Optical fiber sensor technology has been extensively applied in gas pressure sensing in the field of industrial and environmental safety monitoring on account of its high sensitivity, compact structure, and immunity to electromagnetic interference. Compared with long-period fiber gratings and anti-resonance waveguides, optical fiber sensors based on the vernier effect generally have greater advantages in terms of sensitivity. The vernier effect is an effective method for amplifying interferometer sensitivity, which is well-known in optical fiber sensing. However, as the harmonic order j increases, vernier spectra deteriorate, namely that the contrast of the external envelope decreases, and the inner envelope disappears. The objective of this work is to generalize the higher-order vernier effect and obtain high sensitivity through experimental exploration and theoretical analysis. In addition, we intend to explore the reasons for the decrease in external envelope contrast and the loss of internal envelopes that affect spectral contrast. We expect to contribute to the extensive application of the high-order harmonic vernier effect and high-sensitivity sensor design.

Firstly, we theoretically simulate the higher-order vernier spectrum for j=1, 2, 3, 4. Then, we fabricate four parallel structures of the Fabry-Pérot interferometers experimentally and study the corresponding vernier spectra. After that, we investigate the effect of the difference in light intensity between the sensing cavity and the reference cavity on the vernier spectrum by changing the light intensity difference between the two cavities. In addition, we analyze various parameters that affect the vernier magnification factor and design a highly sensitive fiber-based gas pressure sensor.

On the basis of a parallel Fabry-Pérot interferometer, this paper compares the theoretical simulations (Fig. 2) and the experimental results (Fig. 3) of vernier spectra for j=1, 2, 3, 4. The comparison shows that they are consistent, which indicates the vernier effect is valid in the experiment. After that, we simulate the spectra corresponding to different light intensities of the sensing cavity and the reference cavity. It is found that with the increase in the light intensity difference between the two cavities, the contrast of the external envelope decreases, and the internal envelope disappears (Fig. 5). Then, we fundamentally explain the deterioration of the vernier spectrum when the higher-order harmonic vernier effect is applied in the experiment (Fig. 6). In addition, the factors affecting the vernier magnification are discussed from the aspects of a higher value of j and a lower detuning ratio. After that, we put forward reasonable suggestions for obtaining higher magnification when applying the vernier effect in gas pressure sensing. Furthermore, a sample corresponding to the first-order harmonic vernier effect is produced for the gas pressure test. At room temperature, it enjoys gas pressure sensitivity of 152 pm/kPa, a corresponding magnification factor of 35.3, and linearity of 99% in the range of 10-190 kPa (Fig. 4).

This paper studies the higher-order harmonic vernier effect and proposes a method to improve the interference fringe contrast for the external vernier envelope, which is verified by experiments. The reason for the reduction in the vernier spectrum contrast is the reduction in the imbalance of light intensity between the sensing and the reference cavities. The application demonstrates that with the increase in the light intensity difference between the two cavities, the vernier spectrum becomes more susceptible to the quality or noise of the light source. This leads to weaker visibility of the envelope for higher harmonic orders. In addition, we analyze various experimental parameters so as to obtain high sensitivity and demonstrate a parallel Fabry-Pérot interferometer with gas pressure sensitivity of 152 pm/kPa, linearity of 99%, and a magnification factor of 35.3 in the range of 10-190 kPa.