As a beam splitter, multi-value phase grating has a higher diffraction efficiency than the traditional Damman grating due to its increased number of phase values within one period of the grating. In this paper, two multi-value phase gratings are numerically designed within a 120 μm * 120 μm area, which generate 4 * 4 and 5 * 5 focal spot arrays in the far field. Both gratings are fabricated by direct laser writing technology. Their diffraction efficiencies reach 68.58% and 63.4%, respectively. To compare, Damman gratings with the same size and focal spot arrays are designed and fabricated, whose diffraction efficiencies are tested to be 29.55% and 35.04%, respectively. The results demonstrate the better optical properties of multi-value phase gratings and the capability of direct laser writing in three-dimensional nano-scale diffractive optical element fabrication.
We consider a harmonically trapped rotating spin-1 Bose–Einstein condensate with SU(3) spin–orbit coupling subject to a gradient magnetic field. The effects of SU(3) spin–orbit coupling, rotation, and gradient magnetic field on the ground-state structure of the system are investigated in detail. Our results show that the interplay among SU(3) spin–orbit coupling, rotation, and gradient magnetic field can result in a variety of ground states, such as a vortex ring and clover-type structure. The numerical results agree well with our variational analysis results.
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