1. Date of download: 5/28/2016 Copyright © 2016 SPIE. All rights reserved. Refractive index profile for (a) conventional singly π-phase-shifted FBG (i.e., a single π phase shift occurring at L∕2), (b) multiply π- phase-shifted FBG (here, three π phase shifts located at L∕4, L∕2, and 3L∕4), and (c) π-phase-sampled FBG. (d), (e), and (f) are the transmission spectra of (a), (b), and (c), respectively. Figure Legend: From: Design of superstructure fiber Bragg gratings with a Fourier analysis technique and its applications to multiple ultranarrow transmission gratings Opt. Eng. 2008;47(11):115001-115001-7. doi:10.1117/1.3006090

2. Date of download: 5/28/2016 Copyright © 2016 SPIE. All rights reserved. Schematic diagram of SFBG spatial corrugation: (a) square amplitude sampling, (b) single phase sampling at θ, and (c) multiple phase sampling at 0,θ,2θ,3θ,…. Figure Legend: From: Design of superstructure fiber Bragg gratings with a Fourier analysis technique and its applications to multiple ultranarrow transmission gratings Opt. Eng. 2008;47(11):115001-115001-7. doi:10.1117/1.3006090

3. Date of download: 5/28/2016 Copyright © 2016 SPIE. All rights reserved. Spatial Fourier spectra of phase-sampling grating as shown in Fig. : (a) arbitrary θ, (b) θ=π, and (c) θ=0. In the case of θ=0, we have the uniform FBG without sampling. The bars with spacing 2π∕L1 represent the Fourier spectral lines. Figure Legend: From: Design of superstructure fiber Bragg gratings with a Fourier analysis technique and its applications to multiple ultranarrow transmission gratings Opt. Eng. 2008;47(11):115001-115001-7. doi:10.1117/1.3006090

4. Date of download: 5/28/2016 Copyright © 2016 SPIE. All rights reserved. (a) Shows the profile of refractive index and phase for the multiple-phase-sampling FBG with phases 0, θ, and 2θ. (b), (c), and (d) are three independent interleaved SFBGs yielding (a). (e) is the Fourier spectral profile for (b) to (d). (f) is the Fourier spectral profile for Fig.. Figure Legend: From: Design of superstructure fiber Bragg gratings with a Fourier analysis technique and its applications to multiple ultranarrow transmission gratings Opt. Eng. 2008;47(11):115001-115001-7. doi:10.1117/1.3006090

5. Date of download: 5/28/2016 Copyright © 2016 SPIE. All rights reserved. Illustration of Fourier transformation between real space and frequency space. (a) and (c) are the rectangle sampling and sinc- shape sampling, respectively. (b) and (d) are the spatial Fourier spectra of (a) and (c), respectively. Figure Legend: From: Design of superstructure fiber Bragg gratings with a Fourier analysis technique and its applications to multiple ultranarrow transmission gratings Opt. Eng. 2008;47(11):115001-115001-7. doi:10.1117/1.3006090

6. Date of download: 5/28/2016 Copyright © 2016 SPIE. All rights reserved. Illustration of Fourier transformation between the real space and the frequency space. (a) and (c) are the refractive index profiles n(z) with the uniform distribution. There is a π phase shift in (c). (b) and (d) are the spatial Fourier spectra of (a) and (c), respectively. Figure Legend: From: Design of superstructure fiber Bragg gratings with a Fourier analysis technique and its applications to multiple ultranarrow transmission gratings Opt. Eng. 2008;47(11):115001-115001-7. doi:10.1117/1.3006090

7. Date of download: 5/28/2016 Copyright © 2016 SPIE. All rights reserved. Illustration for the Fourier analysis of the traditional SFBG. Figure Legend: From: Design of superstructure fiber Bragg gratings with a Fourier analysis technique and its applications to multiple ultranarrow transmission gratings Opt. Eng. 2008;47(11):115001-115001-7. doi:10.1117/1.3006090

8. Date of download: 5/28/2016 Copyright © 2016 SPIE. All rights reserved. Illustration for the Fourier analysis of the proposed SFBG. Figure Legend: From: Design of superstructure fiber Bragg gratings with a Fourier analysis technique and its applications to multiple ultranarrow transmission gratings Opt. Eng. 2008;47(11):115001-115001-7. doi:10.1117/1.3006090

9. Date of download: 5/28/2016 Copyright © 2016 SPIE. All rights reserved. Transmission spectrum for the proposed SFBGs (a) without a π phase shift and (b) with a π phase shift at the center of the grating. In (a), the two insets are the Fourier components at m=±1. In (b), the four insets are the Fourier components at m=±1 and ±3. Because L2=1.5L1, the components at m=±2,±5,±8,… disappear. The Fourier components at m=1,2,3,… are the same as at m=−1,−2,−3,…. Figure Legend: From: Design of superstructure fiber Bragg gratings with a Fourier analysis technique and its applications to multiple ultranarrow transmission gratings Opt. Eng. 2008;47(11):115001-115001-7. doi:10.1117/1.3006090

10. Date of download: 5/28/2016 Copyright © 2016 SPIE. All rights reserved. Transmission spectrum (a) from the Fourier analysis (i.e., α=π) and (b) after the appropriate adjustment (i.e., α≈1.02π). The theoretical result is simulated from the coupled-mode theory. Figure Legend: From: Design of superstructure fiber Bragg gratings with a Fourier analysis technique and its applications to multiple ultranarrow transmission gratings Opt. Eng. 2008;47(11):115001-115001-7. doi:10.1117/1.3006090

11. Date of download: 5/28/2016 Copyright © 2016 SPIE. All rights reserved. Transmission spectrum for the proposed SFBGs, incorporating a π phase shift at the center of the grating. Figure Legend: From: Design of superstructure fiber Bragg gratings with a Fourier analysis technique and its applications to multiple ultranarrow transmission gratings Opt. Eng. 2008;47(11):115001-115001-7. doi:10.1117/1.3006090