Highly sensitive refractive index sensor based on two cascaded microfiber knots with Vernier effect

A highly sensitive refractive index (RI) sensor based on two cascaded microfiber knots with vernier effect is proposed and demonstrated by theoretical arithmetic. Deriving from high proportional evanescent field of microfiber and sharp spectrum fringes induced by vernier effect, a slight change of ambient RI will cause large variation of effective RI and significant wavelength shift of resonant peaks, indicating high sensitivity and resolution of the proposed compound resonator. Numerical analysis demonstrates a high sensitivity of 10000nm/RIU and a resolution of 5.57×10−5 RIU at the ambient RI around 1.33 for the fiber diameter of 1μm and cavity radii of R1 = 500μm, R2 = 547.62μm


Introduction
Recently, the demands of costless, sensitive and compact refractive index (RI) sensors increase rapidly in the bio/chemical sensing fields. The requirement of measuring slight RI variation in small sample volume makes the bulk refractometers not appropriate for applications because of their relatively large size and weight [1]. Consequently, people have developed various integrated optical RI sensors, including tapered fiber tip [1], fiber grating [2], Fabry-Perot interferometers (FPIs) [3,4], Mach-Zehnder interferometers (MZIs) [5,6], surface Plasmon sensors [7], micro-cavities [8,9] and so on to solve the problem. Among them, the all-fiber RI sensors offer special advantages of low insertion loss and high compatibility with other photoelectric devices.
Micro/nano fiber (MNF) with the diameter of a few micrometers can be served as a reliable candidate of miniaturized RI sensor due to its unique properties such as high fraction of evanescent field, good flexibility and low bending loss [10,11]. So far, many microfiber based structures have been proposed for RI measurement. F. Gao et al. reported a compact RI sensor based on the leaky radiation of single microfiber, with RI detecting resolution of mere 0.001 refractive index unit (RIU) [12]. Besides, microfiber Bragg gratings were intensively investigated, but their sensitivities seem to be limited to only several hundred nm per RIU [13][14][15][16]. The RI sensitivity of microfiber long period gratings could reach to 4623nm/RIU [17], yet the complicated and relatively high cost fabrication process limits their applications [17][18][19]. Much effort has also been dedicated to microfiber based interferometers to improve the RI sensitivity, namely MZIs [20], Sagnac interferometers (SIs) [21] and polarimetric interferometers (PIs) [22]. Particularly, Lipeng Sun et al twisted a highly-birefringent microfiber to form a PI which showed RI sensitivity up to 24373nm/RIU. However, the specifically required rectangular fiber is difficult to connect with standard single-mode fiber, and the large bandwidth is unfavorable for accurately tracing the wavelength shift. Moreover, microfiber coil resonator with compact size and high Q-factor was researched for high resolution RI detection, whereas its sensitivity of only 700nm/RIU remains to be improved [23]. Meanwhile, as one of the most common resonators, microfiber knot resonator (MKR) has been used as laser filter [24], add-drop filter [25], temperature sensor [26] and magnetic field sensor [27]. Nevertheless, there was no reported systematical study about its RI sensing performance.
Vernier-scale commonly used in calipers and barometers is a method to enhance the measurement accuracy. It consists of two scales with different periods, of which one slides along the other one. The overlap between lines on the two scales is used to perform the measurement [28]. Recently, Vernier effect has also attracted interest from optical sensing field due to the spectrum magnification function. Cascaded fiber ring resonators for strain measurement with sensitivity of 0.0129nm −1 /με and detection limit of 0.125με is proposed and demonstrated [29]. By combining a fiber ring resonator with a passively mode-locked fiber laser, a micro-strain sensor with sensitivity higher than 40 pm/με is realized [30]. Moreover, two cascaded intrinsic FPIs are employed to induce Vernier effect for magnetic field detection with sensitivity of 71.57 pm/Oe [31]. However, Vernier effects generated by optical fiber are scarcely applied to RI sensors to the best of our knowledge. Although the two cascaded silicon micro-ring resonator (CMRRs) based on Vernier effect has been studied for RI sensing [32][33][34], the high cost, complicated fabrication process and low coupling efficiency with fiber limit their applications in the popular all-fiber sensing systems.
In this paper, we propose a small-sized RI sensor based on cascaded microfiber knot resonators (CMKRs) with Vernier effect. The spectrum magnification function of Vernier effect renders a significant RI sensitivity enhancement to the CMKRs. Theoretical analysis is carried out to investigate the Vernier transmission spectrum of the CMKRs and then the RI sensing principle. By knotting two MKRs subsequently through a bus microfiber, a CMKRs is fabricated for experimental demonstration. Furthermore, Lorentz fitting method is adopted to accurately trace the wavelength shifts in the sensing response.

Physical design and Vernier effect analysis of the CMKRs
Based on single MKR [see Fig. 1(a)], we design the all microfiber compound resonator as illustrated in Fig. 1(b). Two MKRs are cascaded in series through a bus microfiber, forming four coupling regions I~IV. To present the working principle of the CMKRs more clearly, the single MKR is investigated in priority. As shown in Fig. 1(a), a fiber taper is knotted with the cavity of the MKR and used for coupling out the resonant modes from the drop port 7. Assume the coupling efficiencies and coupling loss coefficients of the two coupling region s I, II are 1 where 1 β is the propagation constant in MKR, α is the total transmission loss coefficient containing the propagation loss coefficient and bending loss coefficient, 11 l and 12 l represent the fiber lengths from port 3 to port 5 and from port 6 to port 2, respectively. By solving Eq. (1), the ratio of 7 E and 1 E can be deduced as: For the CMKRs assembled as Fig. 1(b), the light propagates as follows: Light launched into the first MKR (MKR1) through coupling region I oscillates in clockwise direction. At coupling region II, part of the power can be coupled to the bus microfiber and then transmits to the second MKR (MKR2) through coupling region III. Similarly, the light oscillates in MKR2 and at coupling region IV, the power is partly coupled to the output port 13. Therefore, based on the discussion about the single MKR, the ratio of electronic fields in port 13 ( 13 E ) and port 1 ( 1 E ) can be deduced as: where 2 β is the propagation constant in MKR2, s l is the length of connecting microfiber, 21 l and 22 l represent the fiber lengths from port 10 to port 11 and from port 12 to port 9, respectively. 3 where 1 R and 2 R represent radii of MKR1 and MKR2, respectively. Being restricted by resonant principle, only the signal light whose frequency matches both MKRs could solidly exist, while others will be suppressed and can't be output. According to Eq. (4), the phase resonant condition of the CMKRs can be described as: , every m-th resonant peak of MKR1 will overlap with (m + 1)-th resonant peak of MKR2, as displayed in Fig. 2. Only the mutual resonant peaks of MKR1 and MKR2 rise to the maximum, while the other resonant peaks of MKR1 or MKR2 are suppressed. Another important item for the CMKRs is the extinction ratio (ER) of Vernier spectrum, which is defined as the difference between the intensities of the highest fringe (I max ) and the lowest fringe (I min ), as marked by the red lines in Fig. 2(c). According to Eq. (4), ER depends on coupling efficiencies ( 1 2 3 4 , , ,  Figs. 3(a) and 3(b). It is obvious that ER monotonously increases with the coupling efficiencies while almost linearly decreases with the coupling losses. Therefore, in theory the ER can be augmented by increasing the coupling efficiencies and decreasing the coupling losses of the coupling regions I~IV.

RI sensing principle of the cascaded MKRs with Vernier effect
According to the discussion above, the CMKRs is expected to be a highly sensitive RI sensor. Actually, CMKRs can work as a RI sensor under three conditions, namely, (1) the ambient RIs of both MKR1 and MKR2 are varied; (2) only the ambient RI of MKR1 is varied; (3) only the ambient RI of MKR2 is varied. It can be inferred from Fig. 2 that the CMKRs has the highest sensitivity when working under the third condition. Therefore, to optimize the RI sensing performance of the CMKRs, only the ambient RI of MKR2 is varied.
When we slightly change the ambient RI of MKR2 ( a n ), the resonant wavelength of MKR2 ( 2 λ ) will shift as: 2 a e f f e f f a n n n n where 2 , eff a n n Δ Δ represent the variations of effective RI and ambient RI of MKR2, respectively. Then, the corresponding wavelength shift of certain Vernier peak of the CMKRs can be derived as: Therefore, the RI sensitivity can be deduced as:  [20]. For a detailed view into the RI sensing response of the CMKRs, we simulate the Vernier spectra with different ambient RIs of MKR2 by employing the typical parameters listed in Table 1 as an example. Figure 4 illustrates the transmission spectra of the CMKRs evolving as the ambient RI of MKR2. It is obvious that the Vernier peak experiences a red shift as the ambient RI increasing, with the sensitivity calculated to be 6591nm/RIU.
By substituting the parameters listed in Table 1 into Eq. (10), the theoretical minimum detectable RI is calculated as 5 3.59 10 − × RIU. Moreover, the fringe alignment between spectra of MKR1 and MKR2 is discrete, resulting in discrete RI measurement, which is a serious limitation of practical application.
Besides, because the fringes bandwidths in spectra of MKR1 and MKR2 are nonzero, when the m-th resonant peak of MKR1 does not totally overlap with (m + 1)-th resonant peak of MKR2, the Vernier spectrum could also be generated. However, in this condition, the distinction between the highest peaks and the sidelobe peaks is blurry. Hence, it may result in the inaccuracy of locating the peak wavelength of the Vernier envelope, bringing noise to the RI sensing of CMKRs.
In order to conquer the above limitations, we apply the Lorentz fitting algorithm to the measured Vernier spectra according to Eq. (1) [28]. Consequently, the RI detection becomes continuous, and the minimum detectable RI is only determined by the resolution of the adopted spectrum analyzer.

Fabrication and experiment
We propose the technique named "Drawing-Knotting-Assembling (DKA)" to fabricate the CMKRs. The whole fabrication process is displayed in Fig. 5. Firstly, three microfibers are fabricated by using flame-heated taper-drawing technique, and then two of them are cut off and made into two MKRs using the method reported in [24], as presented in Figs. 5(a)-5(c). After anchoring the two MKRs on two ridges of a glass substrate, the third microfiber is also cut off, fixed and knotted with the cavities of the two MKRs in series, as illustrated in Figs. 5(d) and 5(e). After micro-adjusting the sizes of two MKRs and coupling regions, the whole structure is finished. The tensile force from anchoring points and the intertwisted force of coupling regions support the fabricated CMKRs. It should be pointed out that since the microfibers, the resonant cavities and the coupling regions can be controlled and repeated by manipulating step-by-step with the same processing parameters on stable fabrication platform, the reproducibility of the CMKRs fabrication can be easily achieved. In the traditional way, MKR is constructed by tying just one time in the coupling region [24,25]. Here, we modify the MKRs by tying two or more times in the coupling regions, which offers two merits as follows: (1) increased tying times make the coupling region longer, leading the whole structure to be mechanically more robust and optically more stable; (2) controllable tying times make the coupling length variable, bring controllable and repeatable coupling coefficients of the coupling regions.
For experimental demonstration, three identical microfibers with the lengths of 75mm and waist diameters of 1.9μm are drawn to construct the CMKRs. The propagation losses of three microfibers are measured as low as 1dB immediately after they are fabricated. Besides, due to the thin diameter and the extremely good flexibility of microfiber, their bending losses can be too low to consider. In the fabricated CMKRs, each coupling region contains two knotting turns, and cavity radii of MKR1 and MKR2 are 1.178mm and 1.230mm, respectively. Figures 6(a)-6(c) illustrate the microscope images of the waist region of the drawn microfiber, the coupling region with two knotting turns and the MKR with two coupling regions, respectively.
The experimental setup displayed in Fig. 6(d) is built to investigate the RI sensing performance of the fabricated CMKRs. The interrogator (Micron Optics sm250) combining with a circulator is employed to measure the transmission spectrum of CMKRs and record it to the computer. Since MKR1 and MKR2 inherently contain the SMF-ends, the coupling between the external fiber and the CMKRs can be directly achieved through the connection of the SMF-ends of MKR1 and MKR2 to the external fiber. Then, water with RI of 1.3315 is dropped onto the substrate to immerse and float the CMKRs. Subsequently, the ambient RI of MKR2 is increased by locally injecting the pure glycerin with large viscidity and high density into the region of MKR2, while keep the ambient RI of MKR1 unchanged. Simultaneously, the ambient RI of MKR2 is measured by Abbe refractometer for calibration.

Experimental results and discussions
In the experiment, the ambient RI of MKR2 is increased from 1.3315 to 1.3349 by injecting pure glycerin with the amount of 1ml per time, while the ambient RI of MKR1 is kept at 1.3315, and then the transmission spectra of the CMKRs is traced and recorded. A typical transmission spectrum of the CMKRs with ambient RI of MKR2 equaling to 1.3320 is depicted by purple line in Fig. 7. The periodical envelop indicates the generation of Vernier effect. FSR of the envelope is measured as 5.05nm which is 22 times of FSR of the resonant sub-peaks. By applying the measured structure parameters to calculation, the coupling parameters and the theoretical spectrum can be obtained, as presented in Table 1 and Fig. 7, respectively. The coupling loss in each coupling region of the CMKRs is calculated to be 0.1, which mainly comes from the slightly unmatched propagation coefficients of two sections of microfiber. In addition, as shown in Fig. 7, within the wavelength band from 1535nm to 1550nm, the experimental spectrum almost overlaps with the numerical simulation, indicating good consistency between them. However, the ER of experimental Vernier envelope is 5dB, relatively lower than the simulating ER of 6dB. This may be caused by two reasons: (1) the lower coupling efficiency, larger coupling loss and thus lower Q-factor of the CMKRs in experiment; (2) the Vernier effect may be generated under the condition that the m-th resonant peak of MKR1 slightly misalign with (m + 1)-th resonant peak of MKR2, but the two resonant peaks are still partly overlapped. Then, I max will decrease and I min will increase, resulting in the smaller ER than the condition of strict Vernier effect. Practically, the experimental ER can be enhanced by improving the fabrication techniques and controlling the length of coupling regions according to the theoretical analysis.
Then, the RI response of the fabricated CMKRs is investigated. The transmission spectra with different ambient RIs of MKR2 are shown in Fig. 8(a). The spectra are fitted by the Lorentze procedure for locating the Vernier peaks more accurately as discussed above. It is observed that the spectra experience red shift as the RI increasing. The exact dependence of the wavelength shift on the ambient RI is presented in Fig. 8(b) with black squares. Linear response with a high R-square of 0.9992 is obtained, and the sensitivity is calculated to be 6523nm/RIU, which agrees well with the simulation sensitivity of 6591nm/RIU. It should be noted that although there are relative intensity noise (RIN) in the light source as well as thermal noise and shot noise in the photo-detector of the spectrum analyzer, these noises mainly bring about the fluctuation of light intensity. For the proposed RI sensor, the RI is measured by tracing wavelength shift of the transmission spectrum, which is an absolute parameter dependent on the relative optical intensity variation. Hence the RI detection is not affected by the noises from laser and photo-detector. In addition, the noises from ambient environment are well isolated by conducting experiment in a stable table with constant temperature and careful operation. Consequently, the experimental noises resulting from the interrogator and the ambient environment can be neglected, while only the resolution of the interrogator determines the minimum detectable RI of the CMKRs. Due that the resolution of the interrogator is 1pm and the experimental RI sensitivity is 6532nm/RIU, the resolution of this RI sensor can be deduced to 1.533 × 10 −7 RIU.
For practical application, the CMKRs can be embedded into a solid matrix with low RI such as PDMS and Teflon [23,36], to increase the robustness and long-term stability as well as ensure MKR1 completely immunizing to the ambient RI change. Furthermore, since the Vernier peak can be located more accurately with higher ER of Vernier envelope, we can also improve the detection resolution by optimizing the fabrication techniques and controlling the length of coupling regions. Besides, adopting thinner microfiber and small-sized CMKRs could also enhance the sensitivity and the resolution.

Conclusion
In this paper, a highly sensitive RI sensor based on CMKRs with Vernier effect is proposed and experimentally demonstrated. Theoretical analysis investigates the principle of Vernier effect and its magnificent function on the transmission spectrum of the CMKRs. By using the method named "Drawing-Knotting-Assembling (DKA)", a robust sensing device is fabricated for experimental demonstration. In order to accurately trace the wavelength shift of the Venier resonant peaks, Lorentz fitting algorithm is applied to the transmission spectra. Within RI range from 1.3320 to 1.3350, a linear response of wavelength shift to the ambient RI with high sensitivity of 6523nm/RIU and resolution up to 1.533 × 10 −7 is obtained in the experiment, which shows good agreement with numerical simulation. The proposed all-fiber RI sensor with compact size and low cost can be widely used for chemical and biological detection, as well as the electronic/magnetic field measurement.