2.3.3. Manufacture

Figure 5 shows the MZI waist-enlarged bitaper before etching, and Figure 8 shows the bitaper after etching. The 40% hydrofluoric acid solution was directly dropped on the optical fiber sensing arm and etched for 20 min. The diameter of the sensing arm of the 40/125 multimode fiber is reduced to 85 µm. The diameter of the fiber bitaper is reduced from 152 µm to 112 µm, and the length of the waist-enlarged bitaper shows little change. *Micromachines* **2022**, *13*, x FOR PEER REVIEW 8 of 19

**Figure 8. Figure 8.**  The etched waist-enlarged bitaper in ESMBMS MZI. The etched waist-enlarged bitaper in ESMBMS MZI.

### **3. Spectral Pattern Analysis**

There may be multiple modes in the fiber, and due to the different propagation constants between these modes, the optical path difference between the modes will appear under the same transmission length. When these modes are coupled, interference between

the modes occurs. Through fabrication experiments, it is found that the position of the waist-enlarged bitaper has little effect on the SMBMS and ESMBMS spectra, so the position of the waist-enlarged bitaper is not distinguished when displaying the spectra. Figure 9 shows the transmission spectra of the MZIs, which show that the density of the interference fringes change due to the addition of waist-enlarged bitaper and corrosion. waist-enlarged bitaper has little effect on the SMBMS and ESMBMS spectra, so the position of the waist-enlarged bitaper is not distinguished when displaying the spectra. Figure 9 shows the transmission spectra of the MZIs, which show that the density of the interference fringes change due to the addition of waist-enlarged bitaper and corrosion.

There may be multiple modes in the fiber, and due to the different propagation constants between these modes, the optical path difference between the modes will appear under the same transmission length. When these modes are coupled, interference between the modes occurs. Through fabrication experiments, it is found that the position of the

*Micromachines* **2022**, *13*, x FOR PEER REVIEW 9 of 19

**3. Spectral Pattern Analysis** 

**Figure 9.** Measured transmission spectra with different L. **Figure 9.** Measured transmission spectra with different L.

According to the transmission spectrum, the higher-order mode is found, and the frequency spectrum obtained after Fourier transform is shown in Figure 10. The main peak amplitudes are located at 0.0199164 nm−<sup>1</sup> , 0.0300104 nm−<sup>1</sup> , and 0.0412538 nm−<sup>1</sup> . *Micromachines* **2022**, *13*, x FOR PEER REVIEW 10 of 19

**Figure 10.** Spatial frequency spectra of the MZIs with different lengths. **Figure 10.** Spatial frequency spectra of the MZIs with different lengths.

Using the Taylor expansion to expand the wavelength the phase

φ

φ <sup>Δ</sup>*neff* <sup>⋅</sup> *<sup>L</sup>* <sup>Δ</sup> <sup>≈</sup> <sup>0</sup> <sup>2</sup>

Due to the MZIs spectra corresponding to mathematical cosine patterns, the follow-

cos cos(2 ) Δ= Δ

2 1

lengths of the MZIs are all 20 mm. Through the Fourier transform, the spatial frequency *ξ* are 0.0199164 nm−1, 0.0300104 nm−1, and 0.0412538 nm−1. Therefore, the parameter Δneff calculated from Equation (15) are 0.002392458, 0.003604999, and 0.004955613. In other words, as the sensing arm is spliced with waist-enlarged bitaper and etched, higher-order modes are excited, affecting the optical path of transmitted light in the optical fiber core and cladding. Subsequently, the refractive index responses of the three sensors were

 *n L* λ

Considering the modal dispersion, we established the relationship between Δneff and

Figure 11 is a schematic diagram of a refractive index sensing system. The measurement system consisted of a broadband light source (BBS, Lightcomm, Shenzhen, China, ASE-CL), a spectrum analyzer (OSA, Anritsu, Kitakyushu, Japan, MS9740A), and a vessel for placing the refractive index solution. The spectrometer resolution was set to 0.02 nm,

πξ

<sup>0</sup> is the initial phase, and we assume it is equal to 0, the spatial frequency *ξ* [20]

*eff*

λ

0 is a initial phase, and

λ

λ

λ

π

2 -

φ

φ

ξ

*4.1. The Refractive Index Sensitivity Response Characteristics of SMS MZI* 

φ

λ

(8)

is around 1550 nm, and the

(7)

= Δ⋅ (9)

is formulated as:

is the wavelength

is the wavelength difference,

different modes, based on OptiFiber. The wavelength

where Δ

If φ

is:

λ

ing equation is obtained:

measured experimentally.

**4. Experiment** 

of spectral valley.

Using the Taylor expansion to expand the wavelength the phase *φ* is formulated as:

$$
\phi \approx \phi\_0 - \frac{2\pi\Delta\lambda}{\lambda^2} \Delta n\_{eff} \cdot L \tag{13}
$$

where ∆*λ* is the wavelength difference, *φ*<sup>0</sup> is a initial phase, and *λ* is the wavelength of spectral valley.

Due to the MZIs spectra corresponding to mathematical cosine patterns, the following equation is obtained:

$$\cos \Delta \phi = \cos(2\pi \xi \Delta \lambda) \tag{14}$$

If *φ*<sup>0</sup> is the initial phase, and we assume it is equal to 0, the spatial frequency *ξ* [20] is:

$$\mathcal{L} = \frac{1}{\lambda^2} \Delta n\_{eff} \cdot L \tag{15}$$

Considering the modal dispersion, we established the relationship between ∆neff and different modes, based on OptiFiber. The wavelength *λ* is around 1550 nm, and the lengths of the MZIs are all 20 mm. Through the Fourier transform, the spatial frequency *ξ* are 0.0199164 nm−<sup>1</sup> , 0.0300104 nm−<sup>1</sup> , and 0.0412538 nm−<sup>1</sup> . Therefore, the parameter ∆neff calculated from Equation (15) are 0.002392458, 0.003604999, and 0.004955613. In other words, as the sensing arm is spliced with waist-enlarged bitaper and etched, higher-order modes are excited, affecting the optical path of transmitted light in the optical fiber core and cladding. Subsequently, the refractive index responses of the three sensors were measured experimentally.

### **4. Experiment**

### *4.1. The Refractive Index Sensitivity Response Characteristics of SMS MZI*

Figure 11 is a schematic diagram of a refractive index sensing system. The measurement system consisted of a broadband light source (BBS, Lightcomm, Shenzhen, China, ASE-CL), a spectrum analyzer (OSA, Anritsu, Kitakyushu, Japan, MS9740A), and a vessel for placing the refractive index solution. The spectrometer resolution was set to 0.02 nm, and the bandwidth of the BBS was 80 nm. In the experiment, sucrose solutions with different concentrations were used as refractive index samples, and their refractive indices are 1.351, 1.369, 1.379, 1.387, 1.394, and 1.402 after being tested by Abbe's refractive index detector. The MZI was uniformly soaked in a sucrose solution of each refractive index for 5 min at a stable room temperature of 23 ◦C. The wavelength shift was observed and the data were recorded. *Micromachines* **2022**, *13*, x FOR PEER REVIEW 11 of 19 and the bandwidth of the BBS was 80 nm. In the experiment, sucrose solutions with different concentrations were used as refractive index samples, and their refractive indices are 1.351, 1.369, 1.379, 1.387, 1.394, and 1.402 after being tested by Abbe's refractive index detector. The MZI was uniformly soaked in a sucrose solution of each refractive index for 5 min at a stable room temperature of 23 °C. The wavelength shift was observed and the data were recorded.

**Figure 11. Figure 11.**  Refractive index sensing experimental device schematic diagram. Refractive index sensing experimental device schematic diagram.

The length of the sensing arm of the SMS MZI is about 20 mm. From Figure 12, we see that there is only one wavelength valley in the spectrum of the SMS MZI. We monitored the wavelength of the valley, and Figure 13 shows that the refractive index sensitivity of SMS MZI is 57.623 nm/RIU, and the linearity of the refractive index sensitivity response characteristic is 0.999. Therefore, as the refractive index sensitivity is a positive number, it is seen that the wavelength shifts to the long-wavelength direction; however, the refractive index sensitivity of SMS MZI is too low.

the refractive index sensitivity of SMS MZI is too low.

The length of the sensing arm of the SMS MZI is about 20 mm. From Figure 12, we

see that there is only one wavelength valley in the spectrum of the SMS MZI. We monitored the wavelength of the valley, and Figure 13 shows that the refractive index sensitivity of SMS MZI is 57.623 nm/RIU, and the linearity of the refractive index sensitivity response characteristic is 0.999. Therefore, as the refractive index sensitivity is a positive number, it is seen that the wavelength shifts to the long-wavelength direction; however,

**Figure 12.** Spectra of SMS MZI at different refractive indices. **Figure 12.** Spectra of SMS MZI at different refractive indices.

**Figure 13.** The sensitivity response characteristic diagram of SMS MZI. **Figure 13.** The sensitivity response characteristic diagram of SMS MZI.

### *4.2. The Refractive Index Sensitivity Response Characteristics of SMBMS MZI*

In view of the low refractive index sensitivity of SMS MZI, an improvement was made on the basis of SMS MZI, by melting a waist-enlarged bitaper in the middle of the sensing arm. The photo of the waist-enlarged bitaper is shown in Figure 5. The SMBMS MZI was fabricated, in which the length of the sensing arm of the SMBMS sensor is about 20 mm, the experimental temperature is 23 ◦C, and the refractive index range is from 1.351 RIU to 1.402 RIU. The sensing arms were uniformly soaked in a sucrose solution for each refractive index for 5 min. The wavelength drift was observed and the data were recorded, shown in Figure 14. At the same time, we changed the position of the waist-enlarged bitaper, and found that the position of the waist-enlarged bitaper had little effect on the spectral shape. Subsequently, we performed refractive index experiments on the sensor with the waist-enlarged bitaper position at one-third of the sensing arm, shown in Figure 15.

*4.2. The Refractive Index Sensitivity Response Characteristics of SMBMS MZI* 

In view of the low refractive index sensitivity of SMS MZI, an improvement was made on the basis of SMS MZI, by melting a waist-enlarged bitaper in the middle of the sensing arm. The photo of the waist-enlarged bitaper is shown in Figure 5. The SMBMS MZI was fabricated, in which the length of the sensing arm of the SMBMS sensor is about 20 mm, the experimental temperature is 23 °C, and the refractive index range is from 1.351 RIU to 1.402 RIU. The sensing arms were uniformly soaked in a sucrose solution for each refractive index for 5 min. The wavelength drift was observed and the data were recorded, shown in Figure 14. At the same time, we changed the position of the waist-enlarged bitaper, and found that the position of the waist-enlarged bitaper had little effect on the spectral shape. Subsequently, we performed refractive index experiments on the sensor with the waist-enlarged bitaper position at one-third of the sensing arm, shown in Figure 15.

**Figure 14.** Spectra of SMBMS MZI(1/2L) at different refractive indices. **Figure 14.** Spectra of SMBMS MZI(1/2L) at different refractive indices.

**Figure 15.** Spectra of SMBMS MZI(1/3L) with the position of the bitaper set to one third of the sensing arm at different refractive indices. **Figure 15.** Spectra of SMBMS MZI(1/3L) with the position of the bitaper set to one third of the sensing arm at different refractive indices.

From Figures 14 and 15, we see that there are two valleys within the spectrum of SMBMS MZI. In order to facilitate the comparison with SMS MZI, the valley of the wavelength around 1536 nm was selected for monitoring. Figure 16 shows that the refractive index sensitivity of the SMBMS MZI is 61.607 nm/RIU, and the linearity of the refractive index sensitivity response is 0.999. It can be seen that the wavelength still drifts in the long-wavelength direction, and the refractive index sensitivity of SMBMS MZI improves, compared to SMS MZI. Overall, the sensitivity improvement effect is still not obvious. The reason for this is that the diameter of the sensing arm was relatively thick, and the coupling effect with the refractive index solution was not obvious.

pling effect with the refractive index solution was not obvious.

**Figure 16.** The sensitivity response characteristic diagram of SMBMS MZI.

### **Figure 16.** The sensitivity response characteristic diagram of SMBMS MZI. *4.3. The Refractive Index Sensitivity Response Characteristics of ESMBMS MZI*

*4.3. The Refractive Index Sensitivity Response Characteristics of ESMBMS MZI*  Since the refractive index sensitivity of SMBMS MZI was still low, improvements were made on the basis of SMBMS MZI. The method used was to corrode the sensing arm of SMBMS MZI with hydrofluoric acid for 20 min. The waist-enlarged bitaper is shown in Figure 8. The sensing arm of the fabricated ESMBMS MZI is about 20 mm long, and the fiber diameter is reduced by 40 µm after 20 min of hydrofluoric acid etching at 23 °C. The refractive index of sucrose solution ranges from 1.351 RIU to 1.402 RIU. The sensing arm was immersed in the sucrose solution of each refractive index for 5 min to observe the wavelength and record the data, shown in Figures 17 and 18. Since the refractive index sensitivity of SMBMS MZI was still low, improvements were made on the basis of SMBMS MZI. The method used was to corrode the sensing arm of SMBMS MZI with hydrofluoric acid for 20 min. The waist-enlarged bitaper is shown in Figure 8. The sensing arm of the fabricated ESMBMS MZI is about 20 mm long, and the fiber diameter is reduced by 40 µm after 20 min of hydrofluoric acid etching at 23 ◦C. The refractive index of sucrose solution ranges from 1.351 RIU to 1.402 RIU. The sensing arm was immersed in the sucrose solution of each refractive index for 5 min to observe the wavelength and record the data, shown in Figures 17 and 18. *Micromachines* **2022**, *13*, x FOR PEER REVIEW 17 of 19

From Figures 14 and 15, we see that there are two valleys within the spectrum of SMBMS MZI. In order to facilitate the comparison with SMS MZI, the valley of the wavelength around 1536 nm was selected for monitoring. Figure 16 shows that the refractive index sensitivity of the SMBMS MZI is 61.607 nm/RIU, and the linearity of the refractive index sensitivity response is 0.999. It can be seen that the wavelength still drifts in the long-wavelength direction, and the refractive index sensitivity of SMBMS MZI improves, compared to SMS MZI. Overall, the sensitivity improvement effect is still not obvious. The reason for this is that the diameter of the sensing arm was relatively thick, and the cou-

**Figure 17.** Spectra of ESMBMS MZI(1/2L) at different refractive indices. **Figure 17.** Spectra of ESMBMS MZI(1/2L) at different refractive indices.

**Figure 18.** Spectra of ESMBMS MZI(1/3L) with the position of the bitaper set to one third of the sensing arm at different refractive indices. **Figure 18.** Spectra of ESMBMS MZI(1/3L) with the position of the bitaper set to one third of the sensing arm at different refractive indices.

It can be seen from Figures 17 and 18 that for monitoring the valley with the center wavelength around 1545 nm, the refractive index sensitivity of ESMBMS MZIs is 287.65 nm/RIU, and the linearity of the refractive index sensitivity response is 0.999, as shown in Figure 19. Therefore, it is demonstrated that the wavelength still drifts to the long-wavelength direction, and the refractive index sensitivity of ESMBMS MZI increases almost four-fold compared to SMBMS MZI. Overall, the advantages of ESMBMS MZI refractive index sensitivity response characteristics are obvious. The reason is that the sensing arm cladding of the SMBMS structure was etched with hydrofluoric acid to reduce its diameter, which greatly improved the sensitive response characteristics. Therefore, the refractive index sensitivity of ESMBMS MZI is obviously improved. It can be seen from Figures 17 and 18 that for monitoring the valley with the center wavelength around 1545 nm, the refractive index sensitivity of ESMBMS MZIs is 287.65 nm/RIU, and the linearity of the refractive index sensitivity response is 0.999, as shown in Figure 19. Therefore, it is demonstrated that the wavelength still drifts to the long-wavelength direction, and the refractive index sensitivity of ESMBMS MZI increases almost four-fold compared to SMBMS MZI. Overall, the advantages of ESMBMS MZI refractive index sensitivity response characteristics are obvious. The reason is that the sensing arm cladding of the SMBMS structure was etched with hydrofluoric acid to reduce its diameter, which greatly improved the sensitive response characteristics. Therefore, the refractive index sensitivity of ESMBMS MZI is obviously improved.

*Micromachines* **2022**, *13*, x FOR PEER REVIEW 19 of 19

**Figure 19.** The sensitivity response characteristic diagram of ESMBMS MZI. **Figure 19.** The sensitivity response characteristic diagram of ESMBMS MZI.
