Fig. 2: Simulations of the mechano-sensor under an external force F_r.

a Schematic illustration of the experimental device and FEM model of the mechano-sensor under an external force F_r (φ = 180°). Inset: Top view of the mechano-sensor. b Schematic illustration of the deformation of the flexible microbubble under an external force F_r. Negative and positive radial strains are observed in the same and opposite directions of F_r, respectively. c Stress field distribution in the r-φ plane under an external force F_r (φ = 180°). d, e Field distributions of the radial strain and strain-induced effective refractive index change along the microbubble’s equatorial cross-section under an external force F_r (φ = 180°). The dR/R and dn_eff/n_eff values are the averages of their field distribution integrals. f Relations between the direction of the external force F_r and dR/R, dn_eff/n_eff, and the displacement sensitivity (S_D). g Comparisons of dR/R and dn_eff/n_eff between the microbubble-based mechano-sensor and the microsphere-based mechano-sensor under different external displacements (φ = 180°). h Relations between S_D and the capillary size (i.e., radius (R_capillary) and wall thickness (T_capillary)) under an external force F_r (φ = 180°). The solid black line corresponds to the contour of R_bubble = 190 μm. The star label corresponds to the R_capillary and T_capillary selected for the micro-hair. (i) Relations between S_D and the mechanical properties of the polymer matrix (i.e., Poisson’s ratio (υ) and elastic modulus (E)) under an external force F_r (φ = 180°).