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Abstract
We propose an electric field tunable nematic liquid crystal (NLC) infiltrated single-hole hollow fiber sensor for voltage measurement. Due to only an air hole, the proposed sensor got a straightforward structure, and the liquid-filling process will be uncomplicated. The addition of the gold wire successfully incorporated the surface plasmon resonance (SPR) phenomenon as a sensing methodology in the proposed sensor. Besides that, the use of metal wire instead of the metal film will reduce the complicacy associated with the acquisition of uniform film thickness. The sensor characterization and performance evaluation have been done using the finite element method (FEM) for a wide voltage range from 200V to 400V. The sensor exhibits wavelength sensitivity (WS) and linearity as high as 5 nm/V and 0.9935, respectively. In addition, maximum amplitude sensitivity (AS) and wavelength resolution (R) is attained of −353.46 RIU−1 and 0.02V, respectively. Due to its excellent performance with a wide sensing range, and a simple and compact structure, the proposed sensor can be used for voltage measurement in a sophisticated place.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The growing demand for miniaturized and highly sensitive portable sensors has inspired researchers to incorporate surface plasmon resonance (SPR) technology in the sensing domain. In the SPR mechanism, an electromagnetic wave called surface plasmon wave (SPW) generates due to the excitation of free electrons by the p-polarized light and propagates throughout a dielectric-metal boundary. The SPW occurs when the frequency matches between the free electrons and the incident photon [1]. The change in surrounding environments (mainly, the refractive index (RI)) greatly influences the SPW generation, and SPR wavelength undergoes an obvious blue or red shift. Due to this unique feature, the SPR phenomenon is extensively used in diverse applications such as bio-sensing, water testing, environmental monitoring, food testing, etc [2,3].
Photonic crystal fibers (PCFs), which consist of plenty of air holes, can be filled with numerous functional materials; thus, the guiding characteristics can be tuned to realize diverse optical devices, including polarization filters [4], splitters [5], fiber lasers [6], sensors [7], and optical switches [8]. So far, a great number of sensors have been investigated using fiber infiltrated with sensitive materials, which are very responsive, highly sensitive, compact, and suitable for remote operation. Optical fiber-based electric fields or voltage sensors can play a vital role in detecting faults and observing voltage levels in the power grid, electronic devices, and electric machinery. However, several voltage sensors have been demonstrated by using methods like the Pockels effect, electrostatic effect, and piezoelectric effect [9–12]. These sensors have a large size, heavy weight, and poor stability as they usually contain a large bulk polymer, ceramic, and crystal, making them inappropriate for hardly-accessible conditions.
Several optical fiber-based sensors have also been demonstrated in the last few years [7,13–20]. In 2008, Du et al. proposed an electrically tunable photonic bandgap fiber using a Sagnac filter and achieved an average tuning sensitivity of 0.53 nm/V [13]. In the next year, Wei et al. successfully realized a tunable all-in-fiber device with a sensitivity of 0.42 nm/V using liquid crystal (LC) filled PCF [14]. A microresonator based on nematic liquid crystal (NLC) filled grapefruit-shaped optical fiber was experimentally demonstrated in the voltage range from 160 to 220V, and its wavelength sensitivity (WS) was 0.01 nm/V [15]. Later, improved sensitivity of 3.88 nm/V and 5.594 nm/V was achieved with NLC-filled side-hole fiber [16] and PCF modulator [17], respectively. Liu et al. inserted NLC-filled PCF into a Sagnac loop and achieved a tremendous WS of 7.37 nm/V in the voltage range from 325V to 425V [7]. Polarization maintaining PCF with a sensitivity of 1.1137 nm/V was proposed and experimentally demonstrated in [18]. Very recently, Mach-Zehnder [19] and Sagnac interferometer [20] incorporated with NLC filled PCF sensors have been demonstrated with a lower sensitivity of 1.1 nm/V and 3.49 nm/V, respectively. However, the performance of the above-mentioned sensors is not so satisfactory in terms of tunable voltage range and sensitivity. Now the research motivation is to design an optical fiber-based voltage sensor with improved sensitivity and a wide voltage range.
Here, we propose a simple hollow fiber made of FK51A glass and filled with NLC for the detection of external voltage. A gold wire is included at the hollow fiber’s upper side to introduce the unique and highly sensitive SPR phenomenon. Plasmon modes are formed on the surrounding of the gold wire, and resonance occurs at a particular wavelength when the plasmon mode is coupled with the core mode. Any change in the external voltage effectively changes the RI of NLC, and resonance wavelength (RW) are appeared at a different wavelength. RWs of the proposed sensor are investigated for a wide voltage range from 200V to 400V, and performances are carried out in terms of WS and amplitude sensitivity (AS). Moreover, the reason for considering such sensor geometry and optical characteristics is explained properly.
2. Sensor design and numerical analysis
The 3D view of the proposed hollow core voltage sensor is illustrated in Fig. 1(a). The design and performance assessment of the voltage sensor has been done using commercially available finite element method (FEM) based Electromagnetic wave, Frequency Domain (EWFD) solver COMSOL 5.6. In order to avoid any complexity in terms of fabrication, we use only a single-hole hollow fiber with a gold wire to design the sensor. For ideal performance, we set the fiber diameter (F) to 40 $\mathrm {\mu }$m, hole diameter (H) to 20 $\mathrm {\mu }$m, gold wire diameter (D) to 1 $\mathrm {\mu }$m, and the distance between the gold wire and hollow core (d) to 0.5 $\mathrm {\mu }$m which are optimized properly in section 4. We use FK51A glass as the fiber material instead of silica. The voltage-sensitive NLC, which is proposed to be infiltrated into the hollow core, has a RI higher than FK51A glass. Generally, fiber-based SPR sensors exhibit better sensitivity when the RI difference between the fiber material and the analyte is lesser [21]. Hence, to maintain the smallest RI difference between the NLC and background material, FK51A glass is chosen, which has a higher RI than silica. It should be noted that FK51A glass has already been used to fabricate optical fiber using stack and draw technology [22]. The RI of the FK51A glass can be calculated from the Sellmeier formula as follows [4],
Fig. 1. (a) 3D view of the proposed nematic liquid crystal (NLC) filled sensor indicating all geometric parameters (fiber diameter (F) = 40 $\mathrm {\mu }$m, hole diameter (H) = 20 $\mathrm {\mu }$m, gold wire diameter (D) = 1 $\mathrm {\mu }$m, and the distance between the gold wire and hollow core (d) = 0.5 $\mathrm {\mu }$m), (b) experimental setup with all necessary equipment.
The performance of the SPR sensor mostly depends on the plasmonic metal. So far, researchers have used numerous plasmonic materials; however, the most common metals are aluminum, copper, gold, and silver. Among them, gold is comparatively more chemically stable, bio-compatible, and easy to structure [23]. The optical characteristics of gold can be determined by Drude-Lorentz theorem as follow [24],
Figure 1(b) represents the experimental setup for voltage measurement using the proposed NLC-infiltrated hollow fiber sensor. The fiber structure is so straightforward that it can be comfortably fabricated by using the familiar stack and draw method. The gold wire can be added to the fiber by inserting it inside a capillary, as demonstrated in [25]. Then, the hollow fiber needs to be filled by the NLC. The simple way of filling the fiber with NLC is that one end of the hollow fiber drowns in the NLC, and the other end remains in the air, then capillary force needs to be applied. Lastly, the collapsed section can be cleaved off by a fiber cleaver. However, both sides of the NLC-infiltrated fiber are spliced with single-mode fiber (SMF). The polarizer helps to distinguish two orthogonal polarization modes of the optical power generated by the light source. Due to the variation of the voltage in the conductive glasses, the RW experiences a blue or red shift that can be observed using an optical spectrum analyzer (OSA) and a computer.
The NLC is an anisotropic material whose ordinary RI $(RI_{0})$ and extraordinary RI $(RI_{e})$ can be calculated as follows [7],
where, the value of $X_{o}$, $X_{e}$, $Y_{o}$, $Y_{e}$, $Z_{o}$, and $Z_{e}$ are 1.4998, 1.6993, 0.0067, 0.0085, 0.0004, and 0.0027, respectively, at temperature 20°C. The rotation of the NLC molecules can be controlled by using an external voltage source, and the rotation angle can be evaluated by [7],Fig. 2. The state of NLC molecules (a) with voltage and (b) without voltage, (c) variation of rotation angle with voltage.
3. Results analysis
The light-guiding mechanism of an optical fiber primarily depends on structural parameters such as core, cladding, and fiber diameter. The NLC has higher refractive indices than the FK51A glass, which satisfy the condition of total internal reflection (TIR); hence, the light is transmitted through the NLC-filled core of the proposed fiber. During light propagation, evanescent field (some fields leak from the core and penetrate into the cladding region, which is considered as confinement loss (CL) [27] ) excites free electrons on the gold wire surface, resulting in SPW in the metal (gold wire)-dielectric (FK51A glass) boundary. As wavelength increases, the confinement loss (CL) also rises and reaches a maximum value before a decline. The wavelength at which the maximum CL appears is called RW. A phase matching between the fundamental and SPP mode happens at the RW; hence, energy transfer from the core to the SPP mode reaches its maximum limit.
Figure 3(a) depicts the dispersion relation of the x-polarized mode of the proposed NLC-filled fiber for 310V and 320V applied voltage. The CL is investigated for different values of external voltage by following expression [28],
where $K=2\pi /\lambda$ indicates the wave number, and $\lambda$, measured in $\mathrm {\mu }$m, is known as wavelength, and Im($n_{eff}$) is the imaginary part of the effective refractive index ($n_{eff}$). As depicted in Fig. 3(a), the two-loss peaks (one at 1.11 $\mathrm {\mu }$m and another one at 1.49 $\mathrm {\mu }$m) appear as the operating wavelength varies from 1 $\mathrm {\mu }$m to 1.9 $\mathrm {\mu }$m for 310V. Interestingly, the real value of core and SPP mode matches exactly at the same two points (1.11 & 1.49 $\mathrm {\mu }$m) that justify the condition of RW. According to the coupled-mode theory [29], incomplete coupling happens for both zero-order and first-order SPP mode. At shorter wavelengths, modes are strongly confined at the core region and begin to leak as the wavelength increases [30]. The energy transfer from the core region to the gold wire region is higher at the longer wavelength. Therefore, the CL at 1.49 $\mathrm {\mu }$m (4.723 dB/cm) is larger than the CL at 1.11 $\mathrm {\mu }$m (1.385 dB/cm). Likewise, two CL peaks appear at 1.1 $\mathrm {\mu }$m (1.240 dB/cm) and 1.49 $\mathrm {\mu }$m (4.036 dB/cm) for 320V. The higher CL indicates a strong coupling between the core mode and gold wire. Electric field distributions of the core mode at 1.11 $\mathrm {\mu }$m and 1.49 $\mathrm {\mu }$m and SPP mode at 1.11 $\mathrm {\mu }$m and 1.49 $\mathrm {\mu }$m for 310V are illustrated in Fig. 3(c), (d), (e), and (f), respectively, which helps to understand the light intensity in the core and gold wire. However, a greater RW shift (1.45 $\mathrm {\mu }$m to 1.49 $\mathrm {\mu }$m; 40 nm) is observed for the zero-order SPP mode compared to the first-order SPP mode (1.1 $\mathrm {\mu }$m to 1.11 $\mathrm {\mu }$m; 10 nm). Therefore, the second RW is only considered for further investigation. As shown in Fig. 3(b), for y-polarization, coupling happens only once for the entire wavelength. At RW of 1.08 $\mathrm {\mu }$m and 1.10 $\mathrm {\mu }$m, the maximum loss of 0.42 dB/cm and 0.49 dB/cm are found for 320V and 310V, respectively. Field distribution of y-polarized core mode and SPP mode at 1.10 $\mathrm {\mu }$m for 310V is shown in Fig. 3(g) and (h), respectively. However, the RW shift is much lower than that of the zero-order SPP mode of the x-polarization mode. Hence, the y-polarization mode did not consider for further analysis.Fig. 3. Dispersion relationship of fundamental and SPP mode for 310V and 320V for (a) x-polarized and (b) y-polarized modes. The intersection point between the real value of SPP and core mode for 310V and 320V is highlighted by the red and black circular dot, respectively. Field distribution of x-polarized for core mode at (c) 1.11 $\mathrm {\mu }$m and (d) 1.49 $\mathrm {\mu }$m and SPP mode at (e) 1.11 $\mathrm {\mu }$m and (f) 1.49 $\mathrm {\mu }$m for 310V. Field distribution of y-polarized for (g) core mode and (h) SPP mode at 1.10 $\mathrm {\mu }$m for 310V.
The RW is highly sensitive to the surrounding RI. However, a change in the external DC voltage results in changes in the RI of NLC [26] that leads to the RW shift. The external voltage is varied from 200V to 400V, and the corresponding CL is plotted in Fig. 4. It can be observed that RW appears at different wavelengths for different voltages; hence, any unknown external voltage can be identified by observing RW. The maximum and minimum CL (dB/cm) of 22.539 and 1.298 is attained for 200V and 400V, respectively. In SPR-based optical fiber sensors, loss increases with the reduction of the index difference between the core and cladding [31]. When the external voltage increases, the RI of the NLC increases, leading to a reduction in the RI difference. Therefore, lower CL is obtained for higher voltage and vice-versa.
For SPR sensor, the WS is the most common method to measure the sensitivity, which can be calculated using the wavelength interrogation method [28],
where $\Delta \lambda _{RW}$ is the amount of RW shift due to $\Delta V$ voltage change. The RW shift of 50 nm and 20 nm is due to a 10V change in the external voltage, hence resulting in the maximum and minimum WS of 5 nm/V and 2 nm/V, respectively.Sensor resolution (R) is also a familiar method to evaluate the performance of an SPR sensor which implies how much the smallest change can be identified by the sensor. However, R can be measured as [28],
In the above expression, $\Delta \lambda _{min}$ is the minimum spectral resolution of OSA, $\Delta \lambda _{RW}$ and $\Delta V$ are the same as mentioned in equation (7). Assuming that $\Delta \lambda _{min}$ = 0.1 nm [28], the sensor exhibits the best R of 0.02V, which means the proposed voltage sensor is capable of identifying the surrounding voltage change as small as 20 mV.Since the AS can be measured at a single wavelength, it is well-known as a cost-effective method. AS is calculated by the amplitude interrogation technique [28],
where CL is the loss, and $\Delta CL$ is the amount of CL difference due to $\Delta n$ change. As shown in Fig. 5, a maximum dip of -353 $RIU^{-1}$ and a minimum dip of -264.87 $RIU^{-1}$ are observed in AS spectrum when the voltage is changed from 220V to 230V and from 390V to 400V, respectively.The above-mentioned performance parameters for every individual voltage change are summarized in Table 1.
Table 1. Sensor Performance for every individual voltage with F = 40 $\mathrm {\mu }$m, H = 20 $\mathrm {\mu }$m, D = 1 $\mathrm {\mu }$m, and d = 0.5 $\mathrm {\mu }$m.
The change of RW with the variation of voltage from 200V to 400V is plotted in Fig. 6. The RW changes of the proposed sensor can be characterized by the following linear fitting equation;
where V is in volts and RW is in $\mathrm {\mu }$m. The proposed voltage sensor shows good linearity of 0.9935 for RW changes which is almost close to 1.00 (perfect linear fitting). Hence, the change in RW with an external voltage variation follows almost linear behavior.4. Performance analysis and fabrication tolerance investigation
In the case of performance analysis, the geometrical parameters have been varied, and the optimum value has been chosen on the basis of WS and CL. It is worth noting that only one parameter is varied at a time while the others remain constant.
Figure 7 illustrates the RW changes as the gold wire diameter (D) varies for 310V and 320V. As shown in Fig. 7, the D has a significant impact on the RW and CL. The CL goes up, and RW shifts to the longer wavelength as D decreases. At RW, the CL (dB/cm) is obtained of 7.598, 5.854, 4.723, 4.035, and 3.590 for 310V, and 6.411, 4.929, 4.036, 3.478, and 3.136 for 320V applied voltage for D ($\mathrm {\mu }$m) of 0.8, 0.9, 1, 1.1, and 1.2, respectively. On the other hand, the maximum amount of RW shift ($\Delta \lambda$) is found of 50 nm (WS = 5 nm/V) for 0.8 $\mathrm {\mu }$m of D, and 30 nm (WS = 3 nm/V) of RW shift is obtained for both 1.1 $\mathrm {\mu }$m, and 1.2 $\mathrm {\mu }$m of D. In addition, the WS is the same (4 nm/V) for 0.9 $\mathrm {\mu }$m and 1 $\mathrm {\mu }$ ddd of D. So it is apparent that CL and WS both increase as D decreases. An increase in the CL will lead to a higher signal-to-noise ratio; however, if CL is increased, the sensor length will be reduced to generate the measurable signal at the receiver end [32]. As a result, the practical realization will be difficult. Hence, we pick D = 1 $\mathrm{\mu}$m as a trade-off between WS and CL.
Fig. 7. CL and RW variation with the change of D from 0.8 $\mathrm {\mu }$m to 1.2 $\mathrm {\mu }$m.
The distance between the hollow core and the gold wire (d) also has a substantial impact on CL and WS, as shown in Fig. 8. The CL (dB/cm) rises up from 4.723 to 23.778 for 310V and from 4.036 to 20.790 for 320V as the d is decreased from 0.5 $\mathrm {\mu }$m to 0.25 $\mathrm {\mu }$m. Besides that, the CL (dB/cm) is achieved of 0.562 and 1.486 for 310V, and 0.461 and 1.267 for 320V for 1 $\mathrm {\mu }$m and 0.75 $\mathrm {\mu }$m of d, respectively. Indeed, the CL increases with the reduction of the d. This is due to the fact that the gold wire attracts more electromagnetic waves (more loss happens) when it is closer to the core. On the contrary, the WS remains unchanged (4 nm/V) for the variation of d from 1 $\mathrm {\mu }$m to 0.5 $\mathrm {\mu }$m but improved WS (5 nm/V) is achieved for 0.25 $\mathrm {\mu }$m of d. However, we select d = 0.5 $\mathrm {\mu }$m as a trade-off between CL and WS.
Fig. 8. CL and RW variation with the change of d from 0.25 $\mathrm {\mu }$m to 1 $\mathrm {\mu }$m. For better visualization, the CL for 0.75 $\mathrm {\mu }$m and 1 $\mathrm {\mu }$m of d is shown in the inset.
The effect of the number of gold wires on CL and WS has also been carried out. Figure 9(a), (b), and (c) show the CL variation for three different external voltage ranges when two gold wires use instead of one. In all cases, the use of two gold wires increases the CL significantly. However, no changes appear in the RW shift, meaning the WS remains the same. This justifies that a single gold wire helps to attain the same amount of WS with lower CL than that of two gold wires.
Fig. 9. (a) CL and RW with one and two gold wires for (a) 310V and 320V, (b) 200V and 210V, and (b) 390V and 400V. Field distribution of (d) core mode and (e) SPP mode with two gold wires at 1.49 $\mathrm {\mu }$m for 310V.
Design parameters may change a little bit during the fabrication, and it is demonstrated that optical fiber fabrication is possible with only a 1% deviation from the optimum value [33]. However, the geometrical parameters of the proposed hollow fiber have been varied up to $\pm 5\%$.
Figure 10(a) depicts the CL variation for 320V as the core diameter (H) is varied up to $\pm 5\%$ from its optimum value. As illustrated in Fig. 10(a), the CL (dB/cm) falls from 4.036 to 3.748 for a 2% increment of H and rises up from 4.036 to 4.356 for a 2% reduction of H. Similarly, for a 5% increment and reduction of H, the CL (dB/cm) decreased by 0.703 and increased by 0.921, respectively. Figure 10(b) and (c) illustrates the CL variation for 200V and 400V, respectively. As depicted in Fig. 10(b), CL decreases by 1.937 dB/cm and 4.05 dB/cm for 2% and 5% increment, respectively, and CL increases by 1.737 dB/cm and 5.31 dB/cm for 2% and 5% decrement, respectively. On the other hand, for 400V, the same amount of CL (0.1 dB/cm for $\pm 2\%$ and 0.25 dB/cm for $\pm 5\%$) increases and decreases for reduction and increment of H, respectively. A larger core confines the electromagnetic wave more precisely; therefore, CL decreases with the increment of core size. Note that the RW does not change at all, indicating that the core diameter variation up to $\pm 5\%$ does not affect WS.
Fig. 10. CL and RW variation for $\pm 5\%$ change of core diameter (H), (a) 320V, (b) 200V, and (b) 400V, fiber diameter (F), (d) 320V, (e) 200V, and (f) 400V.
Figure 10(d), (e), and (f) show the effect of variation of fiber diameter (F) on CL for 320V, 200V, and 400V, respectively. It can be clearly seen that the variation of fiber diameter up to $\pm 5\%$ has an almost negligible effect on CL and the RW remains the same as well. In the SPR sensor, as the CL and the RW mainly depend on the metal (gold wire), which is placed near the core, therefore, the increment of fiber diameter in the outer portion has an insignificant impact on both of them.
The influence of gold wire diameter (D) for 320V, 200V, and 400V is illustrated in Fig. 11(a), (b), and (c), respectively. Any increment in the gold wire diameter shifts the RW into the longer wavelength and vice versa. For 320V, the RW shifts $\pm$20nm and $\pm$50nm for $\pm$2% and $\pm$5% changes in D, respectively. At the same time, a maximum of 70nm and 30nm of RW shift appear for $\pm$5% variation of (D) for 200V and 400V, respectively. On the other hand, the maximum CL deviation is calculated of 3.94 dB/cm, 1.024 dB/cm, and 0.315 dB/cm for a 5% variation of D for 200V, 320V and 400V, respectively.
Fig. 11. CL and RW variation for $\pm 5\%$ change of gold wire diameter (D), (a) 320V, (b) 200V, and (b) 400V, the distance between gold wire and hollow core (d), (d) 320V, (e) 200V, and (f) 400V.
As shown in Fig. 11(d), (e), and (f), the RW does not change for $\pm 2\%$ deviation of the distance between the core and the gold wire (d). However, for 320V and 400V, RW shifts longer and shorter wavelengths of 10 nm for a 5% reduction and increment of d, respectively. Simultaneously, $\pm 5\%$ variation of d leads to a maximum 30nm of RW shift for 200V. On the other hand, CL changes up to 0.34 dB/cm, 0.50 dB/cm and 4.93 dB/cm for 400V, 320V, and 200V, respectively, for $\pm 5\%$ variation of d.
Moreover, the effect of changing the position of the gold wire in the angular direction is also investigated up to 90°. As shown in Fig. 12(a), the variation of the $\theta$ does not affect CL or RW. However, as illustrated in Fig. (c)-(l), the polarization direction changes with the gold wire position and the direction of both the x- and y-polarized modes changes exactly 90°for the 90°angular shift of gold wire. Hence, it is recommended that during the experiment, the gold wire position must be along the y-polarized mode of the polarizer. Table 2 shows the performance comparison of the proposed voltage sensor with some prior sensors. It appears that if the voltage range and sensitivity are both taken into consideration, then the proposed hollow fiber sensor exhibits better performance than the prior sensor.
Fig. 12. (a) CL and RW variation with the gold wire position up to 90°of $\theta$. (b) visualize the angular rotation ($\theta$). The direction of (c)-(g) x-polarization, and (h)-(l) y-polarization variation with gold wire position.
Table 2. Results comparison with some prior sensor.
5. Conclusion
In this work, the unique and reliable SPR phenomenon, which is playing a crucial role in designing miniaturized and highly sensitive sensors in recent days, is applied to design an optical fiber-based voltage sensor. The single-hole hollow fiber is made of FK51A glass which is filled with high-index NLC. To incorporate SPR technology in the proposed sensor, a gold wire is added to the fiber. To keep the sensor structure as simple as possible, only a single hole and a single metal wire is considered. The whole sensor geometry is optimized in terms of WS and CL, then the sensor performance is carried out for a wide range from 200V to 400V. The proposed sensor offers a comparatively high WS, AS, and good linearity. The voltage range indicates the proposed sensor can be effectively used to observe the voltage, especially in home and industrial appliances, and its miniaturized size could make this sensor compatible with hardly accessible environments.
Funding
Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah (D-106-135-1437).
Acknowledgment
This work was supported by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant No. (D-106-135-1437). The authors, therefore, gratefully acknowledge the DSR technical and financial support.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. J. Homola, I. Koudela, and S. S. Yee, “Surface plasmon resonance sensors based on diffraction gratings and prism couplers: sensitivity comparison,” Sens. Actuators, B 54(1-2), 16–24 (1999). [CrossRef]
2. V. Portosi, D. Laneve, M. C. Falconi, and F. Prudenzano, “Advances on photonic crystal fiber sensors and applications,” Sensors 19(8), 1892 (2019). [CrossRef]
3. Y. Chen and H. Ming, “Review of surface plasmon resonance and localized surface plasmon resonance sensor,” Photonic Sens. 2(1), 37–49 (2012). [CrossRef]
4. M. F. O. Hameed, A. Heikal, B. Younis, M. Abdelrazzak, and S. Obayya, “Ultra-high tunable liquid crystal-plasmonic photonic crystal fiber polarization filter,” Opt. Express 23(6), 7007–7020 (2015). [CrossRef]
5. E.-L. Wang, H.-M. Jiang, K. Xie, C. Chen, and Z.-J. Hu, “Polarization splitter based on dual core liquid crystal-filled holey fiber,” J. Appl. Phys. 120(11), 114501 (2016). [CrossRef]
6. Y. Chen, N. Zhao, J. Liu, Y. Xiao, M. Zhu, K. Liu, G. Zhou, Z. Hou, C. Xia, Y. Zheng, and Z. Chen, “Yb3+-doped large-mode-area photonic crystal fiber for fiber lasers prepared by laser sintering technology,” Opt. Mater. Express 9(3), 1356–1364 (2019). [CrossRef]
7. Q. Liu, P. Xue, and Z. Liu, “Voltage sensor based on liquid-crystal-infiltrated photonic crystal fiber with high index,” Appl. Phys. Express 13(3), 032005 (2020). [CrossRef]
8. Y. Wang, H. Bartelt, W. Ecke, K. Moerl, H. Lehmann, K. Schroeder, R. Willsch, J. Kobelke, M. Rothhardt, R. Spittel, L. Shan, S. Brueckner, W. Jin, X. Tan, and L. Jin, “Thermo-optic switching effect based on fluid-filled photonic crystal fiber,” IEEE Photonics Technol. Lett. 22(3), 164–166 (2010). [CrossRef]
9. R. C. Allil and M. M. Werneck, “Optical high-voltage sensor based on fiber bragg grating and pzt piezoelectric ceramics,” IEEE Trans. Instrum. Meas. 60(6), 2118–2125 (2011). [CrossRef]
10. H. Yang, Y. Guo, S. Jiao, W. Hong, S. Xu, and Y. Zhang, “Analysis and suppression of nonreciprocal phase shift error of the optical voltage sensor based on the converse piezoelectric effect,” Opt. Fiber Technol. 55, 102142 (2020). [CrossRef]
11. Q. Yang, R. Liu, Y. He, and M. Luo, “Ac/dc hybrid electric field measurement method based on pockels effect and electric field modulation,” Rev. Sci. Instrum. 91(5), 055004 (2020). [CrossRef]
12. L. Fabiny, S. T. Vohra, and F. Bucholtz, “High-resolution fiber-optic low-frequency voltage sensor based on the electrostrictive effect,” IEEE Photonics Technol. Lett. 5(8), 952–953 (1993). [CrossRef]
13. J. Du, Y. Liu, Z. Wang, B. Zou, B. Liu, and X. Dong, “Electrically tunable sagnac filter based on a photonic bandgap fiber with liquid crystal infused,” Opt. Lett. 33(19), 2215–2217 (2008). [CrossRef]
14. L. Wei, L. Eskildsen, J. Weirich, L. Scolari, T. T. Alkeskjold, and A. Bjarklev, “Continuously tunable all-in-fiber devices based on thermal and electrical control of negative dielectric anisotropy liquid crystal photonic bandgap fibers,” Appl. Opt. 48(3), 497–503 (2009). [CrossRef]
15. C. Yang, H. Zhang, B. Liu, S. Lin, Y. Li, and H. Liu, “Electrically tunable whispering gallery mode microresonator based on a grapefruit-microstructured optical fiber infiltrated with nematic liquid crystals,” Opt. Lett. 42(15), 2988–2991 (2017). [CrossRef]
16. Y. Huang, Y. Wang, C. Mao, J. Wang, H. Wu, C. Liao, and Y. Wang, “Liquid-crystal-filled side-hole fiber for high-sensitivity temperature and electric field measurement,” Micromachines 10(11), 761 (2019). [CrossRef]
17. Y. Huang, Y. Wang, L. Zhang, Y. Shao, F. Zhang, C. Liao, and Y. Wang, “Tunable electro-optical modulator based on a photonic crystal fiber selectively filled with liquid crystal,” J. Lightwave Technol. 37(9), 1903–1908 (2019). [CrossRef]
18. C. Zhao, L. Cai, and Y. Zhao, “An optical fiber electric field sensor based on polarization-maintaining photonic crystal fiber selectively filled with liquid crystal,” Microelectron. Eng. 250, 111639 (2021). [CrossRef]
19. Y. Liu, W. Lin, M. I. Vai, P. P. Shum, L.-Y. Shao, W. He, S. Liu, F. Zhao, W. Wang, and Y. Liu, “Fiber optic electric field intensity sensor based on liquid crystal-filled photonic crystal fiber incorporated ring laser,” IEEE Photonics J. 14(1), 1–5 (2022). [CrossRef]
20. Q. Liu, P. Xue, Q. Wu, C. Zhao, W. P. Ng, Y. Fu, and R. Binns, “Electrically sensing characteristics of the sagnac interferometer embedded with a liquid crystal-infiltrated photonic crystal fiber,” IEEE Trans. Instrum. Meas. 70, 1–9 (2021). [CrossRef]
21. S. Cao, Y. Shao, Y. Wang, T. Wu, L. Zhang, Y. Huang, F. Zhang, C. Liao, J. He, and Y. Wang, “Highly sensitive surface plasmon resonance biosensor based on a low-index polymer optical fiber,” Opt. Express 26(4), 3988–3994 (2018). [CrossRef]
22. C. A. Kalnins, H. Ebendorff-Heidepriem, N. A. Spooner, and T. M. Monro, “Radiation dosimetry using optically stimulated luminescence in fluoride phosphate optical fibres,” Opt. Mater. Express 2(1), 62–70 (2012). [CrossRef]
23. T. Wieduwilt, A. Tuniz, S. Linzen, S. Goerke, J. Dellith, U. Hübner, and M. A. Schmidt, “Ultrathin niobium nanofilms on fiber optical tapers–a new route towards low-loss hybrid plasmonic modes,” Sci. Rep. 5(1), 17060 (2015). [CrossRef]
24. A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, and M. L. De La Chapelle, “Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71(8), 085416 (2005). [CrossRef]
25. M. F. Azman, G. A. Mahdiraji, W. R. Wong, R. A. Aoni, and F. R. M. Adikan, “Design and fabrication of copper-filled photonic crystal fiber based polarization filters,” Appl. Opt. 58(8), 2068–2075 (2019). [CrossRef]
26. K. R. Khan, K. Mnaymneh, H. A. Awad, and I. I. Hasan, “Slow light propagation in tunable nanoscale photonic crystal cavity filled with nematic liquid crystal,” Opt. Eng. 53(10), 102705 (2014). [CrossRef]
27. A. Hochman and Y. Leviatan, “Calculation of confinement losses in photonic crystal fibers by use of a source-model technique,” J. Opt. Soc. Am. B 22(2), 474–480 (2005). [CrossRef]
28. A. A. Rifat, G. A. Mahdiraji, Y. M. Sua, R. Ahmed, Y. Shee, and F. M. Adikan, “Highly sensitive multi-core flat fiber surface plasmon resonance refractive index sensor,” Opt. Express 24(3), 2485–2495 (2016). [CrossRef]
29. Q. Liu, S. Li, and H. Chen, “Two kinds of polarization filter based on photonic crystal fiber with nanoscale gold film,” IEEE Photonics J. 7(1), 1–11 (2015). [CrossRef]
30. Z. Zhang, Y. Shi, B. Bian, and J. Lu, “Dependence of leaky mode coupling on loss in photonic crystal fiber with hybrid cladding,” Opt. Express 16(3), 1915–1922 (2008). [CrossRef]
31. N. Luan and J. Yao, “High refractive index surface plasmon resonance sensor based on a silver wire filled hollow fiber,” IEEE Photonics J. 8(1), 1–9 (2016). [CrossRef]
32. A. A. Rifat, M. R. Hasan, R. Ahmed, and H. Butt, “Photonic crystal fiber-based plasmonic biosensor with external sensing approach,” J. Nanophotonics 12(1), 012503 (2017). [CrossRef]
33. W. H. Reeves, J. Knight, P. S. J. Russell, and P. Roberts, “Demonstration of ultra-flattened dispersion in photonic crystal fibers,” Opt. Express 10(14), 609–613 (2002). [CrossRef]
