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Abstract
This paper proposes and demonstrates an ultrasensitive refractive index (RI) sensor based on harmonic Vernier effect (HEV) and a cascaded Fabry–Perot interferometer (FPI). The sensor is fabricated by sandwiching a hollow-core fiber (HCF) segment between a lead-in single-mode fiber (SMF) pigtail and a reflection SMF segment with an offset of 37 µm between two fiber centers to form a cascaded FPI structure, where the HCF is the sensing FPI, and the reflection SMF is the reference FPI. To excite the HEV, the optical path of the reference FPI must be multiple times (>1) that of the sensing FPI. Several sensors have been made to conduct RI measurements of gas and liquid. The sensor’s ultrahigh RI sensitivity of up to ∼378000 nm/RIU can be achieved by reducing the detuning ratio of the optical path and increasing the harmonic order. This paper also proved that the proposed sensor with a harmonic order of up to 12 can increase the fabricated tolerances while achieving high sensitivity. The large fabrication tolerances greatly increase the manufacturing repeatability, reduce production costs, and make it easier to achieve high sensitivity. In addition, the proposed RI sensor has advantages of ultrahigh sensitivity, compactness, low production cost (large fabrication tolerances), and capability to detect gas and liquid samples. This sensor has promising potentials for biochemical sensing, gas or liquid concentration sensing, and environmental monitoring.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Refractive index (RI) is a basic physical parameter that characterizes the optical properties of gas and liquid, and it will change with the variation of material properties such as composition, density, temperature, and other parameters. The measurement of RI is significant in many fields, such as environmental protection, food processing, chemical industry, machinery, pharmacy, and biochemical sensing [1–3]. In recent years, an RI fiber sensor has attracted increased attention due to their small footprint, immunity to electromagnetic interference, high sensitivity, and ease of integration. These optical fiber sensors can be divided into different types, namely, surface plasmonic resonance (SPR) [4], fiber gratings [5], fiber directional coupler [6], and fiber-based interferometers [7], based on different sensing mechanisms.
Among the various optical fiber sensors, fiber-based interferometers have been intensively investigated for RI sensing applications. These sensors can be categorized into several types, such as the Mach–Zehnder interferometer (MZI) [8,9], Fabry–Perot interferometer (FPI) [10,11], and Sagnac interferometer [12,13]. Common MZI structures include core-offset pairs [14], taper or peanut pairs [15], or special optical fiber structures, such us microfiber, dual-core fibers, and photonic crystal fibers (PCF) [16–18]. Common FPI structures include a core-offset structure [19], microcavity structure [20], and sandwich structure [21]. The Sagnac interferometer usually consists of a Sagnac ring structure and polarization-maintaining fiber [22]. The advantages of fiber-based interferometers include good stability, simple structure, and ease of fabrication. Nevertheless, the sensitivity of these sensors is limited to 102∼103 nm/RIU. How to further improve the sensitivity of fiber-based interferometers is a subject that needs to be studied.
The Vernier effect is an effective method to enhance sensitivity and has been widely used and studied in optical fiber sensors in recent years [23–26]. Common fiber sensors based on the traditional Vernier effect (TVE) consist of two parallel or cascaded interferometers, i.e., sensing interferometer and reference interferometer. Typically, TVE occurs when the optical path length (OPL) of two interferometers is close but not equal. The periodic envelope will be generated in the spectrum by the superposition of the sensing interferometer spectrum and reference interferometer spectrum. The sensor sensitivity can be amplified by tracking the position of the envelope.
The RI measurement usually requires an open-cavity structure, and most are realized by utilizing micro-structured fiber or micro-assembling fibers. For example, Lin et al. demonstrated a gas RI sensor based on cascaded dual MZI. Their sensor consisted of a single-mode–multimode–single-mode fiber structure with a micro air cavity in multimode fiber (MMF). The micro air cavities are drilled by a femtosecond laser and act as gas RI sensing element. This sensor has a sensitivity of ∼28320.69 nm/RIU [24], and an expensive femtosecond laser was involved in the sensor fabrication. Hu et al. proposed an RI sensor with a structure of parallel-connected dual MZI. This sensor contains a laterally offset section of side-hole fibers between two sections of coreless fibers and demonstrates a sensitivity of ∼44000 nm/RIU [25]. However, the use of the above two special optical fibers greatly increases the cost of the sensor. Quan et al. proposed a gas RI sensor by cascading a single-mode fiber (SMF) with a hollow-core fiber (HCF) and a PCF to constitute two cascaded FPIs. The sensor has a sensitivity of ∼30899 nm/RIU [26]. However, the smaller cavities and longer channels in PCF limit its applications in liquid RI measurement. Nevertheless, the sensitivity improvement of the TVE is limited by the following reasons: Firstly, the sensitivity amplification factor can be increased by further reducing the detuning ratio of OPL; however, it is hard to decrease the OPL detuning below a micron level with the existing typical fiber sensor fabrication and processing technology, such as fiber cleaving and splicing [27]. Secondly, the FSR of the envelope will tend to approach infinity with the further reduction of the detuning ratio, resulting in the difficulty in identifying the extreme point of the envelope due to the limited spectral range of the spectral demodulation equipment [27].
Recently, researchers have been applying the harmonic Vernier effect (HVE) to further enhance the sensitivities of fiber-based interferometers [28]. The HVE occurs when the OPL of the sensing interferometer or reference interferometer is increased to multiple (j + 1) times of the other one, and its sensitivity will be increased to j + 1 times of the TVE. Luo et al. proposed a highly sensitive gas RI sensor in parallel configuration based on the HVE. The sensor consists of two segments of 75 µm HCF as the sensing and reference FPI. This sensor has a sensitivity of ∼103900 nm/RIU [29]. However, the harmonic order of this sensor is only 3, compared with TVE, and its fabrication tolerance and magnification increase slightly.
This paper proposes and experimentally demonstrates an ultrasensitive RI fiber sensor base on a high-order HEV and cascaded FPI. This sensor has an SMF–HCF–SMF structure. There is a lateral offset of about 37 µm between the HCF and SMF to form an open-cavity FPI. The HCF and the reflection SMF are the sensing FPI and the reference FPI, respectively. The optical path of the reference FPI is multiple times (>1) that of the sensing FPI to excite the HEV. RI variations in the HCF would lead to shifts of the reflection spectrum of the sensor. The detuning ratio was reduced while the harmonic order was increased to further improve the sensitivity of the sensor. This characteristic indicates that the proposed HVE sensor has higher fabrication tolerance to achieve ultrahigh sensitivity, making the fabrication easier and reducing cost. In this work, the intersections of the internal envelope are tracked to solve the problem that the FSR of envelope is too large to track. The experimental results show that the proposed sensor has a sensitivity of up to 378000 nm/RIU. The sensor is featured with extremely high sensitivity, easy fabrication, and capability of sensing of both gas and liquid samples, which making it attractive in environmental monitoring, biochemical, and other industrial applications.
2. Sensor fabrication and principle
Figure 1 illustrates a diagram of the proposed sensor. A segment of HCF (inner diameter of 100 µm and external diameter of 140 µm) is fusion spliced to a lead-in SMF1 (core diameter of 8.2 µm and cladding diameter of 125 µm) with an offset of 37 µm between the two fiber transversal surfaces using a fusion splicer (Fujikura, 80S+). The current of electric arc and arc duration time are ∼16.8 mA and ∼300 ms, respectively. As shown in Fig. 1(b), the HCF will not collapse when using this fusion spliced parameter. The HCF is then cleaved to a specified length (${L_1}$) facilitated with a microscope and translation stage. The SMF1–HCF structure is then fusion spliced to the reflection SMF2 following the same splicing method. This SMF2 segment is then also cleaved into the specified length (${L_2}$). Due to the offset splicing between the HCF and SMFs, the air hole of HCF is not completely blocked by the SMFs at both ends, thus making an open-cavity FPI structure within HCF, which can hold gas and liquid samples.
As shown in Fig. 1, Mirror1 is the interface between HCF and SMF1 with a reflectance coefficient of ${R_1}$, and Mirror2 is the interface between HCF and SMF2 with a reflectance coefficient of ${R_2}$. Mirror3 is the interface between SMF2 and the surrounding medium with a reflectance coefficient of ${R_3}$. The three mirrors constitute three FPIs. FPI1, consisting of Mirror1 and Mirror2, is the sensing FPI. FPI2, consisting of Mirror2 and Mirror3, is the reference FPI. Moreover, FPI3 also consists of Mirror1 and Mirror3. Guided light from lead-in SMF1 will be partly reflected when passing through the three mirrors. The total reflection spectrum function can be expressed as [30]:
Equations (1)–(5) suggest that total reflection spectrum is determined by the light reflected from Mirror1, Mirror2, and Mirror3. The periodic envelope will appear when the OPLs of the FPI1 and FPI2 are close. This is the so-called TVE. Moreover, the FSR of the periodic envelope can be expressed as follows [27]:
where $FS{R_1} = {{{\lambda ^2}} / {2{n_{eff}}{L_1}}}$ and $FS{R_2} = {{{\lambda ^2}} / {2{n_{eff}}{L_2}}}$ are the free spectral ranges of FPI1 and FPI2, respectively. The sensitivity of TVE sensor is M times larger than that of a single-cavity FPI structure through Vernier amplification. M can be expressed as [29]:HVE will be activated when the $OP{L_2}$ (OPL of FPI2) is increased to a multiple (j + 1 times) of the $OP{L_1}$ (OPL of the FPI1). $OP{L_2}\; $ can be expressed as [31]:
Fig. 2. Reflection spectrum theoretically calculated with different j. Black curves, reflection spectrum; dashed curves, lower envelope; full curves with red, blue, green, and purple colors: internal envelope. (a) Traditional Vernier effect. (b) First-order harmonic Vernier effect. (c) Second-order harmonic Vernier effect. (d) Tenth-order harmonic Vernier effect.
As shown in Figs. 2 (a)–(d), HVE can regenerate the lower envelope. Thus, Eq. (5) can be rewritten as:
Equation (9) suggests that the FSR of the internal envelope is (j + 1) times as many as the lower envelope in the reflection spectrum of HVE. The M factor of the HVE j-order can be expressed as [29]:
It is also observed that the FSR of the lower envelope and the internal envelope will tend to approach infinity as $\Delta $ decreases. There are not traceable valleys in the limited spectral range of the optical spectrum analyzer. In this condition, tracking the envelope position will become difficult and challenging. However, the HVE provides rich internal envelope and intersection points. Therefore, the problem can be solved by tracking the intersection points (Fig. 3) of two internal envelopes. Because the relative position of the internal envelope does not change when the RI changes, tracking the intersection points of the internal envelope is equivalent to tracking the internal envelope.
3. Experimental characterization
Figure 4 illustrates the experimental setup for the gas RI sensing. The proposed sensor was sealed in a gas chamber, which is connected with a pressure pump (ConST-168). The gas RI can be controlled by adjusting the gas pressure through the pressure pump. The light from a broadband light source (ASE-EBED-2-2-FC/APC) will enter the sensor probe through a fiber circulator, and the reflected light that returned from the sensor probe could be analyzed by an optical spectrum analyzer (YOKOGAWA-AQ6370D). The relation of RI and pressure of air can be expressed as [26]:
where ${n_{air}}$ is air RI, p is air pressure (Pa), and T is temperature (°C).Four sensors (S1–S4) with different harmonics order (j) were fabricated to assess the RI response of the sensor, as presented in Table 1. The value of Δ can be calculated by substituting the parameters in Table 1 into Eq. (8). The detuning ratio of S1 and S3 is 1.92% and −1.88%, which is smaller than the detuning ratio of S2 and S4 (10.80% and 31.00%). On the other hand, S2 and S4 have higher manufacturing repeatability than S1 and S3 because their $\Delta $ is more than 10 µm. This means that the manufacturing cost of S2 and S4 is lower than that of S1 and S3.
Table 1. Parameters of the four proposed sensors
In the experiments, the pressure of the air chamber was adjusted from ∼0.10 MPa (normal atmosphere pressure) to 0.20 MPa with a 0.01 MPa interval. Equation (12) can be used to calculate the RI of air in FPI1. Therefore, at 20°C, the RI range of air in the experiments is 1.000269–1.000538, with an interval of 0.0000269. Figures 5(a)–(d) show the experimental reflection spectrum for S1–S4, respectively, where S1 excites the spectrum of TVE with j = 0 and S2–S4 excite the spectrum of HVE with j = 2, 4, and 12. All of the spectra can be fitted with cleared internal envelopes. Similar to the theoretical calculation, the number of internal envelopes and intersection points increases with the increase of j. However, the contrast of the lower envelope decreases, and it becomes invisible when j = 12, which cannot be traced in this case. Therefore, the intersection points were tracked in the experiment. In the experiment, we chose a smoother internal envelope and their intersection points to track. Because the smooth internal envelope is formed by fitting high-frequency fringes (HFFs) with smaller noise. Figure 6 shows the positions of the internal envelope and intersection points (Fig. 5) under different refractive indices. In addition, the method mentioned above was used to draw the internal envelope and intersection points of each spectrum (Fig. 6). A linear fitting of the intersection points in response to the RI variations was applied (Fig. 6(e)).
Fig. 5. (a)–(d) Reflection spectrum (black line) obtained for samples S1–S4 at normal atmosphere pressure. Red–brown lines: internal envelopes. Black points: intersection points of the internal envelope.
Fig. 6. Experimentally obtained internal envelope and intersection points with different RIs for samples S1–S4. (a) Internal envelopes 1 and 2 of S1. (b) Internal envelopes 2 and 4 of S2. (c) Internal envelopes 3 and 5 of S3. (d) Internal envelopes 5 and 12 of S4. (e) Linear fitting of the experimental shifts of the intersection points for samples S1–S4 as a function of RI.
According to Eq. (11), when the detuning ratio (${\Delta / {{n_1}{L_1}}}$) is a constant, the M factor of j-order of HVE (${M_j}$) is proportional to j + 1. As presented in Table 1, S1 and S3 have a similar detuning ratio (1.92% and −1.88%). Therefore, the relationship between j and sensitivity can be investigated experimentally by comparing the RI response of S1 and S3. Figures 5(a) and (c) show the reflection spectrum of S1 and S3. As shown in Fig. 6(a), the intersection points of S1 experienced a blue shift as RI increases. Since the detuning ratio of S3 is negative, the intersection points of S3 experienced a red shift as RI increases (Fig. 6(c)). As shown in Fig. 6(e), the RI sensitivities of S1 and S3 are −83100 nm/RIU and 378000 nm/RIU, respectively. It verified that when the detuning ratio (${\Delta / {{n_1}{L_1}}}$) is a constant, by increasing harmonic order j, the TVE sensor can achieve a greater RI sensitivity. Then we use ${L_1}$ (Table 1) and Eq. (11) to calculate the ${M_j}$ of S1 and S3. The ${M_j}$ of S1 and S3 are 52 and 265 respectively. The results show that the ratio of ${M_j}$ of S1 and S3 is close to the ratio of sensitivity of S1 and S3 when the experimental error is allowed. The theoretical calculation is consistent with the experimental results.
In addition, S2 and S4 (Table 1) were made to investigate the effect of harmonics order (j) on RI sensitivity under large detuning ratio conditions (10.80% and 31.00%). Due to the large detuning ratio (10.80%), the FSR of the lower envelope of S2 is only 66 nm (Fig. 5(b)), which is smaller than the FSR of the lower envelope of S1 (252 nm). As illustrated in Fig. 5(b), the intersection points of S2 experienced a blue shift as RI increases. The RI sensitivity of S2 is only −40600 nm/RIU (Fig. 6(e)), which is smaller than the RI sensitivity of S1 (−83100 nm/RIU). However, according to Eq. (11), ${M_j}$ can be amplified by increasing the number of harmonic order j. Therefore, S4 was made with a harmonic order j of up to 12 with a large detuning ratio of up to 31.00% (Table 1). As illustrated in Fig. 6(d), the intersection points of the internal envelopes 8 and 14 of S4 showed a blue shift, as the RI increased, and the RI sensitivity of S4 is −75000 nm/RIU (Fig. 6(e)). Although the detuning ratio of S4 (31.00%) is much larger than that of S2 (10.80%), the sensitivity of S4 (−75000 nm/RIU) is much higher than that of S2 (−40600 nm/RIU). By comparing the RI sensitivity of S2 and S4, it was experimentally verified that high sensitivity sensing can be achieved by increasing the harmonic order j even in the condition of a larger detuning ratio.
As presented by Fig. 6(e) and Table 1, the experimental results of S1–S4 show that both the harmonic order j and detuning ratio have significant impacts on the sensitivity application, and a larger harmonic order j and a smaller detuning ratio result in a larger sensitivity, which agrees well with the theoretical analysis by Eq. (11).
Moreover, sensor5 (S5) was fabricated for liquid RI sensing. In S5, lengths of ${L_1}$ and ${L_2}$ are 48.0 µm and 292.0 µm, respectively, and its detuning ratio (${\Delta / {{n_1}{L_1}}}$) is −28.90%. Therefore, the harmonic order j of S5 is 6. In the experiments of this study, S5 was placed in a breaker with an NaCl solution, so the RI of the liquid in FPI1 could be varied by changing the concentrations of the NaCl solution. The RI range of NaCl solutions in the experiment is 1.3330–1.3350, with an interval of 0.0002. The liquid can almost instantaneously access FPI1 due to the large open-cavity structure. Figure 7(a) shows the reflection spectra and internal envelope for S5 in the RI of 1.3330. The linear fitting of the spectral shift as RI increases can be plotted by tracing the intersection points of internal envelopes 1 and 6 (Fig. 7(b)). The experimental sensitivity of the sensor was then calculated to be 35600 nm/RIU.
Fig. 7. (a) Reflection spectra experimentally measured for S5 in the RI of 1.3330. (b) Linear fitting of the experimental shifts of the intersection points of internal envelopes 1 and 6 for S5 as a function of RI.
4. Discussion
According to Eqs. (6) and (12), the TEV can only improve the M factor by reducing the detuning ratio, while the HEV can improve the M factor by reducing the detuning ratio and increasing the harmonics order. In the experiment, the sensitivity of S1 based on TVE with a detuning ratio (${\Delta / {{n_1}{L_1}}}$) of 1.92% is −83000 nm/RIU, while the sensitivity of S3 based on HVE with a detuning ratio of −1.88% is 378000 nm/RIU. Calculations show that the RI sensitivity of S3 is 4.6 times greater than that of S1, which experimentally proved that the sensitivity can be amplified by increasing the harmonic order when the absolute value of the detuning ratio is similar.
In addition, the detuning ($\Delta $) of S1 and S3 is 3.8 µm and −4.5 µm, respectively. However, even if the sensor fabrications were facilitated with precision fiber tools, the fiber processing, such as fiber cleaving, splicing, and femtosecond laser micromachining, will inevitably have a few micrometers of machining error. Therefore, it is very difficult to further reduce detuning below a micron level. Compared with reducing the detuning, increasing the harmonic order j is much easier to achieve to further increase sensitivity. According to Eq. (8), j can be increased by increasing the length ratio of ${L_1}$ and ${L_2}$. S4 is made by the method mentioned above, which has a large harmonic order (j = 12) and a large detuning ratio (31%) (Table 1). It was found that although its ${\Delta / {{n_1}{L_1}}}$ is as high as 31% (Table 1) due to a large $\Delta $ (12 µm), its sensitivity can still reach −75000 nm/RIU, which is much higher than the sensitivity of S2 and close to the sensitivity of S1 (Fig. 6(e)). Moreover, unlike S1 and S3, in the case of such large $\Delta $ (12 µm), even if there are 1–2 µm of machining error, the value of $\Delta $ varies slightly, so the ${\Delta / {{n_1}{L_1}}}$ will not change too much. In this condition, the fabrication of S4 has the characteristics of lower cost and higher repeatability than S1 and S3, indicating a higher commercial value ultimately.
On the other hand, there are two aspects that need to be improved. Firstly, an ultrahigh sensitivity will inevitably bring about temperature crosstalk, especially when detecting liquids with high thermal optical coefficient. This problem can be solved by temperature compensation. For example, we can fusion splice a fiber Bragg grating (FBG) with a piece of single-mode fiber in front of the sensor probe. The impact of temperature-induced spectral envelope drift on sensor RI measurement can be offset by the following mathematical formula [32]:
5. Conclusion
This paper proposes and experimentally demonstrates an ultrahigh-sensitive RI sensor based on the harmonic Vernier effect. A simple SMF–HCF–SMF structure that constituted the cascaded FPI is used. Moreover, there is a lateral offset of about 37 µm between the two SMFs and HCF to form a large open-cavity structure, which can hold gas and liquid samples. The harmonic Vernier effect could be excited when the optical path of SMF is more than twice that of HCF. The problem that the FSR of the envelope exceeds the range of the spectral demodulation equipment can be solved by tracking the position of the intersection points of the internal envelopes. The experimental results show that the sensitivity of the proposed structure could be as high as 378000 nm/RIU. Compared to other reported results, the proposed sensor achieves a higher harmonic order (j = 12), which will increase the fabrication tolerances while achieving high sensitivity. This sensor features the advantages such as extremely high sensitivity, compactness, low cost (better fabrication tolerances), and capability to detect gas and liquid samples. This sensor has promising potentials for biochemical sensing, gas or liquid concentration sensing, and environmental monitoring.
Funding
Science and Technology Planning Project of Shenzhen Municipality (GXWD20201230155427003-20200731103843002, JCYJ20190806143818818); National Natural Science Foundation of China (61675055).
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.
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