  The metalenses have been extensively studied for their compact and flexible
characteristics in focusing and imaging applications. However, it remains a
significant challenge to design a broadband achromatic metalens that maintains
high efficiency under arbitrary polarization incidence. In this work, we design
a broadband achromatic metalens that achieves polarization-independent,
high-efficiency focusing by effectively utilizing both co-polarization and
cross-polarization components of the transmitted light. Using a minimalist
anisotropic nanofin library, we optimize the phase distribution of the metalens
at each designed wavelength with the particle swarm algorithm. Numerical
simulations demonstrate a stable focal length with a deviation of less than
4$\%$ and an average focusing efficiency of 80.5$\%$ in the visible wavelength
range of 450 to 650 nm. Moreover, we design a multi-wavelength off-axis
bi-focal metalens to demonstrate the flexible control of output light phase and
dispersion achieved by this method. The generality of this design enables its
implementation in various metasurface devices, accelerating applications in
broadband imaging and virtual/augmented reality.
