Simultaneous sensing of strain and temperature based on the inline-MZI embedded point-shaped taper structure with low crosstalk

Xiao-Peng Han; Yun-Dong Zhang; Yun-Dong Zhang; Wuliji Hasi; Wuliji Hasi; Si-Yu Lin; Fan Wang; Yuan Wei; Zhenyu Zhao

doi:10.1364/OE.492550

1. Introduction

Fiber optic sensing technology has become more advanced and mature in domestic and international research with its advantages of high sensitivity, anti-electromagnetic interference, electrical insulation, corrosion resistance, and fast response [1,2]. The Mach-Zehnder interference (MZI) principle is widely used in optical interferometric sensing tests because of its simple and stable characteristics among various interference principles. According to the MZI principle, the single physical parameters tested can be temperature [3–6], refractive index [7–13], liquid level [14,15], strain [16], and curvature [17,18]. However, most MZI-based sensors have multi-parameter responses. It is difficult to measure individual parameters accurately, so simultaneous sensing of strain and temperature is one of the ways to achieve precise measurements.

In recent years, various fiber optic structures have been used to measure temperature and strain simultaneously. For example, cascaded fiber-optic taper-type systems [19,20]. Dong [19] connected four up-tapers in series to achieve simultaneous temperature and strain measurements with sensitivities of 112 pm/°C and 0.4 pm/µε, respectively. The construction of MZI structures based on the principle of core mismatch is also an effective method [21,22]. Xing [21] cascaded multimode fiber and polarization-maintaining fiber (PMF) to obtain more excellent interference fringe contrast. The temperature and strain sensitivities of the sensor are 1.27 pm/µε and 49 pm/°C, respectively. Huang [23] embedded a microcavity structure in an optical fiber as an MZI beam splitter for its smaller size and higher stability than a conventional optical beam splitter. The maximum sensitivity of strain and temperature corresponding to this structure is 4.24 pm/µε and 72.5 pm/°C, respectively. To reduce the influence of the external environment on the experimental results, some special optical fibers have been used as sensing structure materials [24,25]. For example, MZI structures are made by splicing photonic crystal fibers and single-mode fibers (SMFs). Zheng [24] used this approach to avoid cladding mode involvement in coupling with strain and temperature sensitivities of 2.1 pm/µε and 1.24 pm/°C, respectively. However, multiple cascade structures have problems such as a size that is difficult to package, the introduction of more considerable transmission losses, and the photonic crystal fiber increasing the cost in practical applications. In addition, the difference between temperature and strain sensing tests is not characterized clearly, as the majority of structures are demodulated and analyzed using a wavelength approach. Therefore, it is essential to fabricate a low-cost, highly sensitive microstructure device with low cross-crosstalk in two-parameter measurements.

In this paper, an embedded spherical point taper structure (EDT-MZI) with the MZI principle is designed, which is mainly made by using two unique arc discharge fusion methods between single-mode fiber and multimode fiber, and a spherical-like modulation zone exists in the middle of the taper due to the unique fabrication process. Theoretically, we analyze the effect of modulating the spherical modulation zone on the characteristic spectra and the methodology of intensity modulation. The theory's feasibility is verified through several sets of repetitive comparison experiments. Further, the EDT-MZI prepared from single-mode fiber (SMF) and multimode fiber (MMF) with optimized parameters has good strain-temperature simultaneous sensing advantage potential. As demonstrated by multiple sensing experiments, the strain sensing sensitivity of the proposed structure is 0.03 dB/µε in the range of 0-186.99 µε, and the temperature sensitivity is 73 pm/°C in the range of 20°C-75°C. Moreover, the tiny cross-sensitivity of 0.0015 dB/°C makes it possible to differentiate between temperature and strain sensing effectively, resulting in simultaneous sensing test applications. With low temperature-strain cross-talk, high sensing sensitivity, and low response latency, the EDT-MZI structure can be used in precision instrumentation measurements.

2. Principle and simulation analysis

The basic schematic diagram of the structure designed in this paper is shown in Fig. 1, and the embedded spherical point taper structure is composed of the optical beam splitting area, effective interference area, and coupling area, respectively. The first non-adiabatic taper zone (optical beam splitting zone) consists of single-mode fiber, multimode fiber, and spherical dot modulation zone, respectively. When the light propagates to the optical beam splitting zone, the light power is uniformly distributed in the core and cladding zone of the fiber structure through the expanded beam of the multimode fiber, where the length of the multimode fiber used is 300 µm, effectively avoiding the effect of multimode mode interference on the results. As the light is transmitted to the point spherical modulation zone in the middle of the non-adiabatic taper, the coupling and secondary distribution effects on core power and cladding power are carried out based on the splitting ratio caused by the original fiber taper. The single-mode fiber sandwiched between two non-adiabatic taper structures provides an effective interferometric phase accumulation for the interference results. When the incident light transmission to the second non-adiabatic taper zone (optical coupling zone), the first half taper structure part makes part of the cladding light power coupled back into the core, the two parts of the area of light power modulated by the spherical dot modulation zone again realized the coupling distribution. Finally, the multimode fiber acts as an optical coupler function to re-couple the core and cladding power after the second distribution into the derived single-mode thread. This leads to the coupling between different fiber modes.

Fig. 1. Schematic diagram of EPT based on MZI.

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Although interference between the base mode and multiple cladding modes is involved, considering only two main domain modes to analyze the interference results qualitatively is reasonable based on the interference condition of phase mode matching and the approximate consistency of the mode intensity, which can be expressed as the following equation [26]:

(1)$$I = {I_{\textrm{co}}} + {I_{\textrm{cl},\textrm{m}}} + 2\sqrt {{I_{\textrm{co}}}{I_{\textrm{cl},\textrm{m}}}} \cos (\mathrm{\Delta }\varphi ).$$

where I_co and I_cl,m are the mode intensities of the core and microfiber cladding, respectively, and Δφ is the phase difference between the core mode and the cladding mode, which can be expressed as Δφ=2πLΔn_eff/λ, where λ denotes the incident wavelength and Δn_eff= n_core- n_clad-m, n_co and n_cl are the effective refractive indices (RI) of the fiber core and cladding, respectively.

When the phase matching condition Δφ=(2m + 1)π (m∈N+) is satisfied, the corresponding resonant wavelength (denoted by λ_dip) is expressed as:

(2)$${\lambda _{\textrm{dip}}} = \frac{{2\mathrm{\Delta }{n_{\textrm{eff}}}L}}{{2m + 1}}.$$

(3)$$\begin{array}{c} {I = {I_{\textrm{co}}} + {I_{\textrm{co}}}{c_1}{c_2}\alpha (d) + 2\sqrt {{I_{\textrm{co}}}} \cdot {I_{\textrm{co}}}{c_1}{c_2}\alpha (d)\cos (\mathrm{\Delta }\phi )}\\ { = {I_{\textrm{co}}}[{1 + \alpha (d){c_1}{c_2}} ]+ 2{I_{\textrm{co}}}\sqrt {\alpha (d){c_1}{c_2}} \cos (\mathrm{\Delta }\varphi )} \end{array}.$$

where C₁ and C₂ denote the coupling efficiency of the two-coupling zone, respectively. When the structure is subjected to a transverse stress σ_x, it leads to a change in phase difference, which can be expressed by the following equation [27]:

(4)$$\mathrm{\Delta }{(\mathrm{\Delta }\varphi )_\varepsilon } = \mathrm{\Delta }{\varphi _\varepsilon }_L + \mathrm{\Delta }{\varphi _{\varepsilon n}},$$

(5)$$\mathrm{\Delta }{\varphi _{\varepsilon n}} = \{ \mathrm{\Delta }{n_{eff}}{k_0}\frac{{2\mu }}{E} + \frac{{{k_0}}}{{2E}}\mathrm{\Delta }n_{eff}^3[(1 - \mu ){P_{11}} + (1 + 3\mu ){P_{12}}]\} {\sigma _x}L,$$

(6)$$\mathrm{\Delta }{\varphi _{\varepsilon L}} = {k_0}\mathrm{\Delta }{n_{eff}}(\frac{{{\sigma _x}}}{E}L).$$

where µ and E denote the Poisson's ratio and elastic modulus of the fiber material, respectively, P₁₁ and P₁₂ denote the two components of the elastic-optical coefficient of the material, and k₀ is the wave vector. The comprehensive equation above shows that effectively increasing the coupling efficiency of optical power in the core and cladding in strain sensing tests can increase the optical intensity sensitivity.

As the structure is subjected to a change in temperature, this causes a change in the phase difference, which the following equation can express [28]:

(7)$$\begin{array}{l} \mathrm{\Delta }{(\mathrm{\Delta }\varphi )_T} = \mathrm{\Delta }{\varphi _{TL}} + \mathrm{\Delta }{\varphi _{Tn}}\\ = {k_o}[(\alpha L)\mathrm{\Delta }{n_{eff}}\mathrm{\Delta }T + ({\xi _{\textrm{co}}}{n_{\textrm{co}}} - {\xi _{\textrm{cl}}}{n_{\textrm{cl}}})L\mathrm{\Delta }T)]. \end{array}$$

where ξ_co and ξ_cl denote the thermal-optical coefficients of the fiber core and cladding, respectively, and α denotes the thermal-optical coefficient of the material. The following equation indicates that the contrast value of the interference fringe (ER) is predominantly determined by the core power and the power in the m-order cladding involved in the interference. ER can be optimized when these two powers are roughly equal in magnitude.

(8)$$ER = \frac{{{I_{\max }} - {I_{\min }}}}{{{I_{\max }} + {I_{\min }}}} = \frac{{2\sqrt {{I_{\textrm{co}}}{I_{\textrm{c},\textrm{m}}}} }}{{{I_{co}} + {I_{\textrm{cl},\textrm{m}}}}} = \frac{{2\sqrt {\alpha (d){c_1}{c_2}{\kappa _1}{\kappa _2}} }}{{\alpha (d){c_1}{c_2}{\kappa _1}{\kappa _2} + 1}}.$$

The value of ER is directly affected by the coupling efficiency of C₁ and C₂. Within a particular range, a higher coupling coefficient will optimize the spectral quality by making the power distribution ratio of the core and the cladding approximately the same. Also, excessive transmission loss α(d) can reduce the ER. Integrated discussion and analysis show that the core key in the above structural model is the spherical light modulation region, which determines the core power and cladding power distribution and coupling efficiency. The transmission process of light in the EDT region can be represented by the following transmission based on the theory of thin film optics [29]:

(9)$$\begin{array}{l} T = {T_1}{T_2}{T_3} = [\begin{array}{cc} {{f_1}}&{{f_2}}\\ {{f_3}}&{{f_4}} \end{array}] = [\begin{array}{cc} 1&0\\ {\frac{{{n_2} - {n_1}}}{{{n_1}{r_2}}}}&{\frac{{{n_2}}}{{{n_1}}}} \end{array}][\begin{array}{cc} 1&{{d_0}}\\ 0&1 \end{array}][\begin{array}{cc} 1&0\\ {\frac{{{n_1} - {n_2}}}{{{n_2}{r_1}}}}&{\frac{{{n_1}}}{{{n_2}}}} \end{array}]\\ = [\begin{array}{cc} {1 + \frac{{{d_0}}}{{{r_1}}}\frac{{{n_1} - {n_2}}}{{{n_2}}}}&{{d_0}\frac{{{n_1}}}{{{n_2}}}}\\ {\frac{{{n_1} - {n_2}}}{{{n_1}{r_1}}} + \frac{{{n_2} - {n_1}}}{{{n_1}{r_2}}} - \frac{{{d_0}{{({n_2} - {n_1})}^2}}}{{{n_1}{n_2}{r_1}{r_2}}}}&{1 + \frac{{{d_0}}}{{{r_2}}}\frac{{{n_2} - {n_1}}}{{{n_2}}}} \end{array}]. \end{array}$$

The specific details are shown in Fig. 2(a), the lens thickness d₀= 2a, (a and b correspond to the long and short half-axes of the spherical modulation zone), n₁ and n₂ correspond to the refractive index of the core and cladding, respectively. r1 and r2 refer to the individual radii of curvature that correspond to the two convex surfaces within the spherical modulation zone. The spacing between the point spherical modulation zone and the incident light field (W₁) and coupled light field (W₂) are d₁ and d₂, respectively. In addition, $\beta = \frac{\lambda }{{\pi w_1^2}}$ is expressed as the far-field divergence angle. Then the following equation is given:

(10)$${z_0} = \frac{1}{\beta } = \frac{{(\frac{{{f_1}{f_3}}}{{{\beta ^2}}} + {f_1}{f_3}d_{_1}^2 + {f_1}{f_4}{d_1} + {f_2}{f_3}{d_1} + {f_2}{f_4})}}{{(\frac{{f_3^2}}{{{\beta ^2}}} + f_3^2d_{_1}^2 + 2{f_3}{f_4}{d_1} + f_4^2)}}.$$

where z₀ represents the effective distance between the effective focused light field and the exit surface of the spherical modulation zone.

(11)$${W_0} = {W_1}{\{ {({f_1} + {f_3}{d_2})^2} + \frac{{{{[({f_2} + {f_1}{d_1}) + ({f_4} + {f_3}{d_1}){d_2}]}^2}}}{{Z_0^2}}\} ^{\frac{1}{2}}}.$$

After the modulation zone action, the coupling coefficient between the optical field (optical field diameter is W₀) and the optical field at the end face of the single-mode fiber (optical field diameter is W₂) is κ, which the following equation can express:

(12)$$\kappa = \frac{{4{W_2}^2{W_0}^2}}{{{{({W_2}^2 + {W_0}^2)}^2} + \frac{{{\lambda ^2}{d_2}^2}}{{{\pi ^{^2}}}}}}.$$

Fig. 2. (a)Enlarged schematic of EDT zone;(b)-(c) Theoretical simulation of coupling efficiency and loss of EDT.

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The light field W₀ after modulation in the modulation zone and the light field transmission direction x satisfy:

(13)$${W_0}^2(x) = {W_0}^2{(1 + \frac{{\lambda {d_2}}}{{\pi {W_0}^2}})^2}.$$

In summary, the optical coupling efficiency C after modulation by the spherical modulation zone can be expressed as:

(14)$$c = \kappa {e ^{\{ - \kappa [\frac{{{y_0}^2}}{2}(\frac{1}{{{W_0}^2}} + \frac{1}{{{W_2}^2}}) + \frac{{{\pi ^2}{\theta ^2}[{W_0}^2 + {W_0}^2(x)]}}{{2{\lambda ^2}}} - \frac{{{y_0}\theta {d_2}}}{{{W_0}^2}}]\} }}.$$

The equation y₀ indicates the value of the deviation between the modulation zone and the receiving end of the fiber in the y-direction, which can be expressed as y₀=|b-w₁|/2. The modulation zone structure and the receiving end of the fiber in the y-direction deflection angle difference ɵ=atan(b/(a + d₂)) is added here because the fiber, in practice, is operated by aligning the fiber axis direction. Therefore, the approximate lateral angular deviation in the theoretical analysis is zero, while the analytical discussion is in the longitudinal direction.

The loss caused by the mismatch of the optical field due to the angular shift is also not negligible, mainly reflected in the distribution and coupling process of the optical power transmitted within the fiber. This can be expressed in the following equation:

(15)$$\alpha (d) ={-} 10\log _{10}^{{{(\frac{{N{A_2}}}{{N{A_1}}})}^2}} ={-} 10\log _{10}^{{{(\frac{{{W_2}}}{{{W_0}}}\frac{{{W_0}}}{{{W_1}}})}^2}} ={-} 10\log _{10}^{(1 - \frac{{{n_2}\theta }}{{\pi N{A_2}}})}(\textrm{dB)}\textrm{.}$$

where NA₁, NA₂ indicates the numerical aperture size of the incident fiber and the receiving fiber, respectively. From the above equation and shown in Fig. 2(a), it can be seen that when the longitudinal length of the spherical modulation zone gradually increases within a specific range, ɵ gradually increases, and the resulting loss value also gradually increases. Numerical simulations based on the above theory are carried out, as shown in Figs. 2(a) and 2(b) indicate the schematic diagram of the amplified EDT modulation zone, the coupling efficiency and loss simulations, respectively.

A schematic diagram of the spherical modulation zone formed by the SMF-SMF and MMF-SMF, respectively, is shown in Fig. 2(a) above. The only difference between these two cases is the difference in the incident light field diameter W₁, and there is no difference in the analysis process. Set the transverse semi-axial length of the spherical modulation zone as x and the longitudinal semi-axial length b as y. The two axial sizes are simultaneously increased from 2µm to 30µm in steps of 0.01µm. It can be seen from Fig. 2(b) that when the longitudinal length y is sure, the coupling efficiency decreases gradually with the increase of the transverse length of the modulation zone. Vice versa, when the transverse size x is specific, the coupling efficiency increases with the addition of the longitudinal length of the modulation zone. The coupling efficiency rises as the longitudinal length of the modulation zone increases. Therefore, ignoring the effect of transmission loss and enhancing the coupling efficiency alone, it is recommended that the geometric configuration of the spherical modulation zone has a larger longitudinal length and a minor transverse length. Transmission loss α(d) increases gradually with the increase of the lateral length of the modulation zone when the longitudinal length y is certain, as shown in Fig. 2(c). In contrast, when the transverse length x is constant, the transmission loss α(d) increases with the increase of the longitudinal length of the modulation zone. Comprehensive Fig. 2(b), Fig. 2(c) and combined with Eq. (3), it can be seen that the proper reduction of the length difference between the transverse length and the longitudinal length can help to improve the coupling efficiency of the spherical modulation zone, and thus achieve the effect of optimizing the spectrum. Therefore, the design of the modulation zone shape in the experiments aims at a series of detailed analyses of the ellipsoidal modulation zone with different forms based on the spherical shape by changing the transverse and longitudinal lengths. The ellipticity of the spherical modulation zone is set to E according to the geometry for comparative analysis, and its value can be expressed as:

(16)$$E = \frac{{a - b}}{a}.$$

The simulation parameters in Table 1 are used to establish the corresponding structural model, and the simulation analysis is carried out based on the beamprop algorithm. Further, the evaluation of the spectral quality is based on the free spectral range (FSR), loss, and ER. The intensity uniformity (SU) is not negligible in intensity-modulated, which can be expressed as follow:

(17)$$SU = \frac{{{{\overline I }_{\textrm{max}}} - {{\overline I }_{\textrm{min}}}}}{{{{\overline I }_{\textrm{max}}}}}.$$

Table 1. Simulation parameter variables and values

View Table | View all tables in this article

As shown in Fig. 3, the transmission spectrum ER corresponding to the EDT-MZI structure and the ellipticity in the middle modulation zone of the adiabatic taper shows a Gaussian function distribution relationship. The ER of the transmission spectrum is more prominent when the geometry of the spherical modulation zone tends to be more circularly symmetric (E = 0), and the ER decreases with the increase of the corresponding value of E. This is attributed to the fact that the spherical modulation zone in the middle of the taper plays a role similar to that of a convex lens, which regulates the ratio of optical power in the core and cladding according to the lens coupling theory mentioned above. It is known from Eq. (4) that when these ratios are approximately equal, the ER tends to become more significant. As the geometry of the modulation zone tends to change from a flat ellipse (a > b) to a centrosymmetric circle (a = b), the focal length gradually decreases, and most of the optical power in the cladding is recoupled back to the core, leading to increase in coupling efficiency. Therefore, the ER of interference fringe gradually increases. Supplementarily, the difference in deflection angle between the modulation zone structure and the receiving fiber end in the y direction is ɵ. When the geometry of the spherical modulation region tends from a flat ellipse (a > b) to a vertical ellipse (a < b), the increased ɵ value reduces the optical power value coupled back from the core to the cladding, which in turn increases the mode field mismatch loss (based on Eq. (1)5).

Fig. 3. The simulation spectral characterization of EDT-MZI Structures with different ellipticity.

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Since the geometry of the modulation zone directly modulates the light intensity value, the SU is also monitored during the light intensity modulation. As shown in Fig. 3 above, the SU of modulation zone and ellipticity also show a Gaussian functional correlation. The intensity uniformity of the spectrum reaches its maximum when the geometry of the modulation zone is symmetric spherical. In this case, the power of the core and dominant cladding modes involved in the interference are approximately 1:1 equally divided. This has significantly attenuated the interference of the cladding modes of various orders in the structure, thus suppressing the effect of mode crosstalk on the spectrum. The follow simulations show that when the geometry of the modulation zone is symmetrically spherical, the MZI structure has the high spectral quality and optimizes the functional role of light intensity modulation.

Therefore, a comparative analysis of the transmitted optical field and the corresponding optical power is carried out for the EDT-MZI structure consisting of SMF-SMF, MMF-SMF, and double-down taper without modulation zone basis the same non-adiabatic taper parameters, and the results are shown in Fig. 4 respectively.

Fig. 4. Image of the transmitted light field and normalized power of the adiabatic taper: (a) without the intensity modulation zone; (b) With spherical modulation zone formed by SMF;(c) With spherical modulation zone formed by SMF and MMF.

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As can be seen from Fig. 4(a), in the introduction part of the fiber, the incident light power is strictly and steadily confined to the core of the introduced single-mode fiber when entering the primary down taper zone (light splitting), the light power in the core is diffused into the cladding zone, resulting in an uneven distribution of light power due to weakening or superposition of light power. When it entering the secondary down taper zone (light coupling), part of the light power leaking into the cladding is coupled back into the core, completing the mode interference process. For the EDT-MZI structure consisting of SMF-SMF, as shown in Fig. 4(b), the spherical modulation zone in the middle of the down taper allows for the modulation of the light power distribution again in addition to the original light power distribution ratio. Compared to the double-down-taper MZI structure without modulation zone, this structure increases the coupling and distribution between the core and cladding power, making the core power and cladding power approximately equally distributed at the output of the fiber, which will result in a certain degree of ER improvement but increases the transmission loss simultaneously. The MMF-SMF structure EDT-MZI is shown in Fig. 4(c). Compared to the previous two structures, this one has an increased mode field diameter (MFD) due to the introduction of MMF, which further expands the light in the core and increases the total mode power distributed in the fiber cladding. Meanwhile, the cladding power in the effective interference zone is higher than that of the fundamental mode in the core, which also leads to the excitation of multiple cladding modes accordingly. However, in the secondary down taper coupling zone, further equalization of the core-cladding power ratio at the fiber output is caused by the secondary modulation effect of the modulation zone on the optical power and the strong convergence effect of the MMF. This further increases the coupling of the core and cladding power on top of the SMF-EDT-MZI structure, and optimizing the spectral quality. At the cost, however, it also leads to an inevitable increase in output losses compared to the previous two structures.

For the above EDT-MZI structure with a modulation zone and the double down taper MZI structure without a modulation zone, finite element analysis is used to analyze the deformation of each part of the structure when the structure received constant transverse tensile stresses, as shown in Figs. 5(a)–5(e). Where Fig. 5(a) represents the force distribution of the biconcave taper structure without containing the spherical modulation zone. Figures 5(b)–5(e) show the EDT-MZI structure force distribution with different ellipticity (Note: ellipticity gradually progresses from positive to negative) modulation zones under the same down taper parameter, respectively.

Fig. 5. (a) The mechanical simulation characterization for: the double down taper MZI;(b)-(e) The EDT-MZI in different ellipticity.

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The structures apply a transverse stress of 0.5N to one side, and it is easy to observe that the stress value per unit volume increases as the diameter of the taper decreases due to the inhomogeneity of the geometry. This is attributed to the fact that the smaller the unit volume corresponding to the shortest diameter in the middle of the taper, the smaller the stiffness of the corresponding structure. Therefore, when transverse stress is applied, the greater the deformation produced is due to the more significant the unit volume affected by the transverse stress. Conversely, the larger the volume of the structure for the same material, the less susceptible it is to stress-induced deformation. The force per unit volume in the down taper zone is inversely correlated with the corresponding cylindrical waveguide diameter size. In particular, by comparing Figs. 5(d)–5(e), the presence of a geometrically shaped modulation zone in the middle of the tapered zone causes the stress distribution at the center to show a specific difference. Here, defines the length of the structure corresponds to half of the maximum value of the stress applied as the linear stress response zone diameter (LSRD). Characterization of the above structures and values monitoring reveals that: a. As the geometry of the modulation zone changes from flattened elliptical tapering (E > 0) to vertical elliptical (E < 0), the maximum tensile stress applied to the structure gradually increases (0.457 N-0.478 N). b. As the ellipticity of the modulation zone gradually decreases within a specific range, the LSRD also gradually decreases (0.1929mm-0.1641 mm). c. Compared to the down taper MZI structure without the modulation zone, the EDT-MZI structure has a narrower LSRD and is subjected to larger stress values. Therefore, when the EDT-MZI structure is stressed, the light power at the optical coupling/splitting point will be more concentrated due to the force. Moreover, different values of E lead to a more significant change in the intensity of the interfering light. The variation in light intensity also varies due to the geometry of the modulation zone E. The strain sensitivity in light intensity is more favorable when E is more minor. Alternatively, for double-down taper MZI structures without a modulation zone, the wider LSRD result in a more diffuse distribution of light power at the fiber coupling/splitting point, which does not offer good sensing potential in light intensity modulation.

3. Production process and characterization

Based on the theoretical and simulation analysis in Part II, we developed a matching test protocol, setting the taper length parameter to 430 µm, using a single-mode fiber model (SMF-28, Corning) and a multimode fiber model (Nufern S105/125-16A), and a fusion splicer model (Fujikua-45PM) for fusion splicing.

Figures 6(a)–6(f) shows the detailed structure fabrication process. Step 1: The single-mode fiber and the multimode fiber are fused by axial alignment after decorating with a discharge strength of 40bit and a fusion time of 100 ms. Step 2: The MMF is then cut to <400 µm by an optical precision stage-controlled carving knife, effectively avoiding the introduction of multimode interference Step 3: Align the fused SMF-MMF, adjust the program to a weak discharge and increase the distance between the fused end faces to 15µm, and modify the discharge amount to 7 bit, increase the secondary discharge time to 150 ms, and make the two end faces form a similar semi-circular arc shape by discharge fusion. Step 4: Revise the fusion procedure to the arc discharge taper setting, change the overlap fusion amount between the end face structure to 8µm, and shorten the discharge time to 30 ms. The purpose of this operation is to make two inadequate collapses of the end face in a short period by the higher current impact and fixed fixture reverse extrusion effect, resulting in two fiber end faces in the fusion point near the zone of the volume distribution is not uniform, and then stacked expansion to form a similar to the fusion point. This results in stacking and swelling of the two-fiber end face around the fusion point, resulting in a sphere-like modulation zone, and the EDT is finished. Step 5-6: Similar fusion parameters are fine-tuned to fuse the end faces between the SMFs. Finally, the two EDT structures are connected by standard fusion to form the MZI structure.

Fig. 6. (a)-(f) The process of fabricate EDT-MZI structure.

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The effective interference lengths of the EDT (a)-(j) structures are all 2.5 cm. In our experiments, we designed a series of EDT-MZI structures with different E modulation zone, as shown in Fig. 7. From the electron micrographs, it can be observed that: The ER corresponding to EDT-a (2a = 11.25 µm, 2b = 63.22 µm) is 0.6 dB; For EDT-b (2a = 18.36 µm, 2b = 41.58 µm), the corresponding ER is 3.28 dB; EDT-c (2a = 21.73 µm, 2b = 33.92 µm), the corresponding ER = 5.16 dB; EDT-d (2a = 20.36 µm, 2b = 31.55 µm), the corresponding ER = 5.27 dB; EDT-e (2a = 22.82 µm, 2b = 23.25 µm), the corresponding ER = 9.08 dB; EDT-f (2a = 28.75 µm, b = 21.37 µm), the corresponding ER = 6.79 dB; EDT-g (2a = 32.24 µm, b = 20.82 µm), the corresponding ER = 5.05 dB; EDT-h (2a = 33.13 µm, b = 18.18 µm), corresponding to an ER = 4.38 dB; EDT-i (2a = 32.28 µm, b = 17.58 µm), corresponding to an ER = 4.67 dB; EDT-j (2a = 34.01 µm, b = 17.18 µm), corresponding to an ER = 2.17 dB.

Fig. 7. (a)-(j) The microstructure images and corresponding transmission spectra of EDT in different ellipticity.

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The specific data characterization is shown in Fig. 8. The above comparison experiment shows that when the geometry of the modulation zone in the middle of the down taper is closer to the centrosymmetric spherical shape, the ER of the corresponding transmission spectrum is larger. Based on the coupling theory described in the previous section, it is known that when E = 0 in the modulation region, its coupling efficiency to optical intensity is optimal, and the distribution of core mode power and cladding mode power involved in mode interference is relatively uniform. Also, the transmission loss of the corresponding spectrum of the EDT-MZI structure gradually increases when the value of the modulation region E gradually decreases (from E > 0 to E < 0). Furthermore, the uniformity of the corresponding light intensity shows a Gaussian function-type relationship with the change of the modulation zone E. This is consistent with the trend of theoretical simulated spectral characterization, and the feasibility of the theory is also verified again through experiments.

Fig. 8. The experiment spectral characterization of EDT-MZI Structures with different ellipticity.

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Further, as shown in Fig. 9(a), the double-down taper MZI structure without modulation zone (which corresponds to a taper length of 421.52 µm and shortest waist-diameter is 33.54µm) is fabricated using arc pulling taper. Compared to the SMF-EDT-MZI and MMF-EDT-MZI structures with the same fusion parameters, as shown in Figs. 9(b) and 9(c), the ER corresponding to double-down taper is smaller. This is caused by the significant difference between the power values of the core and the cladding due to the lack of light intensity modulation zone. It can be seen that the coupling between the core and cladding modes is weaker, and the ER is smaller combined with Eq. (8). According to the second part of the coupling theory, the modulation region has a double coupling effect between the core and cladding power. The difference between core and cladding power is reduced, which improves the ER. In addition, the shorter MMF further improves the ER based on SMF-EDT-MZI due to the enhanced beam propagation/receiving capability.

Fig. 9. Image of the microstructure and transmission spectrum: (a) With down taper; (b)With EDT formed by SMF;(c) With EDT formed between SMF and MMF;

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To further verify the fiber mode components involved in mode interference in EDT-MZI composed of SMF-MMF, a series of sample structures with different interference lengths (1.6 cm, 2.3 cm, 2.7 cm, 3.1 cm, 3.5 cm, and 3.9 cm) are prepared. Since these structures involve multiple cladding modes interfering with the core modes simultaneously, the wavelength difference between two adjacent interference dips, known as the free spectral range (FSR), is used as the basis for measurement. The results are compared with the theoretical results of the second part of the mode analysis. Figure 10(a) shows the comparison between the theoretically calculated FSR and the experimental spectral FSR, which match almost exactly. Furthermore, the experimental spectra corresponding to structures with different interference lengths are compared in Fig. 10(b), revealing that the FSR decreases with increasing interference length, satisfying the MZI principle. Figure 10(c) shows the corresponding theoretical simulated spectra, which also match the experimental spectra. Therefore, it can be verified that the interference spectrum of this structure is mainly formed by a dominant power cladding mode with the fiber core mode. It is worth noting that the spectra have a regular “comb-like” distribution in most of the wavelength range, and the wavelength range corresponding to relatively uniform interference extinction ratio (ER) is selected for the above analysis. This indicates that the interference between the other cladding modes and the core mode is minor, reducing the effect of inter-mode crosstalk on the subsequent sensing experimental values.

Fig. 10. EDT structures with varying interference lengths: (a) Comparison of theoretical and experimental FSR values;(b) Comparison of experimental spectra;(c) Comparison of simulated theoretical spectra.

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4. Sensing and analysis

To observe the transmission spectrum of the structure, a broad-band light source (BBS) with a wavelength range from 1520 nm to 1630 nm and an optical spectrum analyzer (OSA-CMA5000) with the resolution of 5 pm are connected to the end of the transfer SMF end, respectively. The axial stress sensor is shown in Fig. 11(a). First, the structure level is evenly fixed with ultraviolet curing glue evenly on the free end of the structure on both sides of the structure (the ground distance between the fixed point is L₀= 12 cm), and the glue droplets are guaranteed there is no air gap between three-dimensional precision mobile platforms. Subsequently, by controlling a step electrode (ZOLIX-SC300, the maximum measurement accuracy is 0.02 µm) stretching the three-dimensional displacement platform, due to changes in the tensile distance, the structure is uniformly stressful. At the same time, the spectrometer with the optical fiber output end monitored the change of the optical signal in real time by external intensification. Finally, the data analysis software is used to process data processing analysis on the output optical signal to monitor the corresponding variable structure accurately.

Fig. 11. Sensing test setup (a) Axial strain sensing;(b) Temperature sensing.

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The strain sensing experiments corresponding to the dual up-taper MZI structure without the modulation zone are shown in Fig. 12. The figure shows that with the increase of the applied axial stress, the interference spectrum in the monitored zone changes accordingly, and the changes in wavelength and light intensity are shown in Fig. 12(b) and Fig. 12(c), respectively. Considering the hysteresis of the structure during the sensing process, the following sensing tests are performed by applying strain in multiple groups in the forward direction and reducing strain in the reverse order. The monitored wavelength changes are indicated by the blue and red lines in the figure, respectively. The wavelength strain sensitivity in the range 0-223.575 µε is 7 pm/µε with good linearity (∼0.992). At the same time, the bi-down taper structure showed a nonlinear relationship with the applied strain in terms of light intensity. It conformed to a quadratic distribution with a higher slope of intensity change in the smaller strain range interval than its slope. The slope of the intensity change in the more extensive strain range corresponds to the slope of the light intensity change. Because the taper structure itself no longer satisfied the cutoff frequency condition of the fundamental mode but is a microstructure form based on strong swift field transmission of optical signals, it is easier to be influenced by the external environment at the light intensity level compared with the phase-based commissioning method, so more obvious changes will occur, but due to the larger taper of the adiabatic taper, the light power in the core is not coupled back to the core again while diffusing in the form of swift waves, so the change of light power is more moderate when a more significant strain is applied in the subsequent stages of the test, which is also similar to the trend simulated in Fig. 4(a).

Fig. 12. Strain sensing test of dual up-taper-MZI without modulation zone :(a) Characterization of spectral change ;(b) Wavelength change; (c) Intensity change.

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Further, the experimental strain response of the EDT structure with a spherical modulation zone using a single-mode fiber is shown in Fig. 13 above. The test is performed by applying strain in the forward direction and reducing strain in the reverse direction (indicated by the blue and red lines, respectively). The changes in wavelength and light intensity are shown in Figs. 13(b) and 13(c), respectively. The wavelength strain sensitivity in the range of 0-183.26 µε is 6-7 pm/µε (R²= 0.997). The strain sensitivity corresponding to the optical intensity is 0.006 dB/µε (R²= 0.997), compared with the double down-taper fiber structure without the spherical modulation zone. The optical intensity sensing test performance is improved because the change in the intrinsic structure makes the optical power show a linear correlation with the strain change, which is consistent with the simulated trend in Fig. 5(c). Also, its optical intensity sensitivity is relatively low.

Fig. 13. The EDT-MZI-e strain sensing test with sphere modulation zone formed by SMF:(a) Characterization of spectral change;(b) Wavelength change; (c) Intensity change.

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The EDT structure with a spherical modulation zone using a multimode fiber is further improved in spectral performance by combining the theoretical simulations in the previous paper. The strain response is shown in Fig. 14. The same test is performed with multiple groups of forward-applied strain and reversed reduced strain (indicated by the blue and red lines, respectively). The variations in wavelength and light intensity are shown in Figs. 14(b) and 14(c), respectively. The strain sensitivity of 0.03 dB/µε (R²= 0.998) for light intensity in the range of 0-186.99 µε is five times higher than that of the EDT-MZI prepared from SMF for light intensity modulation. This is due to the optimized structure, which further optimizes the ratio of core-to-cladding power distribution. The coupling and distribution of optical power in the spherically modulated region to the core and cladding of the fiber taper are further improved, which is agree with the simulation study in Fig. 4 above. As strain testing is conducted under multiple sets of repeated and continuous conditions, the presence of mechanical test losses can cause measurement errors in light intensity-type test results. These errors typically arise during the intervals between each set of tests, resulting in a somewhat non-linear response at the start of the test.

Fig. 14. The EDT-MZI strain sensing test with sphere modulation zone formed by MMF-SMF:(a) Characterization of spectral change;(b) Wavelength change; (c) Intensity change.

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Additionally, there is a non-linear correlation between wavelength and strain variation. Equation (3) reveals that the wavelength variation exhibits an opposite trend when the strain sensitivity is sensitized by light-intensity demodulation. As a result, the corresponding wavelength variation of the EDT structure made of MMF-SMF is less than that of the EDT structure made of SMF.

Several groups of SMF-EDT structures with different ellipticity modulation zones are selected for multiple repetitive strain tests to verify the feasibility of the above mathematical theory analysis. The results, shown in Fig. 15, are subjected to comparative analysis, which revealed that: (1) The optical intensity-type strain sensitivity of the corresponding structure gradually increases (0.001 dB/µε to 0.005 dB/µε) as the ellipticity of the modulation zone increases, which is consistent with the trend observed in the mechanical simulation part of Fig. 5. (2) While the optical intensity strain sensitivity increases, the wavelength strain sensitivity decreases (0.012 nm/µε to 0.002 nm/µε), further demonstrating the feasibility of the above analysis. Several groups of SMF-EDT structures with different ellipticity modulation zones are selected for multiple repetitive strain tests to verify the feasibility of the above mathematical theory analysis. Additionally, by analyzing the sensing results and examining Figs. 14 and 15, it is apparent that a modulation zone with ellipticity close to zero greatly enhances both modulated strain sensing and spectral uniformity of light intensity. This performance improvement is primarily due to the geometric properties of the modulation zone, which play a crucial role in its capacity to modulate light intensity, as previously demonstrated through simulations (refer to Figs. 3–5). It is worth noting that a circular shape of the modulation zone yields superior performance in terms of modulating light intensity.

Fig. 15. The EDT-MZI strain sensing test with different ellipticity modulation zone formed by SMF:(a) EDT-MZI-b;(b) EDT-MZI-c; (c) EDT-MZI-i.

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In engineering applications, strain testing is carried out under ideal conditions of constant pressure and humidity, so the effect of temperature on the test results needs to be considered to ensure accurate and reliable measurement. The optimized MMF-SMF-EDT structure is placed in a vacuum temperature-controlled chamber to evaluate the temperature-sensitive performance of the structure, as shown in Fig. 11(b), and the test temperature range is from 20°C to 120°C sub-temperature with a test step of 5°C/point. The temperature response spectrum corresponding to the structure is shown in Fig. 16. It is evident that as the temperature increases/decreases, the resonant wavelength corresponding to the spectral monitoring interference dip moves toward the long/short wave direction, but its temperature response has some variability of 73 pm/°C (20°C-75°C),169 pm/°C (75°C-120°C), respectively. This is because the fiber material is mainly composed of SiO₂, which thermal expansion coefficient and thermo-optical coefficient have a nonlinear relationship with temperature, and the rate of change is faster at higher temperatures. In the entire temperature monitoring range, this structure has a negligible optical intensity-temperature response (∼4.75e^-5dB/°C) and a temperature-strain cross-sensitivity of 0.0015 µε/°C. Combined with the mode coupling theory analysis above, it is clear that precisely because this MZI structure is a dual-mode interference-like structure, it can often reduce the measurement variation introduced by mode competition in multi-physics parameter sensing tests. Therefore, the strain-temperature synchronous sensing test can be achieved with zero crosstalk under the precise control of the temperature parameter variation.

Fig. 16. The EDT-MZI temperature sensing test with symmetrical sphere modulation zone formed by MMF-SMF:(a) Characterization of spectral change; (b) Wavelength and intensity change.

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Fig. 17. Strain response performance test of EDT-MZI formed by MMF-SMF structure.

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Based on the experiments conducted, it is evident that the structure exhibits excellent sensitivity to light intensity-strain in strain testing. Therefore, the response is primarily explored using amplitude variations of the light intensity signal during monitoring analysis, with a control time of 3.5 seconds(s) for each applied strain of ± 28 µε and multiple equal-cycle interchanges. A high-rate spectrum analyzer with a temporal resolution of 100 Hz, wavelength resolution of 0.1 pm, and intensity resolution of 1 mw is used to facilitate accurate strain response measurement. Figure 17 shows that the light intensity signal corresponding to the monitored interference dip demonstrates periodic fluctuations based on the extent of applied strain. Moreover, the amplitude alteration in light intensity is measured at 0.8 dB/28 µε, and the sensitivity between light intensity and strain remains constant. The mean response time of each change is 3.61 s, and the maximum response time difference is 0.7 s, which is fully synchronized with the experimental applied strain time.

A comparison is conducted with recent research studies to assess the sensing performance of the proposed structural advantages in this paper, which are presented in Table 2. The findings demonstrate that the EDT structure displays good discriminative ability in measuring two physical quantities - strain and temperature, mainly due to its unique structural characteristics that involve strain modulation by light intensity and temperature modulation by wavelength. The obtained sensitivity values are also significant. Furthermore, the low strain-temperature crosstalk advantage streamlines the laborious demodulation analysis process to the greatest extent possible.

Table 2. Temperature-strain simultaneous sensing test performance comparison

View Table | View all tables in this article

4. Conclusion

The EDT-MZI microstructure is fabricated using two unique arc discharge fusion methods between SMF and MMF. Theoretically, simulations and experiments for this special conical structure demonstrated the influence of the spherical modulation zone in the middle of the taper on the spectral properties and strain-sensing sensitivity. The feasibility of the unique structure to achieve the light intensity-strain response is demonstrated by multiple replicate experiments and optimized parameter processing. In addition, such a microstructure has a high sensitivity potential in measuring strain and temperature. Experimental results show that strain and temperature sensing sensitivity can reach 0.03 dB/µε (0-186.99 µε), 73 pm/°C (20°C-75°C) and 169 pm/°C (75°C-120°C), respectively, with a cross-sensitivity of 0.0015 µε/°C between temperature and strain. Further, due to the structure's low response latency, this structure has suitable potential applications in precision instrumentation measurements, especially for localized structural health monitoring.

Funding

National Key Research and Development Program of China (No. 2018YFC1503703-3); the Spaceflight (XM44); Shanghai Academy of Spaceflight Technology (No. SAST2019-127).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request

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Parameter	value
n_core	1.45205
n_clad	1.44681
L_taper	425µm
W_taper	35µm
L_{Horizontal length}	6-26µm with the step of 1µm
L_{vertical length}	6-26µm with the step of 1µm

Structure type	Strain sensing sensitivity	Temperature sensing sensitivity	Sensing crosstalk	Ref
PMF-cascade HLPG	-2.13 pm/µε	103.43 pm/°C	49.02µε/°C	[30]
BT-MOC(MZI)	0.043 dB/µε	0.008 dB/°C &75.71 pm/°C	0.186 µε/°C	[31]
MCF + HCF&HCF(MZI + FPI)	19.17 pm/µε	279.99 pm /°C	14.6µε/°C	[32]
SMF + PDF(MZI)	9.5pm/µε	5.718 × 10⁻³mW/°C	/	[33]
NCF + HCF&HCF(MZI + FPI)	-649.18pm/µε	5.76pm/°C	0.009µε/°C	[34]
SMF + SCF(Laser-MZI)	1.80 pm/µε	1.88pm/°C	1.04µε/°C	[35]
	&0.01 dB/µε
MMF + HCF (MZI)	0.002 dB/µε	0.015 dB/°C	7.5µε/°C
MMF + HCF(AR-MZI)	0.016 dB/µε	0.181 dB/°C	11.31µε/°C	[36]
HCMOF(AR-MMI)	0.00359 dB/µε	/	/	[37]
HCMOF(AR-MMI)	0.00359 dB/µε	/	/	[38]
EDT(MZI)	0.03 dB/µε	73 pm/°C (20°C-75°C)	0.0015µε/°C	This work
EDT(MZI)	0.03 dB/µε	169 pm/°C (75°C-120°C)	0.0015µε/°C	This work

Parameter	value
n_core	1.45205
n_clad	1.44681
L_taper	425µm
W_taper	35µm
L_{Horizontal length}	6-26µm with the step of 1µm
L_{vertical length}	6-26µm with the step of 1µm

Structure type	Strain sensing sensitivity	Temperature sensing sensitivity	Sensing crosstalk	Ref
PMF-cascade HLPG	-2.13 pm/µε	103.43 pm/°C	49.02µε/°C	[30]
BT-MOC(MZI)	0.043 dB/µε	0.008 dB/°C &75.71 pm/°C	0.186 µε/°C	[31]
MCF + HCF&HCF(MZI + FPI)	19.17 pm/µε	279.99 pm /°C	14.6µε/°C	[32]
SMF + PDF(MZI)	9.5pm/µε	5.718 × 10⁻³mW/°C	/	[33]
NCF + HCF&HCF(MZI + FPI)	-649.18pm/µε	5.76pm/°C	0.009µε/°C	[34]
SMF + SCF(Laser-MZI)	1.80 pm/µε	1.88pm/°C	1.04µε/°C	[35]
	&0.01 dB/µε
MMF + HCF (MZI)	0.002 dB/µε	0.015 dB/°C	7.5µε/°C
MMF + HCF(AR-MZI)	0.016 dB/µε	0.181 dB/°C	11.31µε/°C	[36]
HCMOF(AR-MMI)	0.00359 dB/µε	/	/	[37]
HCMOF(AR-MMI)	0.00359 dB/µε	/	/	[38]
EDT(MZI)	0.03 dB/µε	73 pm/°C (20°C-75°C)	0.0015µε/°C	This work
EDT(MZI)	0.03 dB/µε	169 pm/°C (75°C-120°C)	0.0015µε/°C	This work

Simultaneous sensing of strain and temperature based on the inline-MZI embedded point-shaped taper structure with low crosstalk

Abstract

1. Introduction

2. Principle and simulation analysis

3. Production process and characterization

4. Sensing and analysis

4. Conclusion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (17)

Tables (2)

Equations (17)

Optics Express