Fig. 1. (a) Experimental setup of the new SPR refractive index sensing system based on the phase and angular interrogations. P1 and P2 are the Glan prisms, M is the mirror, LA is the lens array of the telescopic system, BS is the beam splitter, PBSC is the polarizing beam splitter cube, PM1 and PM2 are the power meters, the geometry of light reflected twice in the orthogonal box is shown in the right side. (b) The three-dimensional structure of the sample box. (c) The details of the sample box.

Fig. 2. Theoretical calculations of the reflectivity and phase angle of the p-polarized light. The samples are water and ethanol in the new system. The wavelength of the He–Ne laser is 632.8 nm, and the refractive indices of glass, water, ethanol, Ag, and air are 1.516, 1.333, 1.362, 0.0564+4.271i^[30], and 1, respectively. The thickness of the Ag film is 50 nm, and the thickness of the glass slide is 170 μm.

Fig. 3. (a) The phase relations between the s- and p-polarization components in the SPR system. Polarizers 1 and 2 are placed vertically. (b) The geometry of the linear polarization interference.

Fig. 4. (a) The interference intensity and the reflectivity of the p-polarization component at different incident angles. The wavelength of He–Ne is 632.8 nm, and the refractive indices of water, Ag, and air are 1.333, 0.0564+4.271i, and 1, respectively. The thickness of the Ag film is 50 nm. (b) The corresponding phase difference at different incident angles, where (a) and (b) are the sign change and (b) and (c) are the 2π jump of the phase angle. The final corresponding phase of the p-polarization component considering the above factors is shown in the inset.

Fig. 5. The reflection intensity, the interference intensity, and the corresponding phase angle of deionized water and different ethanol solutions with concentrations from 0.2% to 1%. The angle of the rotation stage is set at the SPR angle of the deionized water.

Fig. 6. The connected quasi-linear phase ranges and the relationship between the accumulated phase angle and the SPR angle (inset).

Fig. 7. (a) Reflection intensity and interference intensity of deionized water, ethanol, and dichloromethane. The markers are the experimental data, and the solid lines are the numerical fitting. (b) The corresponding phase angles (blue) at different incident angles of deionized water, ethanol, and dichloromethane. The normalized reflection intensities (black) are shown at the same time to indicate the SPR angles.

Fig. 8. The fitted data of reflectivity and the derivative data of the phase angle from the experimental data of ethanol.