Generating Hollow Gaussian Beams with Improved Fresnel Zone Plates

Hollow Gaussian beam is a hollow beam class that does not carry orbital angular momentum, its dark spot size is small and has a simple function formula. Hollow Gaussian beam has potential application in the fields of atomic guiding, particle manipulation, and optical communication. Meanwhile, zone plates, also known as Fresnel zone plates, focus light waves through diffraction onto a receiving object. Therefore, this relationship can be applied to design zone plates which generate hollow Gaussian beams. This study demonstrates that the zone plate focal plane complex amplitude distribution function is proportional to the Fourier-Bessel transform of the equivalent pupil function which describes the effects of transmission on waves. The zone plate equivalent pupil functions were calculated to produce the 1st, 3rd, and 6th order hollow Gaussian beams. Subsequently, the structural parameters of these three zone plates were designed. The wavelength and focal length of the zone plates were also changed to determine their influence on the structure parameters and dark spot size. Next, the focal plane light fields of these three modified zone plates were simulated using the Rayleigh-Sommerfeld diffraction integral. The simulation results are consistent with expectations which verifies the reliability and accuracy of the equivalent pupil function method to design Fresnel zone plates.