With the continuous evolution of the information society, the acquisition and processing of vast, diverse information data have raised higher expectations for the next generation of sensors. Compared with traditional electrical sensors, optical fiber sensors have gained widespread attention owing to their compact structure, anti-electromagnetic interference, and high sensitivity^[1,2]. These sensors are capable of detecting various parameters, including temperature^[3], refractive index^[4], strain^[5], and curvature^[6]. Curvature measurement is increasingly required in various fields, such as human posture detection^[7], medical bone correction monitoring^[8], and bridge and road construction monitoring^[9]. The increasing demand has sparked significant interest in bending sensors.

Recently, various optical fiber bending sensors have been developed, particularly those based on fiber Bragg grating (FBG) and mode interference, attracting extensive research attention. FBG-based bending sensors are particularly effective in bending direction discrimination and are increasingly applied across various fields^[10,11]. However, these sensors are costly and difficult to manufacture, as they require advanced equipment, such as CO2 or femtosecond lasers. Moreover, their demodulation often relies on spectrometers with picometer-level resolution. These sensors also exhibit low curvature sensitivity across a wide range and are susceptible to temperature-induced cross-interference.

In addition to FBG-based bending sensors, sensors utilizing mode interference have also been developed^[12,13]. Specifically, the emergence of specialty optical fibers, such as multicore fibers (MCFs)^[6], photonic crystal fibers (PCFs)^[14], and hollow core fibers (HCFs)^[15], presents new possibilities for the development of bending sensors. Among these, PCF- and HCF-based bending sensors allow air holes for the control of guided-light interactions, enabling novel applications, but they face challenges like low reproducibility and high insertion losses^[14,15]. In contrast, MCF has attracted increasing attention in bend sensing applications due to its unique multicore structure, which enhances sensing capabilities and offers greater integration potential^[6]. Based on the spacing between each core, MCF is typically classified into weakly coupled and strongly coupled types^[16]. Bending sensors based on weakly coupled MCF often require splicing multimode fibers (MMFs) to act as splitters and couplers or involve taper processing^[17], and the inevitable use of the expensive fan-in/fan-out components, further increasing the complexity and cost. Strongly coupled MCF, noted for its unique modal characteristics and high-quality output spectrum, has attracted considerable attention as a promising option for next-generation optical fiber sensors. In particular, the compact core arrangement enables the formation of spatial supermodes, which enhances mode interaction and reduces sensitivity to inter-core crosstalk, thereby supporting more stable and coherent interference patterns for sensing applications. Sensors based on symmetric strongly coupled MCF often lack the ability to discriminate bending directions^[6]. In contrast, sensors based on asymmetric strongly coupled MCF offer new possibilities for identifying bending directions. For example, in 2016, Villatoro et al. developed a bending sensor based on a strongly coupled MCF with three cores. The sensor operates in reflection mode and can distinguish the bending directions by detecting wavelength shift and relative changes of the reflected power. The maximum bending sensitivity is 1.900nm/m−1 in the curvature range of 0–0.842m−1^[18]. Later, they employed two sections of such asymmetric MCFs spliced with single-mode fibers (SMFs) to fabricate a sensor achieving the bending sensitivity of 0.950nm/m−1 within a curvature range of −0.390 to 0.390m−1, allowing the detection of both positive and negative bending directions^[19]. Additionally, Arrizabalaga et al. used a femtosecond laser to change the refractive index of one peripheral core in the seven-core fiber (SCF), and used it for bend sensing, achieving a sensitivity of −17.500nm/m−1 in the curvature range of 0.000–0.150m−1^[20]. Although the asymmetric strongly coupled MCF, as exemplified above, can detect the bending direction and is widely used in various fields, existing bending sensors based on these fibers still face several challenges. For example, the fabrication of optical fibers for these sensors typically involves complex processes, such as drilling, stacking, or modifying specific fiber cores. Additionally, bending sensors based on asymmetric strongly coupled MCFs exhibit a limited curvature dynamic range and low sensitivity, significantly restricting their future development. Recent work on few-mode fiber transmission has further shown that transverse photonic modes, such as orbital angular momentum states, can maintain modal stability under bending-induced perturbations, which supports the feasibility of modal-interference-based directional sensing in multicore or structured fiber systems^[21].

Given the manufacturing challenges and application limitations of current fiber bending sensors, rapidly advancing 3D printing fiber technology provides a highly flexible alternative for optical fiber and sensor fabrication. Although it still faces challenges such as material limitations and post-processing complexity, it remains a promising approach for advancing the development of optical fiber sensors^[22]. In 2021, Alam et al. applied 3D printing to manufacture polymer optical fibers (POFs) for bending sensing^[23]. Experiments have shown that a relationship exists between the bending degree of the optical fiber and light intensity, which can be used to sense the strain or bending in the environment. In 2023, Luo et al. applied a 3D-printed dual-core fiber spliced with SMFs to construct a Mach–Zehnder interferometer (MZI) sensor, enabling multiparameter sensing of temperature, force, refractive index, and bending^[24]. This bending sensor gives out a maximum bending response of 0.210nm/m−1. Sensors based on 3D-printed optical fibers have excellent performance. Through the advantages of 3D printing technology in advanced optical fiber manufacturing, the geometry and material components of optical fibers can be customized. Therefore, for 3D-printing-based sensors, the types of sensing parameters and response performance can be greatly improved, and new possibilities and directions for the development of future sensor technology are explored.

Attributed to the structural flexibility of 3D-printed optical fibers, our previous work focused on the design, optimization, and fabrication of a strongly coupled SCF, with a preliminary exploration of its direction-dependent bending response^[25]. Building on this foundation, this study deeply explores the bending, temperature response, and dual-parameter sensing characteristics of the sensor based on such 3D-printed optical fibers. The strongly coupled SCF exhibits pronounced geometric asymmetry, and the proposed sensor is easily fabricated via only splicing with SMFs. In practical applications, curvature detection is inevitably influenced by temperature. Hence, by combining the FBG with MZI, dual-parameter sensing of temperature and curvature is enabled. Both the sensing characteristics and the direction recognition mechanism are examined theoretically and experimentally. The experimental results show that, since the interferometer and FBG have significantly different responses to the bend and temperature, the sensor can achieve simultaneous measurement of these two parameters. The proposed sensor is easy to fabricate, with the ability to detect the bending directions, a wide dynamic range for curvature recognition, and high bending sensitivity. This provides a valuable reference for developing fiber bending sensors and future innovations in fiber sensor design by 3D printing fiber technology.

The schematic diagram of the proposed sensor is shown in Fig. 1. The fabricated sensor contains two sensing elements. One is an MZI with the structure of SMF-SCF-SMF, and the other is the FBG inscribed into the 3D-printed SCF. For the sensor fabrication, a section of SCF with 21.0 mm long was spliced with two SMFs using the fusion splicer (FITEL s179), aligning the central core of the SCF with the SMF core to form an SMF–SCF–SMF structure. The SCF used was fabricated by 3D printing fiber technology, as previously reported. The previous research mainly focused on the fabrication and fundamental characterization of the SCF^[26], while the present work extends this fiber to sensing applications. Figure 2 shows a cross-sectional image of the SCF taken by the scanning electron microscope (SEM). The central core of the SCF is encircled by six outer cores arranged in a nearly hexagonal pattern. Minor axial and cross-sectional non-uniformities caused by fabrication were mitigated by selecting structurally consistent fiber segments for the sensing experiment. The insertion loss of the SMF–SCF–SMF structure was experimentally evaluated using an ASE light source and an optical power meter and was found to be relatively high, approximately 8 dB. This is attributed to the mode mismatch between the SMF and SCF intermediate cores, as well as the non-uniformity of the SCF. Additionally, there is some coupling among the cores of SCF, and some cores are asymmetric, resulting in significant scattering both inside and outside the core.

Then, a 193 nm excimer laser (Compex 110, Coherent Inc.) was used to inscribe the FBG into the bare SCF via the phase mask method. The position of the cylindrical lens was adjusted to ensure that the focused laser beam covered the central core of the SCF. The excimer laser had an output power of 18 mJ, a repetition rate of 200 Hz, and a scanning speed of 0.1 mm/s. A grating length of 10 mm was selected to ensure that the FBG was fully inscribed into the SCF segment. The phase mask period was 1070.04 nm. The corresponding grating period was 535.02 nm.

The proposed sensor utilizes the principles of both the mode interference and FBG to enable effective sensing of dual parameters simultaneously. When the light from the SMF is injected into the SCF, multi-high-order modes are excited at the splicing point between the SMF and SCF. After propagating a certain distance along the SCF, these modes meet at the end of the SCF and will be coupled back into the SMF, generating the MZI interference. According to Ref. [27], the output light intensity of the MZI sensor based on SMF–SCF–SMF can be expressed as I=I01+∑mnImn+2∑mnI01Imncos(2πΔneffmnLλ),(1)where I is the interference light intensity, I01 and Imn are the intensities of fundamental mode LP01 and high-order mode LPmn, respectively, Δneffmn is the effective refractive index difference between the fundamental mode and high-order mode, L is the interference length, and λ is the center wavelength. When the phase matching meets the following condition: 2πΔneffmnLλ=(2j+1)π,(2)where j is an integer, the interference dip appears at λjmn=2ΔneffmnL2j+1.(3)

The wavelength interval between two adjacent interference dips, or the free spectral range (FSR) of the sensing structure, can be expressed as FSR≈λm2ΔneffmnL,(4)where FSR is inversely proportional to the interference length. With the change of curvature or temperature, the optical path difference Δneffmn, L, and the wavelength of the interference dip λm vary^[28]. By differentiating Eq. (3), we can obtain Δλjmnλjmn=[1+∂(Δneffmn)/∂CΔneffmn]ΔC+[∂(Δneffmn)/∂TΔneffmn+∂L/∂TL]ΔT,(5)where ΔC and ΔT are the variations of the curvature and temperature, respectively.

The FBG only reflects the light at the specific wavelength, which is given by^[29]λFBG=2neffΛ,(6)where neff is the effective refractive index of the core, Λ is the period of the FBG, and λFBG is the center wavelength of the FBG. λFBG is sensitive to the changes of temperature and bending, which can be expressed as^[30,31]ΔλFBGλFBG=(α+ξ)ΔT+(1−Pe)ε,ε=dR,(7)where α and ξ are the coefficient of thermal expansion and the thermal optical coefficient, respectively, ΔT is the variation of temperature, and Pe is the elastic-optic coefficient. ε represents the strain of FBG, R is the bending radius of FBG, and d is the distance from the FBG to the neutral plane.

According to Eq. (5), when the external temperature changes or a curvature is applied to the MZI sensor, the wavelength of the interference dip will shift, and it can be described by ΔλMZI=kC1ΔC+kT1ΔT,(8)where kC1 and kT1 are the sensitivities of the MZI to the curvature change ΔC and temperature change ΔT, respectively. Similarly, the wavelength response of the FBG can be expressed as ΔλFBG=kC2ΔC+kT2ΔT,(9)where kC2 and kT2 are the sensitivities of the FBG to the curvature change ΔC and temperature change ΔT, respectively.

Though the spectra of the MZI and FBG shift with the changes of bending and temperature, the two sensing elements exhibit different sensitivities. By measuring the interference dip of the MZI and the resonant wavelength of the FBG, the curvature and temperature can be measured simultaneously, which can be expressed by the following matrix: [ΔCΔT]=[kC1kT1kC2kT2]−1[ΔλMZIΔλFBG].(10)

The matrix coefficients can be obtained by experimentally measuring the curvature and temperature sensitivities of the MZI and FBG.

In this section, the curvature and temperature responses of the proposed sensor are studied. Figure 3 shows the experimental setup used, including a demodulation system (Micron Optics, SM 125) with a resolution of 0.001 nm and 0.01 dB, an isolator, two 3-axis displacement platforms (Thorlabs, MBT616D/M), two fiber rotators (Thorlabs, HFR007), and a hot plate. The transmission and reflection spectra are recorded simultaneously through the isolator and the two ports of the demodulation system.

In the curvature sensing experiment, the experimental device was built on a stable optical table, and the ambient temperature was maintained at room temperature of ∼20°C. During the experiment, the sensor head was mounted on the hot plate, and both ends of the sensor were fixed by 3-axis displacement platforms equipped with fiber rotators. The heights of the two platforms were adjusted to match that of the hot plate. One displacement platform was fixed, while the other was movable to squeeze the sensor and induce the bending. The curvature C was calculated using the following formula^[32]: C=1R≈24xL03,(11)where C is the curvature, L0 is the initial distance between the two rotators (L0=180mm), and x is the displacement distance. The curvature is applied by displacing the micrometer inward on the displacement platforms with each step of 40 µm.

Before the curvature experiment, the bending direction of the SCF was marked with optical tape and confirmed using a microscope. The bending direction was controlled by adjusting the fiber rotators. The fiber rotators rotated 30° per adjustment, and the bending direction of the sensor was defined as illustrated in the inset of Fig. 3.

Figures 4(a) and 4(b) depict the transmission spectra of the MZI interference dips and the reflection spectra of the FBG reflection peaks under various curvatures when the sensor is bent along the 30° direction. It is noted that the transmission spectra were processed using fast Fourier transform (FFT) filtering and smoothing to eliminate noise signals^[33]. The results illustrate that, as curvature increases, there is a significant red-shift in the MZI interference dips, while the shift of the FBG reflection peaks is relatively small. Additionally, two reflection peaks are observed in the FBG, attributed to the lateral stress exerted by bending on the fiber. This stress causes strain-induced birefringence, leading to the splitting of the reflection peaks^[34].

Figures 4(c) and 4(d) illustrate the responses of the MZI interference dip wavelengths and the FBG reflection peak wavelengths to curvature. Through linear fitting, the curvature sensitivities of the MZI interference dip, FBG reflection Peak1, and Peak2 are 25.782nm/m−1, 57pm/m−1, and 48pm/m−1, respectively, within the curvature range of 0–1.518m−1.

Moreover, the transmission spectra of the MZI interference dip along different bending directions (30°, 90°, 240°, and 270°) can be obtained by adjusting the fiber rotator, as shown in Figs. 5(a)–5(d). The arrows clearly show that the MZI interference dip shifts to different directions. This is due to the asymmetric structure of the SCF, allowing the sensor to recognize the bending directions. When the sensor head is bent along the smaller cores (cores 5 and 6) on the lower right side, the smaller fiber core will be stretched, while the larger core (cores 2 and 3) on the upper left side will be compressed. This deformation causes a change in the stress distribution of the cores, resulting in an increase in the effective refractive index for the smaller cores and a decrease in the effective refractive index for the larger cores, respectively^[15]. From Eq. (3), it can be seen that the transmission spectra have a red shift with bending, and vice versa. In addition, the wavelength shifts of the MZI interference dip are calculated and plotted in Fig. 6 when it is bent along these four directions. As shown in Fig. 6, the proposed sensor has the red-shift of the spectra with bending with bending sensitivities of 20.838 and 8.289nm/m−1 along the bending direction of 30° and 270°, respectively. But it has the blue-shift and bending sensitivities of −9.685 and −6.429nm/m−1 along the bending direction of 90° and 240°, respectively. Such observation is well matched with the simulated results in Fig. 7 by the beam propagation method. The simulated results in Fig. 7 clearly show that the variation of the bending direction will result in the shift with different trends, further validating the experimental results in Fig. 5. It is worth noting that the linearity (R2) of the curvature response varies across bending directions. In particular, lower fitting accuracy observed at 90° and 270° may be attributed to fabrication-related asymmetries and defects, such as core distribution imbalance and local structural defects visible in Fig. 2.

To investigate the temperature response of the proposed sensor, it was placed horizontally on a hot plate for temperature control. And a digital thermometer with a resolution of 0.1°C was used to monitor and calibrate the temperatures of the sensor head during the experiment. The temperature was varied from 20.0°C to 110.0°C with each increment of 10.0°C. To mitigate the effects from an uneven temperature field, the system was stabilized for 5 min at each set temperature.

Figures 8(a) and 8(b) display the spectra of the MZI interference dips and FBG reflection peaks in the sensor within the temperature range of 20.0°C–110.0°C. As the temperature increases, both the MZI interference dips and the two FBG reflection peaks red shift. The wavelengths of the MZI interference dip, FBG-Peak1, and FBG-Peak2 at different temperatures are plotted in Figs. 8(c) and 8(d), respectively. Through linear fitting, the temperature sensitivities of the MZI interference dip, FBG-Peak1, and FBG-Peak2 are 34, 11, and 11 pm/°C, respectively. Clearly, the temperature sensitivities of FBG-Peak1 and FBG-Peak2 are identical, while that of the MZI interference dip is slightly higher than those of the FBG peaks.

The experimental results above reveal the distinct temperature and curvature responses of the MZI and FBG, enabling dual-parameter sensing. According to Eq. (10), the proposed sensor can simultaneously demodulate changes in both curvature and temperature by constructing a sensitivity coefficient matrix as shown below: [ΔCΔT]=[25.7820.0340.0570.011]−1[ΔλMZIΔλFBG],(12)and thus [ΔCΔT]=[0.039−0.121−0.20291.535][ΔλMZIΔλFBG].(13)

According to the matrix equation in Eq. (13), the curvature and temperature can be determined through the measurement of the wavelength shifts of the MZI and FBG. In the experiment, the sensing resolution is constrained by the wavelength resolution of the SM125, which is 1 pm. Consequently, the curvature and temperature measurement resolutions are deduced to be 0.000082m−1 and 0.091333°C, respectively.

The dual-parameter sensing performance of the proposed sensor was experimentally verified by measuring its response to curvature at a constant temperature of 50.0°C and to temperature variations at a constant curvature of 1.148m−1, respectively. As illustrated in Fig. 9, the calculated results from the experimental data correspond closely with the applied curvature and temperature values. The maximum errors were 0.022m−1 for curvature and 2.7°C for temperature, respectively. These experimental errors may result from non-ideal systems of temperature and curvature control. Temperature was regulated using a hot plate, which may have introduced slight thermal gradients. A precision temperature chamber will be considered in future work to further improve measurement accuracy.

To further evaluate the capability of the proposed sensor for simultaneous measurements, both curvature and temperature changes were applied simultaneously, and the results are shown in Fig. 10. Initially, the sensor was set to a temperature of 30.0°C and a curvature of 0.574m−1, and the resulting wavelength shifts of MZI interference dips and FBG reflection peaks were measured. The temperature was subsequently increased to 40.0°C while maintaining the curvature at 0.574m−1, followed by an adjustment of the curvature to 0.703m−1, with wavelength shifts measured at each stage. Then, using Eq. (13), the wavelength shifts were converted to the corresponding variations of the curvature and temperature, and simultaneous measurements were achieved as shown in Fig. 10. The experimental results also indicate that the root mean square deviations for curvature and temperature are ±0.007m−1 and ±0.9°C, respectively. In addition, to evaluate the sensing consistency, repeated measurements have been conducted, and the results have demonstrated acceptable repeatability. With improvements in fabrication techniques and experimental setup in the future, further enhancement in sensing stability and repeatability is anticipated.

Moreover, the proposed sensor is compared with curvature sensors of various structures as listed in Table 1. The FBG-based bending sensor^[35] offers a wide measurement range but has higher fabrication costs and lower curvature sensitivity than sensors based on mode interference, which have higher curvature sensitivity but a narrower measurement range^[36]. Sensors with symmetrical MCFs face challenges in direction recognition^[6,35–37], whereas those with asymmetrical structures or cores with different refractive indices can distinguish direction more effectively^[18–20]. Overall, the 3D-printed SCF sensor proposed in this study exhibits competitive measurement resolution and enables direction recognition through its asymmetric structure. Its fabrication process is comparatively simple, as it avoids tapering, offset splicing, and fan-in/fan-out couplers, thereby enhancing both structural stability and manufacturability. In addition, it offers a wider curvature measurement range and higher curvature sensitivity compared with the conventional designs. These advantages highlight its strong potential for applications in structural health monitoring, smart wearable devices, and aerospace engineering.

This study presents a dual-parameter sensor based on a 3D-printed SCF that simultaneously measures curvature and temperature. The experimental results indicate that, within the curvature range of 0–1.518m−1, the maximum curvature sensitivity of the MZI reaches 25.782nm/m−1 when bent along the 30° direction. The measurement resolutions for curvature and temperature are 0.000082m−1 and 0.091333°C, respectively. In dual-parameter simultaneous measurement with the random curvature and temperature setting, the root mean square deviations of the curvature and temperature are ±0.007m−1 and ±0.9°C, respectively. Compared to conventional sensors, the proposed sensor has a simpler manufacturing process, higher sensitivity, and a temperature compensation function. Although there remain many technical limitations in 3D printing optical fibers, the proposed 3D-printed dual-parameter sensor holds significant potential for applications in human posture detection, bridge and road construction, and structural health monitoring.