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In this paper, based on a full vector-diffraction theory, we present a systematic investigation of the characterization of tight-focused vector fields formed by an off-axis parabolic mirror (OAP), and discuss the effects of offset of an OAP, polarization of light and parabola f-number on the focused field properties by an OAP used with a perfectly aligned beam. Furthermore, we demonstrate a configuration optimization process of an OAP, and obtain an optimum OAP configuration scaling rule which makes it possible to achieve the maximum peak intensity. In addition, we explore the electromagnetic field behaviour in the focal plane at four characteristic times of an optical cycle we explore the electromagnetic field behaviour in the focal plane at four characteristic times of an optical cycle and the dependence of the direction and the amplitude of the focused electromagnetic field on the incident polarization, the offset, and the parabola f-number. we also carry out an assessment analysis of the critical misalignment angle corresponding to a 10% drop of the maximum focused peak intensity. Understanding these effects and scaling laws is of great significance to enhance the focusing performance of OAP in the optimal configuration, especially for the structural design and selection of OAP in ultrashort and ultraintense laser-matter interaction experiments.
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