We demonstrate a method for creating a three-dimensional (3D) array of focal spots by combination of a multi-focal diffractive lens and a two-dimensional multi-value phase grating. The multi-focal Fresnel-based lens is created by means of encoding special nonlinearities into the phase structure of a Fresnel zone plate and is represented as a mathematical superposition of this phase function with a refractive lens. The imposed nonlinearity type enables the creation of multiple focal spots with uniform intensity along the optical axis. We demonstrate the example of a 3D multi-value phase grating, which creates five focal planes with a 5 x 5 transverse array of focal spots with equal energy distribution in each plane. Experimental results are included to verify the theoretical outcomes, where the phase pattern of a 3D multi-value phase grating is encoded onto a spatial light modulator. (C) 2019 Optical Society of America
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