Ultrasensitive refractive index sensor based on enhanced Vernier effect through cascaded fiber core-offset pairs

An ultrasensitive refractive index (RI) sensor based on enhanced Vernier effect is proposed, which consists of two cascaded fiber core-offset pairs. One pair functions as a Mach-Zehnder interferometer (MZI), the other with larger core offset as a low-finesse Fabry-Perot interferometer (FPI). In traditional Vernier-effect based sensors, an interferometer insensitive to environment change is used as sensing reference. Here in the proposed sensor, interference fringes of the MZI and the FPI shift to opposite directions as ambient RI varies, and to the same direction as surrounding temperature changes. Thus, the envelope of superimposed fringe manifests enhanced Vernier effect for RI sensing while reduced Vernier effect for temperature change. As a result, an ultra-high RI sensitivity of -87261.06 nm/RIU is obtained near the RI of 1.33 with good linearity, while the temperature sensitivity is as low as 204.7 pm/ °C. The proposed structure is robust and of low cost. Furthermore, the proposed scheme of enhanced Vernier effect provides a new perspective and idea in other sensing field. © 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement


Introduction
The interferometric fiber sensor (IFS) for refractive index (RI) measurement has attracted high attention in the fields of environmental monitoring, chemical and biological analysis, medical diagnostics and so on. Different structures for IFS have been reported, including fiber Mach-Zehnder interferometers (MZIs) composed of a taper or peanut pairs [1][2][3], core-offset pairs [4][5][6][7], microfiber [8][9][10][11], and other specific structures inscribed or etched in the fiber [12][13][14][15][16]; and some hybrid structure such as a fiber taper inscribed with a fiber grating (FBG) [17][18] or a mismatched pair sandwiching a fiber taper [19]. Among various configurations mentioned above, a branch of IFSs measures direct RI changes induced by the sample in the cavity. For example, an in-line fiber cavity with a large core-offset pair forms a MZI, in which the light propagates through the sample in one interference arm, while through the cladding of the sandwiched fiber in the other arm [5]. A microcavity or a trench is inscribed near the interface between the fiber core and cladding by use of a femtosecond laser [13][14]. In order to improve the stability and sensitivity, further chemical etching is adopted to smooth the side face of the cavity or trench [15]. These RI sensors can offer not only broad measuring range, but also an almost linear response to RI change. Nevertheless, the sensitivity in these designs is limited 10 3 ∼10 4 nm/RIU [5]. Another well-known design is based on the microfiber interferometer, which can realize an ultrahigh sensitivity up to 10 5 nm/RIU [10][11]. However, the high sensitivity is limited only at the dispersion point, and the sensor also suffers from poor linearity, limit measurement range and fragile mechanical performance. Therefore, designs with both high sensitivity and good linearity are highly desired.
In recent years, Vernier effect has been proposed in many kinds of sensors for measurements of gas pressure [20], temperature [21][22][23][24][25][26][27], strain [28][29], refractive index [30][31][32][33][34], etc. to improve the sensitivity of IFSs. These sensors consist of two cascaded or parallel interferometers, one as a sensing interferometer and the other as a reference interferometer. The difference of free spectrum ranges (FSRs) of the two interferometers is very small, in this way, the superimposed spectrum of the sensor will produce an envelope. When environmental parameters change, the envelope shifts much more than the interference fringe of the sensing interferometer. Therefore, the sensitivity of the sensor can be amplified by measuring the shift of the envelope. For all reported sensors based on Vernier-effect, it is required that the reference interferometer is completely insensitive to environment, which however fluctuates inevitably with environment variation, especially in the compact sensor structure.
In this paper, an ultra-sensitive RI sensor based on enhanced Vernier effect by use of cascaded fiber core-offset pairs is proposed. One pair with core-offset of 62.5 µm function as a MZI, and the other one with core-offset of 80 µm as a low-finesse in-line Fabry-Perot interferometer (FPI). Different with the reference interferometer in traditional Vernier-effect sensor, MZI and FPI in this work are both sensitive to surrounding medium. Their interference fringes shift to opposite directions and enhances Vernier effect as ambient RI changes, while shift to the same direction and suppresses Vernier effect as temperature changes. As a result, an ultrasensitive RI of -87261.06 nm/RIU is obtained near RI of 1.33, which is comparable to that realized by microfibers at the dispersion turning point but with excellent linearity [10][11]. In addition, the RI sensing is not affected by the temperature change, which shift the spectrum only as low as -204.7 pm/°C. Figures 1(a)-1(b) illustrate the fabrication process of a fiber core-offset pair. A SMF is cleaved into two flat and smooth end faces. We firstly splice the two cleaved fibers by manually adjusting the motor of a fusion splicer (Fujikura FSM 100P+) to make them aligned along the X axis while with a core offset along the Y axis ( Fig. 1(a)). The discharge duration time, current of the fusion splicer and overlap length are set to be 400 ms, 240 bits and 5µm, respectively. In order to control the phase differences of the two interferometers, precise fiber cleaving is required. The left-side fiber is fixed in a precise three-dimensional translation stage (Newport Model M-561D) with the precision of 1 µm while the right-side fiber is placed on the fiber cleaver (Fujikura CT50). Carefully adjusting the translation stage, then the right-side fiber is cleaved at a designed length under a microscope. The second splicing is as shown in Fig. 1(b), and realized by the following procedure: put back the first spliced fiber into the splicer V groove with the first splicing point being kept at the previous lateral position; then translate the spliced fiber to the left side along the V groove and align it with the remained cleaved fiber along the same X axis while with an opposite core offset along the Y axis, finally splice the fibers. Figure 1(c) displays the fabricated MZI, with designed geometric length of 2.42 mm for the sandwiched fiber, and lateral core offset of 62.5 µm at both splicing points. The light from the lead-in fiber is split into two optical paths at the first splicing point, one in the surrounding medium along the cladding surface of the sandwiched SMF (red arrow) and the other along the cladding of the fiber (blue arrow), respectively, which forms a MZI. Figure 1(d) shows another fiber core-offset pair with the sandwiched fiber with a geometric length of 100 µm and a core offset of 80 µm. Due to the large core offset, the light from lead-in fiber does not penetrate into the cladding of the sandwiched fiber, instead, Fresnel reflections at the two end faces can form a low finesse FPI.  Figure 2 illustrates the schematic diagram of the RI sensor utilizing the MZI cascaded with the FPI to enhance Vernier effect. The MZI is cascaded with the FPI through two ports of a circulator, and is fixed by ultraviolet glue side by side with the distance of ∼ 350 µm, as shown in the microscope image in the insert. The light travels into the MZI and is then reflected by the FPI, the output electric field (E out ) from the third port of the circulator can be expressed as

Fabrication and principle
where E in is the electric field from the lead-in fiber of the MZI. D 1 and D 2 are the normalized coefficients denoting the splitting ratio of the ambient medium path and cladding path of the MZI, correspondingly. D 3 and D 4 denote the reflection coefficients at the end faces of the FPI, respectively. L M and L F are the geometric lengths of the sandwiched fibers of the MZI and FPI, as displayed in Figs. 1(c) and 1(d). n ext is the RI of the ambient medium and n cl is the effective RI of the cladding mode, respectively. λ is the wavelength in vacuum. E in is normalized and the total output strength can be expressed as [26] 1 and ∆ϕ 2 are the phase differences of the MZI and FPI, respectively. To realize the Vernier effect, ∆ϕ 1 is set close with but not equal to ∆ϕ 2 . The m th and n th dip wavelengths for interference fringes of the MZI and FPI can be written as respectively, where m and n are integers. The corresponding FSR can be calculated according to Eq. (5) and Eq. (6) as where FSR 1 and FSR 2 are the FSRs of the MZI and FPI, respectively. And the envelope of the superimposed fringe of the second and third terms in Eq.
(2) has l th dip wavelength and FSR which can be calculated according to Eqs. (2)-(4) and Eqs. (7)- (8): (n cl -n ext ) and L m , or n ext and L F will change as the outside perturbance like the RI variation of ambient medium or temperature fluctuation. Thus the Vernier-effect based resonance dip wavelengths will shift and can be expressed as: δλ n = λ n ∂n ext n ext where δλ m , δλ n are the shifts of λ m and λ n , respectively, while δλ l is the shift of the envelope. λ m = λ n = λ l , according to the resonance condition [26]. Derived from Eqs. (11)-(13), the relationship of δλ m , δλ n , and δλ l can be expressed as where A 1 and A 2 has the same sign, and |A 1 | and |A 2 | denote the amplification factors. The shift direction of envelope (or the sign of the δλ l ) is determined by the shift directions of the two interference fringes (or the sign of the δλ m and δλ n , respectively) and the sign of A 1 (or A 2 ). There are three situations for the envelope shift according to Eq. (14), which are discussed as follow: (1) δλ n =0, then δλ l =-A 1 · δλ m . This situation corresponds to the sensor structure based on traditional Vernier effect, where one of two interferometers acts as reference interferometer, and the other as sensing interferometer [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. The working mechanism for traditional Vernier effect is shown in Fig. 3(a).
(2) 2)δλ m · δλ n > 0, or δλ m and δλ n keep the same sign, indicating the two interference fringes shift in the same direction with the changing parameters. In this condition, the envelope shifts less than that in the first situation, and the Vernier-effect based sensitivity is reduced. Figure 3(b) displays the reduced Vernier effect.
(3) δλ m · δλ n < 0, or δλ m and δλ n are at opposite signs, which means the two interference fringes shift to the opposite directions. Then the envelope shifts more than that in the first situation, and the sensor sensitivity based on Vernier effect is enhanced (Fig. 3(c)). According to above discussion, the sensor based on traditional Vernier effect requires the reference interferometer completely insensitive to the environment, which is difficult to achieve, especially in compact sensors. Moreover, if the interference fringe of the reference interferometer shifts to the same direction as that of the sensing interferometer, the sensor sensitivity will be reduced, even to zero.
In this work, interference fringes of the MZI and FPI are designed to shift to the opposite directions when the RI of ambient medium varies, then the envelope shows enhanced Vernier effect according to Eq. (14). While for temperature variation, the two interference fringes shift to the same direction and Vernier effect is reduced.

Experiment and results
The experimental setup is illustrated in Fig. 2. A supercontinuum broadband optical source (SBOS) (OYSL SC-5-FC) is used, and the output is recorded by an optical spectrum analyzer (OSA) (Yokogawa, AQ6370D). The sensor head is immersed into the deionized water at room temperature.
Working mechanism of Vernier effect based on the proposed sensor is experimentally investigated. Figure 4(a) shows the transmission spectrum of the MZI in the wavelength range of 1350 nm to 1650 nm and with a resolution of 0.02 nm, the corresponding spatial frequency spectrum is calculated by fast Fourier transform (FFT) operation and demonstrated in Fig. 4(b). In Fig. 4(b), three peaks are induced, and the optical path difference (OPD) of peak 1 and peak 2 are 141.1µm and 291.5 µm respectively, indicating that the two cladding modes of sandwiched fiber are excited and interfered with the light passing through the sample, respectively. The OPD of peak 3 is equal to the sum of that of peak 1 and peak 2, i.e. 432.6 µm. Figure 4(c) displays the reflection spectrum of the FPI. A clear sinusoidal fringe is observed, which is a typical low-finesse Fabry-Perot interference fringe. The corresponding spatial frequency spectrum is shown in Fig. 4(d), a peak named as peak 4 with the value of 267.6 µm is observed, representing the OPD of the two end faces of the FPI. The output optical spectrum of the MZI cascaded the FPI is displayed in Fig. 4(e). No obvious envelope based on Vernier effect is observed due to many sets of interference patterns coexisting in the spectrum. The corresponding spatial frequency spectrum is also demonstrated in Fig. 4(f), where peak 1-4 still appear at the same positions as those in Figs. 4(b) and 4(d), respectively. Due to the specifically designed MZI and FPI in cavity lengths, peak 2 (belong to MZI) is close to peak 4 (belong to FPI) in OPD. A band-pass finite impulse response filter with a Hanning window function operates on the output spectrum of Fig. 4(e) to extract superimposed spectrum corresponding to peak 2 and peak 4. The extracted spectrum is revealed by the blue line in Fig. 5(a), where a fringe with a clear envelope originating from Vernier effect appears, the upper envelope curve with FSR of 102.8 nm acquired by curve fitting is shown in orange line. The same operation can also be used to extract the interference fringes corresponding to peak 2 and peak 4 as shown in Figs. 5(b) and 5(c), respectively, with FSRs of 7.71 nm and 8.41 nm. Then according to Eqs. (14) and (15), the amplification factors |A 1 | and |A 2 | are calculated to be 12.19 and 11.20, respectively. Responses of the sensor to ambient RI based on enhanced Vernier effect are tested. The measured solutions with different RIs in the range between 1.3323 and 1.3341 are obtained by changing the concentration of the glycerin solution. The RIs of glycerin solutions are measured by an Abbe refractometer (Reichert AR200). The sensor head is immersed into the glycerin solution at the room temperature. Figure 6 shows RI responses of the sensor to the RI of the intracavity medium at 25°C. Figures 6(a) and 6(b) show extracted spectra corresponding to peak 2 and peak 4 under different RIs, respectively, and Fig. 6(c) the envelopes under different RIs. In Fig. 6(a), because n ext < n cl , the increase of ambient RIs causes the decrease of ∆ϕ 1 , and fringes corresponding to peak 2 shift to the shorter wavelength. By contrast, fringes of peak 4 in Fig. 6(b) shift to the longer wavelength because ∆ϕ 2 increases with RI. The shift of the envelopes shows enhanced Vernier effect because δλ m · δλ n < 0, with the dip wavelengths shift to the shorter wavelength as displayed in Fig. 6(c). Figures 6(d)-6(e) display the variation of the dip wavelength with RI corresponding to Figs. 6(a)-6(c). In Fig. 6(d), a linear fitting shows a high RI sensitivity of -6162.06 nm/RIU at the dip wavelength of 1600 nm. The coefficient of determination (R2) value is 0.98273, showing a good sensing linearity for the MZI. In Fig. 6(e) a sensitivity of 1232.40 nm/RIU at the dip wavelength of ∼ 1600 nm for the FPI is obtained, which agrees with the theoretical value calculated by Eq. (12).
Figure 6(f) shows the relation between the dip wavelength of envelope and the RI corresponding to Fig. 6(c). An extremely high RI sensitivity of ∼ -87261.06 nm/RIU is obtained owing to the enhanced Vernier effect. Compared with the calculated value of -88918.39 nm/RIU according to Eqs. (14)-(15), the difference is 1.9%, which mainly comes from measurement error and dip wavelengths not included in the sampling points of extracted spectra in Fig. 6(c). The RI measurement range is between 1.332-1.334, which is limited by the selected wavelength span, a larger RI measurement range can be achieved by increasing the span. The resolution of the measured RIs is calculated according to the measured sensitivity of the envelope, with the value of 2.29 × 10 −7 RIU when a wavelength resolution of 0.02 nm of the OSA is selected.
To investigate the temperature cross sensitivity to RI measurement, the temperature responses of the sensor are also measured by using the similar system. During the experiment, the sensor head exposed in the air is placed on the heating plate with the precision of 0.1°C, and the temperature is increased from 30°C to 130°C with step of 20°C. Figure 7 displays the temperature responses of the sensor. Figures 7(a) and 7(b) show the extracted interference spectra corresponding to peak 2 and peak 4 under different temperatures. When the temperature increases, the interference fringes corresponding to peak 2 and peak 4 both shift to longer wavelength. For the MZI, this is due to the combined impacts of thermal expansion and thermo-optic effect in the sandwiched fiber, of which thermo-optic effect plays a dominant role in fringe shift; For the FPI, fringe shift only comes from thermal expansion.  Figure 7(c) displays the shift of envelope. Because the temperature responses of both the MZI and FPI show positive sensitivities, or δλ m · δλ n > 0, the shift of the envelope reveals reduced Vernier effect. A sensitivity of 204.7 pm/°C is obtained and as shown in Fig. 7(f). This value is amplified compared with those of the MZI and FPI (19.71 and 1.06 pm/°C), which is because the two sensitivities do not match well and reduced Vernier effect is not obvious according to Eqs. (14)- (15). Nevertheless, the sensor is still not sensitive to temperature variation. If no temperature compensation is used, the error caused by temperature cross-sensitivity will be about 2.34 × 10 −6 RIU/°C. Therefore, the effect of temperature on RI measurement can be ignored.

Conclusion
In conclusion, we proposed an ultrasensitive RI sensor based on enhanced Vernier effect. Vernier effect is realized by cascading two fiber core-offset pairs, one of which function as the MZI, the other as the FPI. In the designed sensor, Vernier effect for RI sensing is enhanced and an ultrahigh sensitivity of -87261.06 nm/RIU around RI of 1.33 with good linearity is realized. Meanwhile, Vernier effect for temperature sensing is reduced to a sensitivity of 204.7 pm/°C. Therefore, the sensor is ultrasensitive to the RI change while insensitive to the temperature change. The proposed scheme has wide applications in other sensing field, and provide a new perspective and idea for high sensitivity sensing.

Funding
National Natural Science Foundation of China (31572343, U1601221).