3.1 The adjustment principle and experiment
The experimental scheme for micro-cavity size adjustment is illustrated in Fig. 5. The laser beam focusing size on the graphite surface is determined by the distance d between graphite surface and the focus plane as in Fig. 5, and as micro-plasma processing scans going on, the wider beam size probably produce bigger micro-cavity size. Based on the above principle, the distance from 0 to 600 µm are fixed to fabricate FMZI samples. The fabricated samples are observed by optical microscope, meanwhile the open cavity length and the MZI length are measured as shown in Fig. 6. It should be noted that two red laser are coupled into the FMZI sample, as these propagating red lasers reach to the surface of fabricated micro-cavity in the fiber core, obvious red point can be seen due to the light scattering on the surface, thus, the distance between these two red points can be regarded as MZI length approximately.
As shown in Fig. 6(a-d), the size of crater-like structure in fiber increases as d distance increases, meanwhile the open cavity length and MZI length also increase, furthermore, MZI length is almost equal to the half of the open cavity length. It should be noted that the open cavity length was measured as 86.0 µm in Fig. 6(d), but was corrected to 101 µm in the same fabrication condition as illustrated in Fig. 2, and the red point is substituted by the blue star in Fig. 6(e). This small discrepancy probably resulted from the different observed direction of the samples. Furthermore, the linearities of the fitted experimental results are quite good in Fig. 6(e). The linear dependence of open cavity length on d distance is easily explained by the discussion based on Fig. 5. With regard to the linear dependence of MZI length on d distance, we think that as the size of micro-cavity mainly depends on the open cavity, and the open cavity is determined by the relative distance d between the graphite surface and focus plane. So the MZI length is linear related to d distance.
As discussed above, the MZI lengths of FMZI are able to be adjusted only by the movement of Z position, meanwhile the fabrication time is not changed, which is superior to the femtosecond laser fabrication system, where the longer MZI length needs longer fabrication time. In addition, in our experiment, the longer MZI length sample was tried to fabricate, however as the laser power is limited (20W) and the laser beam power is also reduced by the aperture in the optical system, the laser beam power of 14.5 W after aperture is maximum, so longer MZI length sample is not obtained in our case, but we believe that longer MZI length samples are possible with higher power nanosecond laser.
3.2 The refractive index sensing
In order to confirm the success FMZI fabrication and investigate the sensitivity of samples with different MZI lengths, these samples are utilized to measure the refractive index of ethanol water solution as in our previous work (Shuhao et al. 2021). For the sample with 25.7 µm MZI length, the transmission spectrum shift is confirmed, but the transmission spectrum dips of solution with refractive index close to water are not shown, thus its transmission spectra and the dependence of resonant wavelength on refractive index is not illustrated in Fig. 7. The experimental and analytical results of other 3 samples with MZI length from 31.4 to 49.2 µm are shown in Fig. 7.
For each FMZI sample, the resonant wavelength of transmission spectrum blue shifts as the refractive index of solution increase as illustrated in Fig. 7(a, c, d), meanwhile, the dependence of resonant wavelength on refractive index shows quite good linearity, which are in good agreement with our previous work (Shuhao et al. 2021). In addition, the absolute refractive index sensitivities are more than 10000 nm/RIU, which is comparable with the femtosecond laser fabricated ones (Zhao et al. 2019). In comparison with each other, firstly, for the longer MZI length sample, the free spectrum range becomes shorter and almost one whole period is shown in Fig. 7(d), which is explained by the Eq. (3) in Ref. (Shuhao et al. 2021). Secondly, the sensitivity increases as MZI length increases, which seems different with the previous work (Shuhao et al. 2021). However, firstly, the experimental tested refractive index range for different samples are different, the longer MZI length sample tests bigger refractive index range and the absolute refractive index is bigger for more resonant wavelengths are shown in the definite spectrum range (1250–1650 nm); secondly, for the solution with same refractive index, its resonant wavelengths of transmission spectra located at different wavelengths, in particular, in our case, the transmission spectrum of the solution with refractive index 1.336, the resonant wavelengths located at around 1350, 1530 and 1650 nm. From the Eq. (2)&(5) in Ref. (Shuhao et al. 2021), the sensitivity can also be expressed as: \({S}_{RI}=-{\lambda }_{m}/{\varDelta n}_{eff}\). The bigger absolute refractive index results in less \({\varDelta n}_{eff}\), the longer located resonant wavelength results in bigger \({\lambda }_{m}\), these both lead to higher absolute sensitivity. Unfortunately, the resonant wavelength location is not definitely determined and possesses random property; meanwhile, for the definite range of refractive index solution, \({\varDelta n}_{eff}\) should be same. Finally, the sensitivity is not definite related with MZI length as discussed in Ref. (Shuhao et al. 2021).