1. Date of download: 6/24/2016 Copyright © 2016 SPIE. All rights reserved. Schematic diagram of rectangle diffraction phase grating with depth h, period Λ, fill factor f, and refractive index ng. A plane wave is incident at the angle θ0. Figure Legend: From: Numerical calculation of the accuracy of approximate analysis methods for binary rectangular groove diffraction phase grating Opt. Eng. 2012;51(12):128001-128001. doi:10.1117/1.OE.51.12.128001

2. Date of download: 6/24/2016 Copyright © 2016 SPIE. All rights reserved. Diffraction efficiency as a function of the fill factor and the groove depth at the grating period of 1000 nm for the −1 order. (a) TE polarization, (b) TM polarization. Figure Legend: From: Numerical calculation of the accuracy of approximate analysis methods for binary rectangular groove diffraction phase grating Opt. Eng. 2012;51(12):128001-128001. doi:10.1117/1.OE.51.12.128001

3. Date of download: 6/24/2016 Copyright © 2016 SPIE. All rights reserved. Transmittance ηm as a function of the normalized period of grating, m stands for the diffraction orders, e.g., 0th order, −1 order, and +1 order. The incident angle of θ0=0 deg 40 deg, and 80 deg, respectively, is shown in each of diffraction orders. The fill factor is fixed at 0.5, and the normalized groove depth is 0.5λ. (a)–(c) shows the refractive index of 1.5; (d)–(f) indicates the refractive index of 2.5; (g)–(i) demonstrates the refractive index of 4.0. Figure Legend: From: Numerical calculation of the accuracy of approximate analysis methods for binary rectangular groove diffraction phase grating Opt. Eng. 2012;51(12):128001-128001. doi:10.1117/1.OE.51.12.128001

4. Date of download: 6/24/2016 Copyright © 2016 SPIE. All rights reserved. Transmittance comparison between Fourier modal method (FMM) and scalar diffraction theory (SDT) for +1 order diffraction as a function of (a) the normalized period and (b) the normalized depth. (a)h=0.5λ, (b) Λ=5.0λ. Figure Legend: From: Numerical calculation of the accuracy of approximate analysis methods for binary rectangular groove diffraction phase grating Opt. Eng. 2012;51(12):128001-128001. doi:10.1117/1.OE.51.12.128001

5. Date of download: 6/24/2016 Copyright © 2016 SPIE. All rights reserved. Error of zero order diffraction efficiencies versus normalized period with the fixed normalized depth of 0.5λ and the fill factor of 0.5 for three incident angles. (a) ng=1.5, (b) ng=3.42. Figure Legend: From: Numerical calculation of the accuracy of approximate analysis methods for binary rectangular groove diffraction phase grating Opt. Eng. 2012;51(12):128001-128001. doi:10.1117/1.OE.51.12.128001

6. Date of download: 6/24/2016 Copyright © 2016 SPIE. All rights reserved. Error of zero order diffraction efficiencies versus normalized depth with the fixed normalized period of 5.0λ and the fixed fill factor of 0.5. (a) ng=1.5, (b) ng=3.42. Figure Legend: From: Numerical calculation of the accuracy of approximate analysis methods for binary rectangular groove diffraction phase grating Opt. Eng. 2012;51(12):128001-128001. doi:10.1117/1.OE.51.12.128001

7. Date of download: 6/24/2016 Copyright © 2016 SPIE. All rights reserved. %Error versus angle of incidence for a lower refractive index and a higher refractive index, respectively, with the different fill factor. The normalized depth is 0.5λ, and the normalized period is 5.0λ. (a) ng=1.5, (b) ng=3.42. Figure Legend: From: Numerical calculation of the accuracy of approximate analysis methods for binary rectangular groove diffraction phase grating Opt. Eng. 2012;51(12):128001-128001. doi:10.1117/1.OE.51.12.128001

8. Date of download: 6/24/2016 Copyright © 2016 SPIE. All rights reserved. Comparison of transmittances between Fourier modal method (FMM) and effective medium theory (EMT) as a function of the normalized period with the element refractive index of 1.5 for the different incident angle and polarization state. The fill factor is fixed at 0.5, and the normalized depth is 0.5. (a)–(c) for TE polarization at θ0=0 deg 10 deg, and 20 deg, respectively; (d)–(f) for TM polarization at θ0=0 deg, 10 deg, and 20 deg, respectively. Figure Legend: From: Numerical calculation of the accuracy of approximate analysis methods for binary rectangular groove diffraction phase grating Opt. Eng. 2012;51(12):128001-128001. doi:10.1117/1.OE.51.12.128001

9. Date of download: 6/24/2016 Copyright © 2016 SPIE. All rights reserved. Comparison of transmittances between Fourier modal method (FMM) and effective medium theory (EMT) as a function of the normalized period. The parameters are the same as Fig. 10 except for the refractive index of 3.42. Figure Legend: From: Numerical calculation of the accuracy of approximate analysis methods for binary rectangular groove diffraction phase grating Opt. Eng. 2012;51(12):128001-128001. doi:10.1117/1.OE.51.12.128001

10. Date of download: 6/24/2016 Copyright © 2016 SPIE. All rights reserved. % Error of transmittances between Fourier modal method (FMM) and effective medium theory (EMT) as a function of the normalized period with the different incident angles. The normalize depth of element is 0.5, and the fill factor is 0.5. (a) and (c) ng=1.5 for TE polarization and TM polarization; (b) and (d) ng=3.42 for TE polarization and TM polarization. Figure Legend: From: Numerical calculation of the accuracy of approximate analysis methods for binary rectangular groove diffraction phase grating Opt. Eng. 2012;51(12):128001-128001. doi:10.1117/1.OE.51.12.128001

11. Date of download: 6/24/2016 Copyright © 2016 SPIE. All rights reserved. %Error of transmittances between Fourier modal method (FMM) and effective medium theory (EMT) as a function of the normalized depth with the different incident angle, the fill factor is fixed at 0.5. (a) and (b) ng=1.5 for TE and TM polarization, respectively, with the normalized period of 0.4λ; (c) and (d) ng=3.42 for TE and TM polarization, respectively, with the normalized period of 0.1λ. Figure Legend: From: Numerical calculation of the accuracy of approximate analysis methods for binary rectangular groove diffraction phase grating Opt. Eng. 2012;51(12):128001-128001. doi:10.1117/1.OE.51.12.128001