The concept of vectorial nonparaxial cosh-Gaussian (ChG) beams is introduced and their free-space propagation equation is derived analytically by using the vectorial Rayleigh-Sommerfeld diffraction integrals. The on-axis and far-field expressions of vectorial nonparaxial ChG beams and the paraxial results are given as special cases of the general propagation equation. It is found that for vectorial nonparaxial ChG beams, the f parameter mainly determines their nonparaxiality, but the decentered parameter affects their transversal intensity profile and nonparaxial behavior.
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