Abstract
We report on a refractive index sensor using a photonic crystal fiber (PCF) interferometer which was realized by fusion splicing a short section of PCF (Blaze Photonics, LMA-10) between two standard single mode fibers. The fully collapsed air holes of the PCF at the spice regions allow the coupling of PCF core and cladding modes that makes a Mach-Zehnder interferometer. The transmission spectrum exhibits sinusoidal interference pattern which shifts differently when the cladding/core surface of the PCF is immersed with different RI of the surrounding medium. Experimental results using wavelength-shift interrogation for sensing different concentrations of sucrose solution show that a resolution of 1.62 × 10 −4 -8.88 × 10 −4 RIU or 1.02 × 10 −4 -9.04 × 10 −4 RIU (sensing length for 3.50 or 5.00 cm, respectively) was achieved for refractive indices in the range of 1.333 to 1.422, suggesting that the PCF interferometer are attractive for chemical, biological, biochemical sensing with aqueous solutions, as well as for civil engineering and environmental monitoring applications.
Introduction
Optical refractometer sensors based on waveguide technology are promising and attractive for chemical and biotechnological applications. The advantages of this type of sensor are their relatively simple construction, compactness, low cost, ease of use, immunity to electromagnetic interference, and high sensitivity to the external refractive index (RI) [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] . Recently, several types of optical waveguide sensors or optical fiber-based refractometer have been proposed, including long-period fiber gratings, Fabry-Perot interferometers and Mach-Zehnder interferometers. The interferometers utilizing a pair of collapsed zones separated by a few centimeters are suitable for sensing applications for they offer many advantages such as robustness, low insertion losses and relatively simple fabrication. However, they suffer from a serious disadvantage: high sensitivity to the environmental temperature. Photonic crystal fiber (PCF) has the potential to compensate for this drawback because its dispersion properties are strongly dependent on the air-hole geometry [11] . This fiber is typically fabricated using the stack-and-draw technique [12] , making it possible to produce a wide variety of geometries. Thus, other than external RI, the operation principle of the PCF interferometers built via micro-holes collapsing is based on the excitation and recombination of two modes. The first collapsing point induces the coupling of a fraction of the incident light propagating in the core mode to the cladding mode, and the second one performs the opposite function, generating the interference of light propagating in different optical paths. PCF-like interferometers and assembly have been used for measuring physical, chemical, and biochemical measurands such as strain, high temperature (up to 1,000 °C), hydrostatic pressure, curvature, biofilm, and chemical vapor [8, 10, [13] [14] [15] [16] [17] [18] [19] [20] .
Introduction
In this paper, we present a PCF interferometer made by fusion splicing a piece of PCF between two standard single mode fibers with a fusion splicer. We report on the investigation and analysis of this class of novel PCF interferometers for refractive index sensing. The ability of the PCF interferometers, with five different sensing lengths (1.34, 2.67, 3.50, 4.40, and 5.00 cm), as a high sensitive RI sensor will be exploited. The unique sensing features of these spectral filters are particularly suitable for a wide variety of applications in sensor systems.
Device Fabrication and Experiment

Principle of Interferometer
According to the interference theory, the value of the fringe period ( Λ ) of the Mach-Zehnder interferometer at any λ can be expressed as follows [13, 14] :
Principle of Interferometer
where λ is the central wavelength of the light source; 1 β and 2 β are propagation constants of the modes involved in the interference, and L is the length of the interferometer. The fringe period is inversely proportional to propagation constant deviation 
Fabrica
The inter was designe a core diam scanning ele spliced with using a fusio experimenta ike interfero a fusion spli both collaps PCF interfe parameters w spectrum of 1,550 nm) an Figure 3 illustrates the experimental setup for refractive index and temperature sensing measurements with the PCF interferometer. The fiber-optic sensing system used to measure the transmission spectrum of the sensor consists of a broadband light source (λ = 1,550 nm), a sensing PCF interferometer, an OSA (ANDO AQ6315A), and a computer for data recording. The characteristic measurements were conducted for interferometers associated with five different sensing lengths (i.e., the length between two collapsed zones, L = 1.34, 2.67, 3.50, 4.40, and 5.00 cm). We fabricated three replicates for each length of interferometer and there are totally 15 interferometers in this study. The interference spectra contain the information of wavelength, transmission loss, and fringe period. The distance between any two consecutive peak fringes is determined as a fringe period. The fringe visibility was calculated for each PCF interferometer as follows [14] 
Fabrica
where I max and I min are the maximum and minimum intensity values of corresponding interference spectrum, respectively. The RI measurements were performed using the above 15 interferometers and the refractive indices were in the range of 1.333 to 1.422. The interference spectra and the relationship between wavelength shift and refractive index were used to characterize the PCF Mach-Zehnder interferometers. During the course of data measurement, the magnetic clamps and a lift platform were used to keep the PCF interferometers straight lines without the bending effect [see Figure 3 (a)]. We have maintained the condition of strain, bending, and temperature quite stable in the laboratory so that they were not the concerns of this work. For precise measurement, we kept the experimental setup and sample materials at a constant ambient temperature (within 1 °C fluctuation). As mentioned in the introduction [11] , we also conducted temperature sensing experiment to prove that the PCF interferometers have the potential to compensate high sensitivity to environmental temperature. For example, a 2.67-cm PCF (a) (b)
Results and Discussion

PCF Interferometer Characteristics
The transmission spectra of a PCF interferometer with different sensing lengths are shown in Figure 5 (a-e). High uniform interference fringes were observed over the available spectral range, and the average fringe periods became larger with the decreasing sensing length. The average fringe periods as a function of sensing length, obtained using a linear regression analysis, was determined to be Figure 5 (f)], indicative of the effect of the Mach-Zehnder interferometer. The fringe visibility was calculated for the 15 PCF interferometers and they were in the range of 62.16-89.39%. Since we used the same type of PCF (Blaze Photonics, LMA-10) and the propagation constant deviation involved in the interference could be assumed the same; thus, based on the Figure 5 (f), the fringe period of the interferometer was almost inversely proportional to the interferometer length (R 2 = 0.996995). In addition, we compared the measured fringe period and the one from a sine curve fitting for each interferometer. Figure 6 (a,b) shows the transmission spectra of measured data and sinusoidal wave using a PCF interferometer with length = 1.34 cm and 3.50 cm, respectively. The sinusoidal curve is given by y = A o + A sin (ωx -φ); where y is the transmission loss, x represents the wavelength, and other parameters are the regression coefficients. Figure 7 (a) illustrates 
PCF Interferometer Characteristics
The box plot (or whisker graph) is a statistical way of graphically depicting groups of numerical data through their five-number summaries: maximum, minimum, median, upper quartile, and lower quartile. In addition, it could be even used to explore outliers [21] . 
Refractive Index Measurement
The ability of the PCF interferometer to detect changes in the surrounding RI was studied. The control of surrounding RI was through the use of sucrose solutions with various concentrations. Based on Figure 13 (a-c), the five different lengths of PCF interferometers were evaluated and the effect of sensor length was discussed about the sensor sensitivity (nm/RIU) and sensitivity variation (sensitivity range). The PCF interferometers with sensing length 3.50 cm and 5.00 cm had both better sensor sensitivity and smaller sensitivity variation than those of other PCF interferometers. Thus, the 3.00-cm and 5.00-cm PCF interferometers possessed comparable performance for the resolution in the range of 1.62 × 10 −4 -8.88 × 10 −4 RIU and 1.02 × 10 −4 -9.04 × 10 −4 RIU, respectively. In addition, the 3.00-cm and 5.00-cm PCF interferometers exhibited relatively small sensitivity variation (less than 5.71 nm/RIU and 5.05 nm/RIU, respectively). However, if the 5.00-cm PCF interferometer is used, the bending effect and package technique should be noticed. 
Conclusions
We have successfully demonstrated the feasibility of fabricating a class of highly sensitive refractive-index sensor based on the PCF interferometer that was realized by fusion splicing a short section of PCF between two standard single mode fibers (Corning SMF-28) using a Fitel-S175 splicer. The interferometer was completed by making two collapsing points in a PCF at localized regions with a fusion splicer. The high uniform interference fringes over the available spectral range (about 1,400-1,675 nm) could be obtained. The realization of the sensor is through the measurement of the transmission spectrum of the PCF interferometer. A red shift in the resonance wavelength was observed with the increase of RI. We demonstrate the sensor resolution for different lengths of PCF interferometers by transmission spectrum interrogation, and the findings indicating that a resolution as low as 1.62 × 10 −4 -8.88 × 10 −4 RIU or 1.02 × 10 −4 -9.04 × 10 −4 RIU (for sensing length = 3.50 cm or 5.00 cm, respectively) can be achieved for refractive indices in the range of 1.333 to 1.422. The 3.00-cm and 5.00-cm PCF interferometers possessed comparable performance for the resolution in the 

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