The focusing properties of radially polarized beam with radial cosine wavefront phase are investigated. For radially polarized beam without any wavefront phase, focus pattern is ring for low numerical aperture, while only one intensity peak for high numerical aperture due to stronger longitudinal field component in focal region. When the radially polarized beam with radial cosine wavefront phase is focused, focal pattern differs with frequency parameter in cosine function. For high numerical aperture, focal shift occurs, and focal patterns also evolve considerably, for instance, from only one peak to two or multiple peaks. Focal shift value fluctuates for low frequency parameter, drops sharply, and then comes back slightly. Simultaneously, Peak intensity ratio of radially polarized component to longitudinal polarized component in focal region decreases slowly, and then increases very quickly.
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