Abstract: Techniques for designing efficient gratings with multiple frequency response channels based on sampled patterns based predominantly on phase modulation of the underlying grating structure. Each period of the phase sampled patterns may include contiguous, discrete phase segments with different phase values, or alternatively, a continuous spatial phase pattern that changes the phase of the underlying grating structure. Moderate amplitude modulation of the underlying grating structure by the sampling structure may also be used together with phase modulation. The grating period or the sampling period may be chirped.