Fig. 1. Diagram of the FMF cross-section structure. (a) Geometrical structure and relative refractive index difference profile; (b) scanning electron microscope micrograph

Fig. 2. Structure of the SFS

Fig. 3. Simulation curves of the propagation constant difference Δβ of LP01 and the LP02 modes propagating in the FMF, and the transmission spectrum of the SFS structure (LFMF=50 cm) under the temperature of 25 ℃ versus wavelength

Fig. 4. Simulation curves of the propagation constant difference Δβ of the LP01 and LP02 modes propagating in the FMF, and the transmission spectra of the SFS structure (LFMF=16 cm) versus wavelength when temperature changes. (a) Δβ without thermal stress; (b) Δβ with thermal stress; (c) transmission spectra without thermal stress;(d) transmission spectra with thermal stress

Fig. 5. Experimental transmission spectra of the SFS structure (LFMF=16 cm) and critical wavelength shifts when temperature changes. (a) Experimental transmission spectra of the SFS structure; (b) critical wavelength shift versus temperature

Fig. 6. Transmission spectra of the SFS structure (LFMF=50 cm) versus temperature

Fig. 7. Simulated and experimental results of temperature sensitivity of the interference fringes in the transmission spectrum of the SFS structure

Fig. 8. Simulation curves of propagation constant difference Δβ of the LP01 and LP02 modes propagating in the FMF under axial strain variation

Fig. 9. Results of experimental measurements. (a) Transmission spectra of the SFS structure (LFMF=30 cm) under axial strain variation; (b) critical wavelength shift of CWL versus axial strain

Fig. 10. Relationship between axial strain sensitivity of the interference fringes in the transmission spectrum of the SFS structure and normalized wavelength

Fig. 11. Output of sensor containing the SFS structure (LFMF=20 cm) varies with temperature and axial strain. (a) Wavelength shifts for PH, 1 and PL, 1 over a 30-min period of the experiment; (b) curves of the applied and calculated axial strains over that time; (c) curves of the applied and calculated temperatures

Fig. 12. Sensor outputs of the polyimide-coated SFS structure (LFMF=15 cm) under relative humidity variation. (a) Transmission spectra; (b) wavelength shifts of interference dips DL, 1, DL, 2, DL, 3, and DL, 4

Fig. 13. Simulation of the propagation constant difference Δβ of LP01 and LP02 modes, and the transmission spectra of the SFS structure (LFMF=35 cm) versus wavelength with different equivalent curvatures of the FMF

Fig. 14. Experimental results of the transmission spectra of the SFS structure (LFMF=35 cm) versus wavelength with different curvatures of the FMF

Fig. 15. Simulation and experimental results of the critical wavelength shift versus equivalent curvature of the FMF

Fig. 16. Displacement sensor with large measurement range based on the SFS structure (LFMF=10 cm). (a) Experimental diagram; (b) experimental setup; (c) geometrical mathematical model of circular helix

Fig. 17. Large displacement sensor based on the SFS structure (LFMF=10 cm). (a) Transmission spectra under different displacements; (b) change of the FMF equivalent curvature and shifts of the critical wavelengths under displacement variation

Fig. 18. Simulation of the critical wavelength shifts in the transmission spectra of the etched SFS structure with different dFMF. The inset is the simulation of the propagation constant difference of the LP01 and LP02 modes versus wavelength with different dFMF

Fig. 19. Transmission spectra of the etched SFS structure (LFMF=20 cm, dFMF=21.3 μm) under different SRIs. (a) SRI is 1.316;(b) SRI is 1.383;(c) SRI is 1.423;(d) SRI is 1.439

Fig. 20. Experimental results (marked with error bars) of the critical wavelength shift in the transmission spectrum of the etched SFS structure under surrouding refractive index variation

Fig. 21. Simulation of the transmission spectra of the etched SFS structure (dFMF=21.3 μm, LFMF=20 cm) and shifts of the critical wavelength and the interference peaks/dips under surrounding refractive index variation. (a) Shifts of the critical wavelength and the interference peaks/dips (DL,1, PL,1, PH,1, DH,1) on each side of the critical wavelength; (b) transmission spectra under the SRIs of 1.350, 1.355, and 1.360

Table 1. Summary of the SFS sensing structure with critical wavelength and its applications in different sensing parameters