cross-section of the designed PCF-SPR sensor. (b) the corresponding 3D.

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 figure: Fig. 2.

Fig. 2. Measurement system setup of the proposed D-type PCF-SPR sensor.

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The performance of the sensor is modeled using the FEM in COMSOL Multiphysics software. Key parameters of the designed PCF-SPR sensor are specified in Table 1. During simulation, FEM conducts a modal analysis, dividing the sensor's 2D x-y plane into 43,396 cells. These cells have a minimum mass of 0.4773 and an average mass of approximately 0.825. To enhance calculation accuracy, the model incorporates a perfect matching layer (PML) and scattering boundary conditions, which absorb scattered light energy effectively. The PML thickness is strategically set at 20% of the lattice constant. The background material for the sensor is silicon dioxide (SiO2), and its dispersion characteristics are defined by the Sellmeier equation [27]:

$${\textrm{n}_{Si{O_2}}}(\lambda )= \sqrt {1 + \sum\limits_{i = 1}^3 {\frac{{{\textrm{A}_i}{\lambda ^2}}}{{{\lambda ^2} - \textrm{B}_i^2}}} }$$
where ${\textrm{n}_{Si{O_2}}}(\lambda )$ is the RI of the proposed sensor’s cladding, $\lambda$ represents the wavelength of the incident light, and the values of the ${\textrm{A}_1}$, ${\textrm{A}_2}$, ${\textrm{A}_3}$, ${\textrm{B}_1}$, ${\textrm{B}_2}$, and ${\textrm{B}_3}$ coefficients in the Sellmeier equation are shown in Table 2. The RI of the air holes in the cladding sector is assumed to be 1. The dielectric constant of Au is based on Johnson and Christy [28]. MgF2, characterized by its low dispersion and high stability, is well-suited as a buffer material between the metallic coating and the optical fiber to optimize the sensor's performance, and its RI is from Ref. [29].

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Table 1. Parameter settings for the designed PCF-SPR sensor

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Table 2. Coefficients of the Sellmeier equation for silicon dioxide

The analytes to be measured are located around the optical fiber, depicted in light blue in Fig. 1(a). For these analytes, the RI values ranged from 1.27 to 1.43. The sensor's performance is evaluated by observing the shifts degree in the loss spectrum at various incident wavelengths, and the loss can be calculated as [30]:

$$\textrm{Loss} = 8.686 \times \frac{{2\pi }}{\lambda } \times {\mathop{\rm Im}\nolimits} ({n_{eff}}) \times {10^4}$$
where $\lambda$ is the free-space wavelength in meter and ${\mathop{\rm Im}\nolimits} ({n_{eff}})$ represents the imaginary part of the effective refraction of the fiber core mode.

Compared to using Au film alone, the use of composite layer material (Au + MgF2) can substantially increase the wavelength sensitivity $(\textrm{WS})$, which is calculated by the following formula [30]:

$$\textrm{WS} = \frac{{\Delta \lambda }}{{\Delta {n_a}}}(\textrm{nm}/\textrm{RIU})$$
where $\Delta \lambda$ denotes the wavelength distance corresponding to the two peaks and $\Delta {\textrm{n}_a}$ denotes the variations in the RI of the analyte to be measured.

Another parameter for evaluating sensor performance is figure-of-merit $\textrm{(FOM)}$, which is defined as [31]:

$$\textrm{FOM} = \frac{{\textrm{WS}(\textrm{nm}/\textrm{RIU})}}{{\textrm{FWHM}(\textrm{nm})}}$$
where $\textrm{RI}{\textrm{U}^{ - 1}}$ is the unit of $\textrm{FOM}$, $\textrm{WS}$ is the sensor sensitivity which is defined in Eq. (3), and $\textrm{FWHM}$ is the full width at half maximum of the resonant loss spectrum.

Finally, to assess the sensor's detection capability, a resolution parameter is introduced. This parameter is calculated as follows [31]:

$$R(\textrm{RIU}) = \frac{{\Delta {n_a} \times \Delta {\lambda _{\min }}}}{{\Delta \lambda }}$$
where $\Delta {n_a}$ is the variation of the RI of the analyte to be measured, $\Delta {\lambda _{\min }}$ indicates the minimum spectral resolution (generally taken as 0.1 nm), and $\Delta \lambda$ indicates the resonance wavelength shift distance.

3. Results and discussion

3.1 Coupling characteristics analysis

Figure 3 presents the loss spectra and the dispersion relation between the core mode and the SPP mode. The orange curve, calculated using Eq. (2), shows negligible loss. The corresponding electric field distribution, as shown in Fig. 3(b), demonstrates that the energy predominantly remains within the fiber core. In contrast, the green curve represents the y-polarization loss curve. This curve exhibits an initial increase with the wavelength, reaching a maximum peak at the resonant wavelength, then subsequently decreases with further increase in wavelength. The resonant wavelength is observed at 755 nm, where the peak's location exactly coincides with the intersection of the two dispersion curves. This intersection, representing the equality of the effective refractive index of the core and SPP modes of the sensor, signifies the phase-matching coupling phenomenon. Figures 3(c) and (d) depict the electric field distributions for the y-polarized fiber core mode and the y-polarized SPP mode at the 755 nm resonance, respectively. These images reveal that the energy of the fundamental mode under y-polarization is not exclusively confined to the core. Instead, a portion of this energy transitions to the surface of the composite material, composed of Au and MgF2 films. This energy then contributes to the coupling of the fiber core and slot surface’s modes. Such intense electromagnetic field coupling is likely to enhance the sensor's sensitivity.

 figure: Fig. 3.

Fig. 3. Loss spectra with dispersion and modal characteristics when $\textrm{r}$= 8.6 µm, $h$= 3 µm, $H$=${\wedge}$= 18 µm, $D$= 58 µm, RI = 1.39, $t$= 50 nm, ${t_1}$= 20 nm. (a) Loss spectra of the fundamental mode in x/y polarization and dispersion relations of the effective refractive index of the fundamental and the SPP modes in y-polarization. Electric field distribution at the resonant wavelength of (b) the non-resonance fundamental mode of x polarization (c) resonance fundamental mode of y polarization coupled to SPP mode and (d) SPP mode of y polarization.

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3.2 Influence on sensing characteristics of structural parameters

This section investigates the impact of various structural parameters on the performance of the PCF-SPR sensor. These parameters include metal layer thickness t, of the dielectric layer thickness ${t_1}$, radius of the air holes $\textrm{r}$, depth of the rectangular slot h, air holes spacing ${\wedge}$, and polished depth H. The study utilizes the control variable method to monitor changes in the loss spectrum, maintaining all parameters constant except for one variable at a time.

3.2.1 Optimization of Au film thickness ($t$) and MgF2 film thickness (${t_1}$)

Figure 4(a) presents the impact of varying Au layer thicknesses on the sensor's overall performance. It is noted that an increase in gold thickness at a constant RI led to a redshift in the resonance wavelength and a decrease in the loss value. Specifically, a 40 nm gold film exhibited the sharpest peak with the narrowest FWHM, whereas a 60 nm film presents a flatter peak and wider FWHM. The latter can potentially lead to false positives in detection due to the SPR effect being diminished when the metal layer is too thick for the electric field to penetrate effectively [32]. To evaluate the influence of gold film thicknesses on sensing performance, the study calculates wavelength sensitivity for thicknesses of 40 nm, 50 nm, and 60 nm. At an RI of 1.40, the resonance wavelengths for these thicknesses are 0.778 µm, 0.814 µm, and 0.830 µm, respectively. With an increase in RI to 1.41, these wavelengths shift to 0.855 µm, 0.896 µm, and 0.915 µm. The sensitivities for 40 nm, 50 nm, and 60 nm thicknesses are determined to be 7700 nm/RIU, 8200 nm/RIU, and 8500 nm/RIU, respectively. Therefore, a 50 nm thickness emerges as the optimal choice, balancing sensitivity and transmission loss. Similarly, Fig. 4(b) investigates the effects of varying the thickness of the MgF2 layer, keeping other parameters fixed. This analysis reveals that an increase in MgF2 thickness results in a shift of the resonance peak to shorter wavelengths, while the loss gradually increases at the same RI. Wavelength sensitivities for MgF2 thicknesses of 20 nm, 30 nm, and 40 nm are calculated to be 8200 nm/RIU, 8100 nm/RIU, and 7900 nm/RIU, respectively. Considering both peak loss and sensitivity, a 20 nm thickness of the MgF2 layer is determined to be the most effective for enhancing sensor performance.

 figure: Fig. 4.

Fig. 4. (a) Variation of loss spectra for RI = 1.40 and 1.41 at different metal layer thicknesses t (${t_1}$= 20 nm, $\textrm{r}$= 8.6 µm, $h$= 3 µm, $H$=${\wedge}$= 18 µm). (b) Variation of loss spectra for RI = 1.40 and 1.41 at different dielectric layer thicknesses ${t_1}$ ($t$= 50 nm, $\textrm{r}$= 8.6 µm, $h$= 3 µm, $H$= ${\wedge}$= 18 µm).

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3.2.2 Optimization of air hole radius $\textrm{r}$, rectangular groove depth h, polishing depth H and air hole spacing ${\wedge}$

The exploration of PCF structural parameters and their impact on the performance of the PCF-SPR sensor is further detailed. Figure 5(a) illustrates the change in the loss spectrum as the air hole size is increased from 8.4 µm to 8.8 µm. The findings indicate that as the air hole radius expands, there is a corresponding increase in loss. This phenomenon occurs due to the squeezing of the fiber core as the air hole enlarges, facilitating more energy to couple into the metal-dielectric interface of the rectangular slot, thereby enhancing the SPR coupling effect and gradually increasing the loss. In Fig. 5(b), the impact of modifying the height of the rectangular slot is examined. An increase in slot depth from 2 µm to 4 µm leads to a gradual increase in loss, while the resonance wavelength remains unchanged. The deepening of the slot brings the fiber core in closer proximity to the polished rectangular slot, enhancing the coupling of the core's energy to the polished surface where the plasma composite is situated, resulting in elevated confinement loss. Figure 5(c) demonstrates that a rise in the lattice constant ${\wedge}$ results in a decrease in peak loss. This outcome is due to a reduction in energy transfer from the core mode to the surface of the SPP mode, ultimately leading to a decrease in loss. Figure 5(d) presents the effects of increasing the PCF polishing depth. Although this increase does not shift the resonance wavelength, it does lead to higher sensor loss. This effect is similar to the impact of deepening the rectangular slot, where the reduced coupling distance between the evanescent wave and the surface plasma wave (SPW) amplifies the coupling strength between the fundamental and SPP modes, thus increasing coupling loss.

 figure: Fig. 5.

Fig. 5. Effect of PCF parameters on loss values and phase matching points at RI = 1.40. (a) Effect of different air hole radius $\textrm{r}$ on loss spectra ($t$= 50 nm, ${t_1}$= 20 nm, $h$= 3 µm, ${\wedge}$= 18 µm, and $H$ = 18 µm).(b) Effect of different rectangular slot depths h on loss spectra ($t$ = 50 nm, ${t_1}$= 20 nm, $\textrm{r}$= 8.6 µm, ${\wedge}$= 18 µm, and $H$= 18 µm). (c) Effect of different air-hole spacings ${\wedge}$ on loss spectra ($t$= 50 nm, ${t_1}$ = 20 nm, $\textrm{r}$= 8.6 µm, $h$= 3 µm and $H$= 18 µm). (d) Effect of different polishing depths H on loss spectra ($t$= 50 nm, ${t_1}$= 20 nm, $\textrm{r}$= 8.6 µm, $h$= 3 µm, ${\wedge}$= 18 µm).

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From the Fig. 5, it is evident that the position of the resonance peak remains largely unaffected by minor alterations in PCF structure, indicating favorable manufacturing tolerances for PCF fabrication. However, given the elevated loss of the PCF at higher analyte RI, it is imperative to maintain a consistent loss value throughout the entire RI range. Consequently, the PCF with air hole radius $\textrm{r}$= 8.6 µm, rectangular slot depth $h$= 3 µm, lattice constant ${\wedge}$= 18 µm and polishing depth $H$= 18 µm is selected for future experiments and analysis.

3.3 RI sensing characteristics of the designed sensor

In order to analyze the RI sensing capabilities of the PCF-SPR sensor, we computed its loss spectrum across an RI range of 1.27 to 1.43, with increments of 0.01 in RI. The outcomes of this analysis are depicted in Fig. 6. The trend observed demonstrates a gradual red-shift and an increase in the loss peak as the RI of the external environment escalates. Specifically, at a wavelength of 552 nm and an RI of 1.27, the sensor exhibits the lowest peak loss, recorded at 0.871 dB/cm. Conversely, with an RI of 1.43, the peak loss intensifies to 39.158 dB/cm at a resonance wavelength of 1.356 µm, which indicates the strongest coupling between the fundamental mode and the SPP mode. Table 3 presents the detailed data on peak loss and resonance wavelengths for various analyte RIs. It can be seen that when the RI alters from 1.42 to 1.43, the maximum shift is 318 nm. Utilizing Eq. (3) and Eq. (5), the maximum RI sensitivity and the corresponding resolution are computed to be 31800nm/RIU and 3.14 × 10−6 RIU, respectively. Additionally, FOM for the PCF-SPR sensor, as derived from Eq. (4), is calculated to be 211 RIU-1, highlighting its potential for high-precision sensing applications.

 figure: Fig. 6.

Fig. 6. Loss spectrum of PCF for analyte RI varying from 1.27 to 1.43.

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Table 3. Performance of the designed sensor in the range of 1.27 to 1.43

Figure 7 displays the relationship between resonance wavelength and sensitivity changes in response to varying analyte RI. The curves exhibit similar trends, highlighting a strong linear response in both wavelength resonance and sensitivity within the RI range of 1.27 to 1.34, achieving an R2 value of 0.98166. This linearity is beneficial for practical and straightforward calibration of the fabricated sensor before actual analyte testing.

 figure: Fig. 7.

Fig. 7. Variation in resonance wavelength and sensitivity of analyte RI across the range

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Additionally, the FWHM and FOM across the complete measurement range have been calculated, as illustrated in Fig. 8. In line with Eq. (4), an inverse proportional relationship is observed between FWHM and FOM. The sensor's FOM progressively improves as the FWHM decreases, reaching an optimal performance of 211 RIU-1 at an analyte RI of 1.43.

 figure: Fig. 8.

Fig. 8. Variation in FWHM and FOM of analyte RI across the range

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Moreover, Fig. 9 presents the peak loss and resolution within the RI range of 1.27 to 1.43. Notably, in the RI interval of 1.27 to 1.43, which aligns with the resonance wavelengths shown in Fig. 7, the sensor has a peak loss fit with a coefficient of determination R2 value of 0.93127, indicative of high linearity. The resolution is observed to increase gradually with a decrease in RI, equaling at RI values of 1.30 and 1.31, and achieving a minimum wavelength resolution of 1.25 × 10−4 RIU. At an RI of 1.43, the wavelength sensitivity attains its maximum, and the resolution reaches up to 3.14 × 10−6 RIU. This demonstrates the sensor's ability to detect minute changes in the RI of external analytes to an order of magnitude of ×10−6.

 figure: Fig. 9.

Fig. 9. Variation in peak loss and resolution of analyte RI across the range

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MgF2 reduces the damping typically associated with plasmonic materials like gold and silver, sharpening the resonance peak and enhancing sensor resolution and sensitivity [33]. Therefore, we simulated the performance of the PCF-SPR sensor without MgF2 by setting up a control group. The results of the corresponding WS, FWHM and FOM calculations are shown in Table 4. By comparing the theoretical simulation results of the sensing performance parameters of PCF/Au sensor and PCF/MgF2/Au sensor, it can be seen that by adding MgF2 as the buffer layer material between the optical fiber and Au, the wavelength sensitivity of the sensor can be increased from 14100 nm/RIU to 14200 nm/RIU, and the FWHM can be reduced from 76 nm to 68 nm. FOM is an essential metric for assessing the performance of a sensor. It has been determined that there has been a significant enhancement in this metric, with an increase from 185.53 RIU-1 to 209.04 RIU-1, representing a performance gain of 1.13 times. These comparisons underscore the critical role of the MgF2 buffer in strengthening core-SPP mode coupling.

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Table 4. Comparative performance analysis of two sensor structures

4. Temperature characterization of the designed sensor

Finally, we explore the temperature sensing detection characteristics of the proposed sensor, utilizing RI-based sensing techniques. In this approach, the matching liquid of the analyte is substituted with a temperature-sensitive liquid, whose thermal properties depend on the RI of this fluid. The relationship between temperature and the RI of the filled analyte is defined as follows [34]:

$$\textrm{n} = {n_{liquid}} + {{dn} / {dT}}({T - 25} )$$
where n represents the RI of the filled liquid at room temperature 25°C, ${n_{liquid}}$ is the RI of the analyzing liquid, and $dn/dT$ is the thermo-optical coefficient. In the PCF-SPR sensor, material dispersion of the filled liquid is not considered. Here, the chosen material is an ethanol-glycerol mixture, comprising 34% ethanol and 66% glycerol. The RI of this temperature-sensing liquid is 1.436, with a thermo-optical coefficient of -2.8 × 10−4/°C [35,36]. The temperature sensing mechanism operates on the principle that a change in the RI of the sensing liquid leads to a shift in the loss peak, thereby enabling temperature detection through measuring shifts in the resonance wavelength.

Figures 10(a) and (b) illustrate the loss spectrum's variation with temperature. As the temperature increases, a progressively blue shifted resonance wavelength occurs. This shift is attributed to the decrease in RI of the temperature-sensing liquid with rising temperature, causing the effective refractive indexes of the fundamental and SPP modes to resonantly couple at shorter wavelengths. In Fig. 10(a), the most significant offset, occurring between 45°C and 50°C, is approximately 111 nm. Figure 10(c) presents the fitting curve correlating different temperatures with their corresponding resonance wavelengths, with a fitting coefficient of 0.98832. For more accurate detection, the loss was measured for temperatures between 45°C to 50°C in 1°C increments, as depicted in Fig. 10(b). This data reveals a maximum offset of 49 nm between 45°C and 46°C. Additionally, the peak wavelength in relation to temperature is calculated and displayed in Fig. 10(d), yielding an R2 value of 0.94802. The temperature sensitivity can be calculated by replacing $\Delta {n_a}$ with ΔT in Eq. (3), using data from Figs. 10(c) and (d). The calculated temperature sensitivity are 111 nm/°C and 49 nm/°C for a 5°C and 1°C step, respectively. The corresponding temperature resolution are 4.5 × 10−3 RIU and 2.04 × 10−3 RIU, respectively, which can be calculated by Eq. (5).

 figure: Fig. 10.

Fig. 10. (a) Loss spectra with temperature increasing from 45°C in 5°C steps by 100°C. (b) Loss spectra with temperature increasing from 45°C in 1°C step by 50°C. (c) Fitted functional relationship between peak wavelengths and temperature (45°C-100°C). (d) Fitted functional relationship between peak wavelengths and temperature (45°C-50°C).

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The comparison of the proposed two-parameter detection sensor with other reported SPR-based sensors is shown in Table 5. This comparison highlights that the designed sensor features a simple structure, yet offers high sensitivity and a broad detection range. It effectively enables dual detection functions for both RI and temperature.

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Table 5. Comparison between the designed in this work and already reported PCF-SPR sensors

5. Conclusion

In summary, an ultra-sensitive, two-parameter sensor utilizing SPR technology with a micro-rectangular channel design in PCF is systematically investigated. This design incorporates a micro-rectangular channel coated with a 50 nm Au layer and a 20 nm MgF2 layer to enhance sensor sensitivity. Finite element analysis indicates that for RI sensing, the sensor has a maximum RI sensitivity of 31,800 nm/RIU, a maximum resolution of 3.14 × 10−6 RIU, and a FOM of 211.07 RIU-1 in the analyte RI range of 1.27-1.43. Regarding temperature sensing, the sensor demonstrates a maximum temperature sensitivity of 49 nm/°C within over 45°C to 100°C range, along with a corresponding resolution of 2.04 × 10−3 RIU. These simulation results demonstrate that the sensor is competitive within the two-parameter sensor device, with good fabrication tolerances and reducing the precision requirements. Its unique features of single-layer air-hole structure and low loss make it ideal for chem/bio sensing. It can be used to detect and quantify biological elements such as proteins, antibodies, DNA, and small molecules. The sensor's dual function of detecting RI and temperature makes it useful in medical diagnostics and health monitoring for analyzing various disease markers in body fluids such as blood or urine. In addition to this, the sensor can also be used for environmental detection, such as water quality testing and detection of pollutants in gases. Thus, the wide range of analyte objects and high sensing performance of the sensor make it a valid candidate for SPR-PCF sensor applications.

Funding

National Development and Reform Commission Major Platform Project (B2023118), National Natural Science Foundation of China (62275102), Youth Talent Support Program of Fujian Province (Eyas Plan of Fujian Province) (Z02104), Science and Technology Major Project of Fujian Province (2022HZ022019, Second-Phase Subsidy of Key External Cooperation Projects of Fujian Province (2022CXY0313), Marine and Fishery Development Special Fund of Xiamen (21CZB013HJ15).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data will be made available on request.

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Data availability

Data will be made available on request.

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Figures (10)

Fig. 1.
Fig. 1. Structural schematic of (a) 2D cross-section of the designed PCF-SPR sensor. (b) the corresponding 3D.
Fig. 2.
Fig. 2. Measurement system setup of the proposed D-type PCF-SPR sensor.
Fig. 3.
Fig. 3. Loss spectra with dispersion and modal characteristics when $\textrm{r}$= 8.6 µm, $h$= 3 µm, $H$=${\wedge}$= 18 µm, $D$= 58 µm, RI = 1.39, $t$= 50 nm, ${t_1}$= 20 nm. (a) Loss spectra of the fundamental mode in x/y polarization and dispersion relations of the effective refractive index of the fundamental and the SPP modes in y-polarization. Electric field distribution at the resonant wavelength of (b) the non-resonance fundamental mode of x polarization (c) resonance fundamental mode of y polarization coupled to SPP mode and (d) SPP mode of y polarization.
Fig. 4.
Fig. 4. (a) Variation of loss spectra for RI = 1.40 and 1.41 at different metal layer thicknesses t (${t_1}$= 20 nm, $\textrm{r}$= 8.6 µm, $h$= 3 µm, $H$=${\wedge}$= 18 µm). (b) Variation of loss spectra for RI = 1.40 and 1.41 at different dielectric layer thicknesses ${t_1}$ ($t$= 50 nm, $\textrm{r}$= 8.6 µm, $h$= 3 µm, $H$= ${\wedge}$= 18 µm).
Fig. 5.
Fig. 5. Effect of PCF parameters on loss values and phase matching points at RI = 1.40. (a) Effect of different air hole radius $\textrm{r}$ on loss spectra ($t$= 50 nm, ${t_1}$= 20 nm, $h$= 3 µm, ${\wedge}$= 18 µm, and $H$ = 18 µm).(b) Effect of different rectangular slot depths h on loss spectra ($t$ = 50 nm, ${t_1}$= 20 nm, $\textrm{r}$= 8.6 µm, ${\wedge}$= 18 µm, and $H$= 18 µm). (c) Effect of different air-hole spacings ${\wedge}$ on loss spectra ($t$= 50 nm, ${t_1}$ = 20 nm, $\textrm{r}$= 8.6 µm, $h$= 3 µm and $H$= 18 µm). (d) Effect of different polishing depths H on loss spectra ($t$= 50 nm, ${t_1}$= 20 nm, $\textrm{r}$= 8.6 µm, $h$= 3 µm, ${\wedge}$= 18 µm).
Fig. 6.
Fig. 6. Loss spectrum of PCF for analyte RI varying from 1.27 to 1.43.
Fig. 7.
Fig. 7. Variation in resonance wavelength and sensitivity of analyte RI across the range
Fig. 8.
Fig. 8. Variation in FWHM and FOM of analyte RI across the range
Fig. 9.
Fig. 9. Variation in peak loss and resolution of analyte RI across the range
Fig. 10.
Fig. 10. (a) Loss spectra with temperature increasing from 45°C in 5°C steps by 100°C. (b) Loss spectra with temperature increasing from 45°C in 1°C step by 50°C. (c) Fitted functional relationship between peak wavelengths and temperature (45°C-100°C). (d) Fitted functional relationship between peak wavelengths and temperature (45°C-50°C).

Tables (5)

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Table 1. Parameter settings for the designed PCF-SPR sensor

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Table 2. Coefficients of the Sellmeier equation for silicon dioxide

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Table 3. Performance of the designed sensor in the range of 1.27 to 1.43

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Table 4. Comparative performance analysis of two sensor structures

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Table 5. Comparison between the designed in this work and already reported PCF-SPR sensors

Equations (6)

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n S i O 2 ( λ ) = 1 + i = 1 3 A i λ 2 λ 2 B i 2
Loss = 8.686 × 2 π λ × Im ( n e f f ) × 10 4
WS = Δ λ Δ n a ( nm / RIU )
FOM = WS ( nm / RIU ) FWHM ( nm )
R ( RIU ) = Δ n a × Δ λ min Δ λ
n = n l i q u i d + d n / d T ( T 25 )
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