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Based on the vector angular spectrum theory of electromagnetic waves and the method of stationary phase, analytical vector structures of four-petal Gaussian beams (FPGB) in the far field are derived. The energy flux for the TE term, TM term and the whole beam are represented and illustrated with numerical examples. Effects of beam orders and paraxial degrees on energy flux distributions are discussed in detail, and the corresponding analytical explanations are also given. These results may provide a new approach to manipulate other higher-order laser beams in the far field.
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Li et al. (2010) studied this question.
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