Systems and methods using a pair of rotated volume Bragg gratings for spectral phase modulation

A device comprising:

• two rotated volume Bragg gratings (r-VBGs) formed as planes of refractive index variation with periodicity along parallel grating vectors, wherein periods of the two r-VBGs are chirped along the respective grating vectors to vary along the respective grating vectors, wherein the two r-VBGs are spatially separated along a separation direction oriented at a nonzero angle relative to the grating vectors;
• and
• a phase modulator between the two r-VBGs with a spatially non-uniform phase distribution in a plane orthogonal to the separation direction;
• wherein a first of the two r-VBGs is configured to reflect portions of an input beam propagating along an incidence direction satisfying a Bragg condition into the separation direction towards the phase modulator as spectrally-spread beam, wherein the Bragg condition is satisfied for different wavelengths at different locations of the first r-VBG along the incidence direction to provide that a spectrum of the spectrally-spread beam is dispersed along the incidence direction;
• and
• wherein a second of the two r-VBGs is configured to reflect portions of the spectrally-spread beam satisfying the Bragg condition into the incidence direction, wherein the second r-VBG is positioned to provide that the Bragg condition is satisfied for different wavelengths at different locations of the first r-VBG along the incidence direction to provide that the spectrally-spread beam is spectrally recombined into an output beam.