Spectral hole burning for pulse repetition frequency analysis

We demonstrate an optical processor based on spectral hole burning (SHB) that maps the carrier frequency into the time domain and the pulse repetition frequency (PRF) into the spatial domain by illuminating an SHB crystal with a signal beam that is scanned by a tilting mirror across a slice of the crystal. This time-to-space mapping makes it possible to measure signal envelopes with a resolution of image. A signal with a pulsed envelope engraves a vertical absorption grating with a spatial periodicity given by the product of the PRF and the scan velocity. Reading the grating, which the crystal stores for up to image, with a collimated beam yields orders diffracted at angles proportional to the PRF, which are Fourier-transformed to produce spots displaced from the DC position by distances proportional to the PRF. Increasing the PRF increases the grating periodicity, causing the diffracted spots to move away from the DC position.