Three-dimensional printed microcantilever with mechanical metamaterial for fiber-optic microforce sensing

Detection of micro–nano-force is important in many fields, including biomedicine,^1–4 cytology,^5–7 molecular chemistry,⁸ genetics (DNA),⁹ environmental detection (detection of bacteria),¹⁰ food industry (detection of micro-organisms),¹¹ nanoscale manufacturing,^12–14 and other fields. The commonly used microelectromechanical systems (MEMS) microforce sensors are badly affected by the large demodulation systems required, low detection sensitivity, and poor electromagnetic compatibility. In this respect, optical fiber sensors offer advantages that include stable operation, small size, high sensitivity, and resistance to electromagnetic interference.^15–18 It is also important to use optical fibers to replace the complex and huge optical path space required for the conventional sensors to reduce the device size. As a highly sensitive MEMS device, the microcantilever boasts no labeling requirements, real-time operation, precise positioning, and specific detection capabilities, and the optical fiber Fabry–Pérot interferometer (FPI) sensor configuration consisting of a microcantilever has garnered considerable research interest.^19–22 The most direct way to integrate a microcantilever beam with an optical fiber is to connect a commercial microcantilever beam probe to the optical fiber end face. Although microcantilever beams with various shapes that are made from different materials can be integrated into the optical fiber end face, each cantilever beam must be aligned accurately to the fiber end face using high-precision instruments and fixed with adhesives, consequently compromising the repeatability and the stability of the resulting sensor.

Optical fiber integrated microcantilever systems have been prepared by picosecond and femtosecond laser ablation techniques,^23–25 focused ion beam processing,²⁶ and other methods.^27–29 Because of the limited machining accuracy of these techniques, rough and thick surfaces are produced on the cantilever by picosecond laser ablation and stress sensing based on cantilever deformation is then affected by the surface quality. Femtosecond laser ablation reduces this roughness but increases the manufacturing time. Microcantilevers fabricated by a focused ion beam are smooth and thin, although the fabrication process requires expensive equipment and long manufacturing times. In contrast to the reduction technology, the femtosecond laser-induced two-photon polymerization (TPP) three-dimensional (3D) nanoprinting technology is based on the manufacturing principle of layer-by-layer stacking, which greatly improves the flexibility and forming ability for microstructure designs.^30,31 With the continuous development and improvement of the TPP 3D nanoprinting technology, the application of this technology has been greatly enriched and expanded, such as micro-optical devices, integrated optical devices, MEMS and biomedical devices, and other fields of application research. In 2018, Thompson et al.³² reported a microscale fiber-optic force sensor printed on fiber tip by TPP and realized a force resolution of 1.5 µN. In 2021, our group²⁰ reported a printed clamped-beam based fiber-optic force sensor and achieved a force resolution of 55 nN. In 2023, our group³⁰ proposed an optimized microcantilever based fiber-optic force sensor with a force resolution of 2.1 nN. With the growing maturity of and continuing improvements in the femtosecond laser-induced TPP 3D nanoprinting technology, mechanical metamaterials with designable internal unit structures have opened the door to exploration of special structural mechanical properties. Therefore, it is expected to adjust and control the overall performances of mechanical metamaterials through the design of the internal structures of artificial construction units, thus greatly expanding the design space for new materials.^33–35 

Herein, we combine the femtosecond laser-induced TPP 3D nanoprinting technology with mechanical metamaterials to fabricate the fiber end for a fiber-optic microforce sensor. The microcantilever beam constructed from the mechanical metamaterial shows good force sensitivity. The static mechanical properties of the proposed structure are analyzed by applying the finite element method (FEM) to the honeycomb structure of the cantilever beam. The elastic constant k of the fiber-optic microforce sensor can be adjusted by two orders of magnitude, from 0.165 to 46 N/m, and the cantilever geometry can be tailored to vary the mechanical properties of the probe and match the mechanical properties of relevant biological specimens. The resulting force resolution ranges down to 130 pN, which is much lower than the resolution of any other optical fiber microforce sensors reported to date. In addition, the optical fiber microforce sensor shows an ultra-high sensitivity of 154 nm/µN and thus has immense potential for use in biomechanics and materials measurement applications.

Honeycomb is a magical product of nature, with the largest available space, which can minimize the amount of material used, thereby achieving minimum weight and showing great mechanical potential. The structure of the cantilever beam adopts the metamaterial of honeycomb structure. The metamaterial of honeycomb structure is a new type of porous topological material, which has the advantages of variable topological structure, high specific stiffness, and high resilience.^37,38 By introducing it into the cantilever structure, the stiffness coefficient of the cantilever beam can be tuned in a wide range. By adopting the control variable method, the details of the microcantilever beam with a honeycomb structure are completely consistent except that the side length (a) and length of the cantilever beam (L) are different, as shown in Fig. 2. The cross-sectional area of the base under the cantilever beam is 60 × 60 µm², which can improve adhesion with the end face of the glass insert. By keeping the thickness to 5 µm, the side length of the honeycomb cell in the microcantilever beam increases from 0.5 to 15 µm and the beam length increases from 60 to 200 µm. The sensor design details are presented in the supplementary material, S1.

To study the static mechanical properties of the honeycomb cantilever probe, the FEM is implemented to establish force sensor models with different structural parameters for the same stress, and the simulation results from this model are shown in Fig. 2. The material parameters, which include Young’s modulus, the Poisson ratio, and the density of the polymer cantilever, are 2.34 GPa, 0.33, and 1499 kg m⁻³, respectively. A quantitative relationship is established between the microstructure size and the controllable elastic coefficient to predict the sensor size and guide preparation of the fiber-optic microforce sensor. The same microforce of 1 µN is applied to the probe, and the deformation of each area when subjected to this force is as shown in Figs. 2(a) and 2(c). The deformation increases with increasing honeycomb cell side length (a), and the deflection of the microcantilever beam is shown in Fig. 2(a). The relationship between a and the flexural elastic coefficient k of the cantilever beam, as illustrated in Fig. 2(b). Figure 2(c) shows that the deflection of the microcantilever beam increases with the length (L) of the cantilever beam, as shown in Fig. 2(d). The reason for this behavior is that a smaller side length (a) and smaller beam length (L) reduce the effective area of the cantilever beam. A smaller effective surface area for the cantilever beam enables greater flexural deformation and leads to higher sensitivity for the sensor. This result is consistent with the theoretical formula for a rectangular cantilever beam, which can provide theoretical guidance for the design of the required adjustment and control of the elastic coefficient k of the honeycomb cantilever beam. The illustration in Fig. 2(c) shows the parameters for each unit cell, as encircled by the red dotted line, including the edge width t, the edge length a, and the microcantilever thickness d. Because of the low stiffness of the polymeric materials used, the cantilever beam thickness d cannot be too small, and thus, a thickness of 5 µm was selected to ensure good support and high sensitivity for the cantilever beam. The edge width t of 0.5 µm was selected for the microcantilever beam structure in each of the following designs.

Figures 3(a)–3(h) show scanning electron microscopy (SEM) images of the microcantilever beam. Figures 3(a)–3(d) show the honeycomb cell lattices with side lengths of 4.5, 6, 8.5, and 15 µm, where the other parameters remain unchanged (L = 60 µm). When the honeycomb cell lattice side length is 15 µm, the beam lengths of microcantilever are 80, 100, 150, and 200 µm, as shown in Figs. 3(e)–3(h), respectively. The SEM images in Figs. 3(a)–3(h) show that the actual microcantilever beam size remains consistent with the designed size. The structure basically consists of three parts. At the bottom, the sectional area of the base is 60 × 60 µm², and at the top, the microcantilever is attached to a base with a width of 30 µm and a thickness of 5 µm. Above the cuboid block (15 × 30 × 5 µm³) at the end of the microcantilever beam, a probe with a height of 15 µm and a diameter of 4 µm is located for use in mechanical testing. The top view shows that the surface is smooth and confirms that the shape is complete. The rectangular block located at the end of the microcantilever blocks the fiber core to stimulate interference.

To determine the mechanical properties of the fiber-optic microforce sensor, a nano-indenter (Hysitron TI980) is used. A cone tip (tip radius: 10 µm) of this nano-indenter pushes and pulls at the center of the probe at a constant speed of 400 nm/s. The effects of the side length of the honeycomb cell and the beam length on the mechanical properties of the microcantilever structure are studied. The honeycomb cell side length is increased from 0.5 to 15 µm initially, and as shown in Fig. 3(i), the force curves of six sets of microcantilevers show well-separated line shapes. Figure 3(g) shows that the elastic constant k ranges from 0.98 to 46 N/m. As can be seen in Fig. 3(i), the elastic constant k (46 N/m) is the highest and the displacement is the shortest when the honeycomb cell side length is 0.5 µm. The main reason is that the smaller the honeycomb cell side length, the larger the effective width of the microcantilever beam and the larger the elastic constant k. The k value of the microcantilever is related to the sensitivity, and a smaller k value indicates higher sensitivity. In fact, k can be adjusted by two orders of magnitude by varying the honeycomb cell side length a, and the mechanical properties of the microforce sensor can also be optimized by adjusting the length L to match the mechanical properties of biological samples. In the next step, L is increased from 60 to 200 µm, and as shown in Fig. 3(k), the elastic constant k decreases gradually with the length L when the size of hexagonal honeycomb elements in the microcantilever beams remains constant. Figure 3(l) shows that the first-order elastic constant k ranging from 0.165 to 0.98 N/m is also observed. It can be seen from Fig. 3(k) that the elastic constant k (0.98 N/m) is the highest and the displacement is the shortest when L = 60 µm. Furthermore, the smallest elastic constant k (0.165 N/m) is close to the minimum value for the AFM tip, and the range realized for the overall elastic constant k basically covers that of a typical commercial AFM probe.^40,41 Finally, the stability of the microcantilever beam is evaluated by repeating the experiments above five times. Figures 3(m) and 3(n) show that the force curves of these five cycles overlap each other and that k remains constant (6.9 ± 0.2 N/m). The small fluctuations observed in the sensitivity confirm that the structure has excellent mechanical stability and resilience under compression conditions. All the k values are designated as linear fitted values for the structural compression process. Compared with the simulation results in Figs. 2(b) and 2(d), the k value measured in the experimental results is larger, which is mainly caused by the dimensional error of the preparation. This dimensional error is mainly caused by layer-by-layer printing and followed by structural shrinkage or deformation in development, which depends on the used laser power, scanning speed, surface tension of photoresist, and developer volatilization. Thus, these above fabrication parameters need to be repeatedly optimized to improve the printing quality.

The elastic properties, optical properties, and mechanical properties of the probe are determined next. The elastic properties of the honeycomb cantilever probe were discussed earlier, and the cantilever probe with the lowest elastic coefficient k is analyzed here. The morphology of the probe was examined by SEM, as shown in Figs. 4(a)–4(c). The honeycomb cantilever probe on the optical fiber end face is clearly visible in these images, and its morphology is maintained. The sensor fabrication details are presented in the supplementary material, S3. Figures 4(a)–4(c) show the SEM images at different angles, and a smooth surface and parallelism between the optical fiber end face and the microcantilever can be observed. The structure used here improves the intensity of the reflected light and the sensitivity of the device to deformation.

Figure 4(d) shows the reflection spectrum of the microcantilever beams. The interference spectrum shows three-beam interference formed by the resonances of three mirrors on the fiber end face and on the upper and lower surfaces of the microcantilever beam. The small envelope within the spectrum is formed by the F–P cavity of the air medium, which contains the deflection information of the microcantilever beam to be monitored. The free spectral range of the microcantilever near the wavelength of 1451.22 nm is 24.5 nm, and the extinction ratio is 9.6 dB. According to Eq. (1), the cavity length of the prepared microcantilever is ∼43 µm.

According to Eq. (2), the microforce sensitivity can be obtained based on the interference spectrum shift caused by the unit force of the honeycomb cantilever probe. The device test system consists of a broadband source (BBS), an optical spectrum analyzer (OSA), a 3 dB coupler, and a 3D electric displacement platform for micromanipulation, as shown in Fig. 5(b). A cover glass is placed on the sample holder, and the sensor probe is then placed on the cover glass surface such that the honeycomb structured cantilever beam deflects. The elastic coefficient k of the sensor probe is 0.165 N/m, as measured by in situ quantitative nano-indentation. The reaction force acting on the sensor probe is determined based on formula (3). Here, the elastic coefficient (k) of the microcantilever is 0.165 N/m, and the microcantilever probe is pressed with a phase-synchronous carry displacement each time, i.e., the bending deformation (d) of the microcantilever is 50 nm. According to Eq. (3), the microforce acting on the microcantilever beam is 8.25 nN at each step of 50 nm. During application of the progressive force, the reflection spectra are acquired in real time. Figure 5(a) shows the change in the reflection spectrum when the force is increased gradually from 0 to 66 nN. A blue shift can be observed clearly at the tilted wavelength, as indicated by the arrow. The extinction ratio of the reflection spectrum decreases with increasing force because of the bending action of the cantilever beam. The relationship between the dip wavelength and the force is shown in Fig. 5(c). The force exerted on the cantilever is translated into the spectral shift of the light reflection minima in the fiber tip. As the applied force increases, the interference spectrum shifts toward the left. Based on linear fitting of the dip wavelength change, the force sensitivity is calculated to be 154 nm/µN. The resolution of the force sensor is 130 pN under the limited resolution of 0.02 nm of the OSA.^42–44 In the microforce sensing measurement regime, the sensor probe works within the framework of the linear elastic range, and there exists no lag between the force and the change in the cavity length.

As shown in Table I, when compared with previous optical fiber sensors, the optical fiber sensor described in this paper shows superior sensitivity and other advantages that include flexible manufacturing capability, high mechanical strength, and ultra-low force resolution. The resulting force resolution ranges down to 130 pN, which is much lower than that reported previously for any other optical fiber microforce sensors. The proposed optical fiber force sensor is applicable to measurement of weak forces of the order of piconewtons (pN) for biological samples.

Femtosecond laser-induced TPP 3D nanoprinting technique is designed to print a fiber-optic microforce sensor on the end face of a single-mode fiber with a glass insert. The elastic constant k of the fabricated fiber-optic microforce sensor can be adjusted by two orders of magnitude from 0.165 to 46 N/m, and the geometric configuration of the cantilever beam can be tailored to match the mechanical properties of biological specimens. The all-fiber microforce sensor shows an ultra-high force sensitivity of 154 nm/µN and an ultra-low force resolution of 130 pN; these values are superior to those reported recently for similar optical fiber force sensors. Because of the flexibility of the polymeric materials used, the sensor shows excellent stability and repeatability over multiple mechanical cycles. The proposed sensor boasts advantages that include simple manufacturing, high sensitivity, high flexibility, and reproducibility, and it has excellent prospects for use in biomechanical detection.

See the supplementary material for the design and simulation and the materials and methods.

This work was supported by the Shenzhen Science and Technology Program (Grant No. RCYX20200714114524139), Shenzhen Key Laboratory of Ultrafast Laser Micro/Nano Manufacturing (Grant Nos. ZDSYS20220606100405013 and JCYJ20200109114001806), the Science and Technology Innovation Commission of Shenzhen (Grant No. JSGG20201102152200001), the Natural Science Foundation of Guangdong Province (Grant Nos. 2022B1515120061 and 2022A1515110971), the National Natural Science Foundation of China (Grant Nos. 62122057, 62075136, 62105217, and 62305223), and the China Postdoctoral Science Foundation (Grant No. 2022M722173).

The authors have no conflicts to disclose.

F.W. and M.Z. contributed equally to this work.

Famei Wang: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal). Mengqiang Zou: Conceptualization (equal); Resources (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (supporting). Changrui Liao: Conceptualization (equal); Funding acquisition (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal). Bozhe Li: Investigation (supporting); Software (supporting). Dejun Liu: Writing – review & editing (supporting). Jie Zhou: Data curation (supporting); Writing – review & editing (supporting). Haoqiang Huang: Investigation (supporting); Writing – review & editing (supporting). Jinlai Zhao: Investigation (supporting); Software (supporting). Chao Liu: Supervision (supporting); Writing – review & editing (supporting). Paul K. Chu: Writing – review & editing (supporting). Yiping Wang: Conceptualization (supporting); Funding acquisition (supporting); Project administration (supporting); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding authors upon reasonable request.