A method to engineer phase-encoded photon sieve for intensity pattern generations

We propose a novel type of photon sieve where phases of its sieved waves are encoded as radial positions of the pinholes and use such phase-encoded sieves for generating designed intensity patterns in Fresnel domain. The sieve pinholes are arranged around Fresnel-rings to eliminate the quadratic Fresnel phase factor of diffraction of the sieved waves, leading the wave propagation to be equivalent to Fraunhofer diffraction. The pinholes take constant size in this paper and realize equal amplitude in the multiple sieved waves. Their positions are adjusted radially from corresponding rings to encode wave phases, taking effect by resulting in different optical paths from them to the observation plane origin. Then along with wave propagation, the encoded phases are decoded and the required phase differences are obtained in the discrete waves. We first conduct numerical simulations to show satisfactory performance of such phase-encoded photon sieves in generating arbitrarily designed intensity patterns and describe the quality of the reconstructed patterns. Then for qualitatively verifying the phase-encoding method, we experimentally fabricate three such sieves with relatively small pinhole number and obtain the designed patterns.