Fig. 1. Schematic of a typical GMR sensor and the incident light propagation path under oblique incidence. It usually consists of substrate, waveguide, grating, and cover medium. Light of wavelength λ is incident on the structure; part of the light undergoes reflection (R) and transmission (T), while the remaining light is coupled into the waveguide through the +1st and −1st diffraction orders to form guided modes.

Fig. 2. Calculated sensitivity heatmap of the GMR sensor about grating period and waveguide thickness: (a) TE±1st; (b) TM±1st; (c) TE−1st; (d) TM−1st; (e) TE+1st; (f) TM+1st.

Fig. 3. GMR sensitivity as a function of incident angle. The grating period and waveguide thickness are 720 nm and 200 nm, respectively; calculated “zero angles” are 7.23° (TE) and 15.98° (TM), and “critical angles” are 14.79° (TE) and 34.73° (TM), respectively.

Fig. 4. GMR sensitivity of TM+1st mode as a function of waveguide thickness. Grating height is 10 nm, 30 nm, 60 nm.

Fig. 5. GMR sensitivity of TM+1st mode versus waveguide thickness. (a) Grating filling factor is 0.3, 0.5, and 0.7; (b) grating refractive index is 2.12 and 1.60; (c) grating profile is rectangular and sinusoidal.

Fig. 6. Calculated resonance wavelength versus the effective refractive index of the guided mode: (a) TM±1st; (b) TM+1st; (c) TM−1st. Insets are enlarged areas of the red circles.

Fig. 7. (a) Photograph of the fabricated GMR sensor; (b) 3D image of the holographic grating pattern obtained by AFM; (c) profile of the holographic grating scanned by AFM; the measured grating period is 722.5 nm, and grating depth is 89.50 nm.

Fig. 8. Schematic illustration of the experimental setup for measuring the reflectance spectra of the GMR sensor.

Fig. 9. (a) GMR reflection spectra of TE mode at normal incidence, with the refractive index of the aqueous solutions varying from 1.333 to 1.388 with a step of 0.0136. Inset: resonance spectra simulated by FDTD Solutions. (b), (c) Experimental reflection spectra for TM+1st at 10° and TE−1st at 40°. (d) Resonance wavelength change versus refractive index. Blue dots are experimental resonance wavelength, and red dots are calculated resonance wavelength by FDTD Solutions. Lines are linear fittings representing sensitivity.

Fig. 10. GMR sensitivity as a function of incident angle. The solid lines are calculated curves by the proposed theory (T), and the scattered points are the measured values in the experiment (E).