In recent years, vernier effect has attracted much attention in the field of optical fiber sensing due to its sensitivity amplification effect, which has been used to measure gas pressure, temperature, strain, refractive index, etc. The configurations used to introduce optical vernier effects fall into two broad categories. The first type consists of configurations containing a single type of interferometer. The second type consists of a hybrid configuration in which two different types of interferometers are combined. The optical vernier effect can be applied to different types of interference structures, such as Mach-Zehnder interferometers (MZIs), Fabry-Perot interferometers (FPIs) and Sagnac interferometers (SIs), etc. Since the double-helix micro-nano fiber coupler (DHMC) is highly birefringent, the superposition of two orthogonal polarization interference spectra in x direction and y direction with slightly different interference periods can form the vernier envelope. However, how to get the DHMC that can produce the vernier envelope spectrum? What’s more, when the optical vernier effect of the DHMC is applied to temperature, strain and refractive index sensing, whether the sensing characteristics are consistent or not is a problem that needs to be considered. In the present study, the internal mechanism and spectral characteristics of the vernier effect of the DHMC are studied theoretically. DHMCs with different diameters are fabricated, and experiments of the strain, temperature and refractive index sensing are carried out. We hope that the above results have a good guiding significance for the preparation of DHMC and the applications of refractive index, temperature and strain sensing.
Theoretical and experimental analysis methods are employed in this paper. Firstly, COMSOL software was used to establish the DHMC simulation model (Fig.1). Then, by setting parameters such as wavelength range, diameter and refractive index, the effective refractive indices of odd and even modes in x- and y-polarization states were obtained, and then the simulated vernier spectra were obtained through Eqs. (5) and (6). Secondly, two standard single-mode fibers (SMF-28) were used to fabricate DHMC, for which the optical fibers with the coating layer stripped off were twisted in parallel direction to obtain helical structures with different turns. The optical fiber pulling machine (OB-612) was used to pull the DHMC, and the broadband light source (1250-1650 nm) and optical spectrum analyzer (OSA) were connected at both ends of the optical fiber. The spectrum of DHMC was observed in real time during the pulling process, so as to estimate the diameter and waist length of the prepared DHMC online. Thirdly, we used the fabricated DHMC to conduct the strain, temperature and refractive index sensing experiments. The spectrum evolutions of the DHMC under different strain, temperature and surrounding refractive index were recorded, respectively. Fast Fourier transform (FFT) and bandpass filtering method were used to extract the characteristic interference spectra, thus obtaining the spectra in x- and y-polarization states, and then the vernier spectrum was obtained by the superposition of the interference of the extracted x- and y-polarization spectra. At last, the sensitivities of the strain, temperature and refractive index of DHMC for x polarization, y polarization and vernier spectrum were analyzed.
The free spectral range (FSR) of the vernier spectrum of the DHMC is related to the waist length, wavelength and the difference of effective refractive index between x- and y-polarization states. The waist length L plays a major role in FSR, and the increase of L leads to the decrease of FSR (Fig.3). It can be concluded that when L is fixed and the surrounding refractive index (SRI) is 1, with the increase of wavelength, the absolute value of the effective refractive index difference increases faster than the increase of wavelength square, and the envelope FSR also decreases [Fig.3(a)]. When the SRI is larger than 1.3310, the results are the opposite, and the envelope FSR increases accordingly [Fig.3(b)]. Under the same SRI of 1.3328, the odd-even refractive index difference between x- and y-polarization states decreases and FSR increases with the increase in the diameter of DHMC. In the liquid environment (SRI is 1.3328), when the diameter is 6 μm, only a complete vernier envelope can be observed in the wavelength range of 1250-1650 nm (Fig. 4).
In general, the axial strain sensitivity of vernier spectrum of the DHMC is lower than those of x- and y-polarization spectra (Fig.6). Similarly, the temperature sensitivities of DHMC in x- and y-polarization spectra are higher than that of vernier spectrum of DHMC (Fig.7). Conversely, the refractive index sensitivity of vernier spectrum of the DHMC is larger than those of x- and y-polarization spectra (Fig.9
DHMC has the advantages of high sensitivity, compact structure, easy preparation and low cost. In this work, the internal mechanism and spectral characteristics of the vernier effect of DHMC are studied in detail, and its sensing characteristics of refractive index, temperature and strain are analyzed. The simulation results show that the waist length of DHMC plays a major role in the FSR of its vernier envelope, and the FSR decreases with the increase of the waist length. In the process of DHMC preparation, the waist length and diameter of DHMC can be estimated by monitoring the number of envelopes in the wavelength range of 1250-1650 nm with the OSA online. The vernier spectrum formed by the superposition of the interference spectra of x- and y-polarization states of DHMC is compared with the interference spectra of single x- and y-polarization states. The vernier spectrum shows a weakened optical vernier effect for strain and temperature sensing, while it shows an enhanced optical vernier effect for refractive index sensing. The conclusion of this paper has a good guiding significance for the preparation of DHMC sensor and its application in the sensing field.
