Objective Refractive index ( RI) is one of the most important parameters to guide light and control light-matter interaction. Recently optical fiber RI sensors have attracted great attention in various areas such as physics, photonics, chemistry, biology, and environment monitoring due to their remote on-line sensing. The optical Vernier effect produced by the cascade of two interferometers with close free spectral ranges (FSRs) has been developed to improve the sensitivity of RI sensors. The wavelength shift of the spectral envelope of the cascaded sensors is much larger than that of the unit sensing interferometer when the environmental refractive index is changed. FSRs of the two unit interferometers, determined by the interferometer's cavity lengths, should be carefully designed and calibrated to improve sensitization fold as much as possible. Additionally, both of the two unit interferometers should have high fringe visibility and stable interference components for obtaining obvious cascaded spectral envelopes. Till now, the most reported unit interferometer for Vernier sensitization is the Fabry-Perot interferometer (FPI). Unfortunately, the fabrication of an FPI interferometer requires complicated fiber alignment and fine cavity length adjustment, which leads to poor reproducibility in the sensor fabrication. Michelson interferometer (MI) can also be employed as a unit interferometer for Vernier sensitization. Those traditional MI unit interferometers usually include multi-mode fiber, twin core fiber, and coreless fiber. In the aforementioned fibers, multiple cladding modes are inevitably stimulated and multiple modal interference are involved in the spectrum of the cascaded sensor. As a result, interference component analysis of the spectrum is complex. In addition, controllable stimulation of these modes is difficult. Few-mode fiber (FMF) could only support the transmission of limited modes. The decreased mode quantity leads to a simple interference component, which is beneficial to the sensor cascade. The interference component in an FMF-based MI is stable since all the modes in FMF are confined in the fiber core and immune to environmental refractive index changes. Meanwhile, MI could be naturally formed by the two end faces of a single FMF, without the necessity for fiber alignment and fine cavity length adjustment. Thus, FMF-based MI is a good candidate for reference interferometers in Vernier sensors. In this study, an FMF-based MI-FPI Vernier sensor has been developed for RI sensitization. FPI acts as a sensing interferometer because of its open cavity, and MI made from an FMF serves as the reference interferometer due to its simple interference component and stable interference spectrum. Due to FMF and MI, the dual cavity mismatching problem and poor controllability of traditional dual FPI sensors could be solved. Methods For the proposed FMF-based MI-FPI sensor, MI is implemented by fusing an incident single-mode fiber (SMF) with an FMF in a certain core-offset, and FPI is formed by the cavity sandwiched between the free end face of the FMF and one of the end face of an another SMF. Both FMF and the two SMFs are fixed on a slide by UV glue. The interference spectrum of the FMF-based MI is mainly affected by two structural parameters including the offset between incident SMF and FMF, and the FMF length. Offset fusion will induce asymmetrical optical mode field distribution in fiber and excite the specific mode. Thus, the influence of core-offset distance between SMF and FMF on mode excitation efficiency, and the effect of FMF length on the Vernier sensitization effect are simulated. Moreover, a virtual MI is developed to analyze the Vernier enhancement effect on unit FPI to provide theoretical guidance for the FMF length selection. The interference component in the cascaded structure is analyzed by taking a fast Fourier transform (FFT) of the experimental spectrum. Due to FFT, the spatial frequency of a certain interference component can be ascertained, and based on simulation data the cascaded MI-FPI sensor is fabricated. The sensor fabrication is as follows. Firstly, an FMF-based MI with the FMF length of 32. 4 cm and the core- offset of 3 mu m is fabricated. Then, an FPI is formed by gradually drifting another SMF to the end face of the FMF. Both FMF and the two SMFs are fixed on a slide by UV glue. The interference spectrum of the fabricated MI-FPI sensor is recorded by an optical spectrum analyzer (YOKOGAWA, AQ6370) with a resolution of 0. 02 nm. A super-luminescent light-emitting diode (SLED) with a wavelength range from 1500-1600 nm is adopted as the light resource. For RI measurement, NaCl solutions with different RI in a range of 1. 3384-1. 3412 are employed and the RI of each NaCl solution is determined by an Abbe refractometer. Results and Discussions Refractive index response sensitivity of the cascaded MI-FPI sensor is measured to be 12466. 956 nm/RIU in the range of 1. 3384-1. 3412, which is 12. 29 times enhanced over the FPI sensor without MI cascade. The amplification limit and the influence factors are analyzed, and the sensitization limit of the sensor is determined by the ratio of xi(S)/|xi(R) -xi(S)|. Thus the sensor sensitivity could be further improved in the following two ways. One is to adopt a light source with a wider spectrum to decrease |xi(R)-xi(S)|, and the other is to raise the FPI cavity to increase xi(S). The experimentally measured magnification factor slightly deviates from the theoretical one. The possible reasons are discussed. Firstly, followed by inverse Fourier transform, a frequency filtering method is utilized, which is suitable for analyzing cosine signals. However, since the spectrum of the experimental MI is not a regular cosine spectrum, the FSR at short wavelengths is smaller than that at long wavelengths, leading to a deviation between the experimentally measured magnification factor and the theoretical one. Secondly, during the experiment, there are small errors in the length control of FMF and FPI, which is the cavity length of MI (L-R) and FPI (L-S), also resulting in certain deviation of the magnification factor. Conclusions A refractive index Vernier sensor based on an FMF-MI is developed. The sensor consists of an MI serving as the reference unit interferometer and an FPI serving as the sensing unit interferometer. Experimental results show that the MI-FPI sensor has a refractive index sensitivity of 12466. 956 nm/RIU in the range of 1. 3384-1. 3412, which is 12. 29 times improved compared with the FPI sensor without MI cascade. The proposed MI-FPI sensor is characterized by high sensitivity, simple fabrication, and sound reproducibility. Therefore, it can be a suitable choice for various applications in biological and chemical fields. Furthermore, the FMF-based MI has the unique advantages of simple structure, high extinction ratio, excellent stability, and mode controllability, which is suitable to be employed as a reference interferometer cascaded with other interferometers to achieve the Vernier effect.
