Focusing characteristics of space-variant quadratic phase modulated linearly polarized Bessel–Gaussian vortex beam

The focusing characteristics of the Bessel–Gaussian (BG) beam, characterized by a tailored space-variant quadratic (SQ) phase, are explored based on the principles of vector diffraction theory. The effects of different parameters on the optical field distribution and the optical gradient force distribution are discussed in detail. The results show that the two intensity peaks will move toward the central region and merge into a single intensity peak when the beam parameter less than 3.2 and will separate along the X-axis when the beam parameter exceeds 3.2. Moreover, an optical trap appears in the focal area, and multiplied small-intensity peaks will be observed due to adjusting the fractional topological charge number. Besides, gradient force evolution differs for the variation of beam parameter and topological charge number. Novel patterns of gradient force emerge as a result, such as force rings, banded gradient force, square array gradient force. Our research results will benefit the development of optical manipulation fields, such as optical tweezers systems, particle capture and particle classification applications.