Tailoring nondiffracting fields with a non-Markovian phase imprint.

We experimentally generate nondiffracting speckles that carry non-Markovian properties by encoding the wavefront of a monochromatic laser beam with ring-shaped non-Markovian phases. The resulting non-Markovian nondiffracting fields present a ring-shaped pattern and central dark notches, which are analyzed with an expression of the orbital angular momentum spectra of the wavefront possessing ring-shaped non-Markovian phases. Furthermore, we demonstrate that the intensity profiles of these non-Markovian nondiffracting fields exhibit stability over multiple Rayleigh ranges, and their statistical properties could be controlled with the non-Markovianity of the input phase masks. This work presents an approach for simultaneously tailoring the diffracting property and non-Markovianity of optical fields and provides a deeper understanding of non-Markovian processes.