\(k=\frac{2\pi}{\lambda}=ω\sqrt[]{ε_0μ_0}\) \(2α=\frac{\sqrt{\pi}κ^2\exp[-2/3(γ^3⁄\ (β_g^2))R]}{e_vγ^{3/2}V^2\sqrt{R}K_{\left(v-1\right)}(γa)K_{\left(v+1\right)}(γa)}\)

 

Here,  is the amplitude-loss coefficient,  is the propagation constant of the guided mode, R is the bending radius, a is the radius of the fiber,  is the order of guided mode and  is the solution of Bezier’s equation.

With k=λ2π=ωε0μ0 ,

                         (2)

.                        (3)

                          (4)

and

                        (5)

n₁ and n₂ is defined to be the refractive index of the fiber core and the cladding, respectively.

From equation (1), we can see that the bending loss is negatively correlated with the bending radius. Figure S1 shows the COMSOL simulated cross section of the filmy sensor under pressure. The centered white line is the optical nanofiber. Since the thickness of the PDMS membranes (400 μm) is much larger than the diameter of optical nanofiber (800 nm), the influence of the optical nanofiber on the overall deformation of the filmy sensor can be ignored.

The shape of the cross section of the filmy sensor can be considered as the combination of two identical S-bends, which consists of four identical arcs with bending radius R. The total length of the filmy sensor L is set to be 6 mm, which corresponds to the size of sac base. The simulated amount of vertical displacement d and the corresponding calculated bending radius R under different pressure are as listed. According to the simulated and calculated results, the bending radius decreases as the applied pressure increases. Therefore, a greater transmission loss in the optical nanofiber is achieved with greater applied pressure.

Figure S2 Photograph of the testing system for force-intensity calibration. The intender has a diameter of 2 mm.

 

 

Figure S3 The wavelength-dependent transmittance response to different temperatures of NFPSU.

 

 

Figure S4 Schematic diagram of entire testing system for controlling robotic hand with gesture-recognition wristband. (SVM: support-vector machine)