Abstract
The vectorial nonparaxial four-petal Gaussian beam (FPGB) isintroduced. The closed-form propagation expressions for the free-spacepropagation of FPGBs are derived and their more general applicableadvantages are illustrated analytically and numerically. Some specialinteresting cases, in particular the paraxial one, are discussed. Itis found that the parameter f = 1/kw0 with the kbeing the wave number and w0 being the waist width playsa crucial role in determining the nonparaxiallity of FPGBs. For smallvalues of the f parameter the paraxial approximation isallowable. In the nonparaxial regime the beam order nadditionally affects the vectorial and nonparaxial behaviour of FPGBs.
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