An improved iterative algorithm for designing diffractive phase elements for laser beam shaping in free space is presented. The algorithm begins with the Gerchberg-Saxton approach to obtain a stable solution. This is followed by several new iterations, in which modified constraining functions are imposed in the Fourier domain while the phase distribution of each iteration remains unchanged. For super-Gaussian beam shaping suitable for inertial confinement fusion applications the mean-square errors of the amplitude and the intensity profile of the entire beam fitted to the corresponding parameters of the 12th-power super-Gaussian beam are approximately 0.035 and 9.75x10(-3), respectively. Approximately 97.4% of the incident energy is converged into the desired region.
Tightly focused spots with small central lobes, high central intensity and low sidelobe intensity are desirable for many light-emitting diode based micro-projection system applications. Diffractive optical elements (DOEs) offer a potentially low cost and flexible choice for realizing this task. We have approached the design of suitable elements using two methods: various step size simulated quenching (VSSQ) and multiresolution various step size simulated quenching followed by direct binary search (M-VSSQ-DBS). M-VSSQ-DBS greatly increases the central intensity of the spots, and only slightly influences the sidelobe intensity, most often favourably reducing it. When the central lobe size is 0.8 times that of the geometrical-optics limit, the peak intensity can be as high as 97.73% that of the geometrical spot, and the relative maximum sidelobe intensity is 51.14% of the peak intensity. The designs are tolerant to variations in the actual width of the light source and to lateral misalignment. We verify the designed DOE using rigorous diffraction theory, i.e. the finite-difference time-domain method. The results obtained by scalar and rigorous diffraction theory are in excellent agreement with each other.
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