Singular optics is an important and meaningful subject that has attracted widespread attention. The famous vortex beam and vector beam carrying different singularities have found broad applications, and there are four kinds of optical singularities including one kind of phase singularity and three kinds of polarization singularities. However, the classification of optical singularities remains incomplete, as the polarization singularity with indeterminate ellipticity and determinate orientation has not been defined. Here, we propose a kind of E-point singularity, where the ellipticity of polarization is indeterminate and the orientation is determinate. The amount, positions, and topological charges of the E-point singularities can be theoretically and experimentally manipulated on the wave front of the beam. It is found that the E-point singularity has a function of polarization purification in propagation, and the E-point singularity acts like catalyst when achieving pure transverse spin angular momentum (SAM) in tight focusing process. The proposed E-point singularity not only supplements the theoretical framework of singular optics, but also enables SAM manipulation during propagation and focusing processes, demonstrating broad application potential across various regions.

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• Beam polarization
• Classical optics
• Spin polarization
• Structured light