Silicon phase-shifted grating has good wavelength selectivity.Through the coupling equations of phase-shifted grating

the impact of different phase-shift values and grating lengths on the reflectivity of phase-shifted grating has been discussed.By introducing chirp and apodization method

the purpose of broadening the bandwidth

suppressing the side-lobe and the timedelay can be achieved.We design and simulate a silicon phase-shifted chirp apodization grating with 0.18 nm bandwidth and -3 795 ps/nm time delay

which provide the theory foundation for wavelength-controllable coupler and wavelength filter.