On the generation of optical fields satisfying the upper bound diffraction efficiency using phase holograms

This paper presents a mathematical framework for the generation of optical field with upper bound diffraction efficiency. The first part of the contribution provides the necessary and sufficient condition for the optical field to be encoded with upper bound diffraction efficiency. Our approach shows that an arbitrary field is encoded using its kinoform and the upper bound amplitude gain. In this way, the energy of the kinoform is composed by the energies of the encoded field and the coding noise. Removing the coding noise, the optical field is generated with upper bound diffraction efficiency. In the second part, we analytically show that the Fourier spectra of the field and coding noise for the class the periodic and quasiperiodic nondiffractive optical fields composed by superposition of plane waves are not overlapping.