Fig. 1. Geometry of the planar waveguide with the microprism array. L0, L1, L2, and L3 are the length of the total OFRS, grating, microprism array, and width of detector; h is the thickness of the planar waveguide; n0   and n1 are the refractive indices of the circumstance medium (air) and the optical waveguide, respectively; d is the width of the single microprism; and θ1 and θ2 are the slope angles of the two facets s1 and s2, respectively.

Fig. 2. Simulation model of a metallic grating. (a) 3D vision and (b) 2D vision of the front view. PR is photoresist (ARP 3500-6, Allresisit Co.). The symbols h2 and h1 represent the height of the grating and metal; θs represents the slant angle of the grating; Lu and Ld are the up and down length of the grating.

Fig. 3. −1st order diffraction efficiency spectra of TE and TM polarized light with different parameters. Spectra of (a) TE and (b) TM polarized light with parameters: dc=0.58; h2=370  nm; θs=0∼30°; and ΔL=0. Spectra of (c) TE and (d) TM polarized light with θs=25° in (a) and (b).

Fig. 4. Fingerprint images from the detector under prism angles θ=25° and 40° while θ1=1° and d=0.05  mm.

Fig. 5. (a) The light paths for different values of θ2, (b) the fingerprint images from the detector under θ2=0.5°, 1°, and 35° while d=0.05  mm and θ1=25°.

Fig. 6. Fingerprint images from the detector under different widths 0.05, 0.07, and 0.1 mm, of a single microprism.

Fig. 7. Fingerprint images from the detector under different divergent angles of light source, with θ1=25°, θ2=1°, and d=0.05  mm.

Fig. 8. Profile of the microprism with: (a) ideal angle and non-gap; (b) non-sharp vertex angle and a small gap between two adjacent microprisms. Fingerprint images from two sensors while the microprisms are not ideal: (c) the corner radius is 0.01 mm and (d) the distance between two microprisms is 0.03 mm.