A method for forming planar-waveguide Bragg grating in a curved waveguide comprises: forming a long chirped planar-waveguide Bragg grating in an Archimedes' spiral such that a long length of the waveguide can fit in a small chip area where the grating is formed in the curved waveguide; using periodic width modulation to form the planar-waveguide Bragg grating on the curved waveguide, and where the formation of the periodic width modulation occurs during the etching of the waveguide core; using rectangular width modulation to create Bragg gratings with a higher order than 1st order to allow a larger grating period and larger modulation depth, using waveguide width tapering while keeping the width modulation period constant to introduce chirp to the planar-waveguide Bragg grating where the index of refraction is a function of waveguide width, by applying a specific width tapering to create a desired arbitrary chirp profile.