Results and discussion In the equivalent prism model, adding the blazed gratings significantly increases the energy proportion of the -1st order diffracted light, which proves the feasibility of the optimization mechanism (Fig. 1). The hollow grating lens decorated with the blazed structure can significantly increase the focal field energy with the peak value increasing to 2.91 times, while the focusing position is slightly shifted and the focusing width is broadened (Fig. 2). Under different preset focal lengths, the deflection of the beam passing through the lens varies, and the relationship between the focal field energy and the height of the blazed structure also changes. At near and medium focal lengths, the focal field energy first increases and then decreases with the height, and at far focal lengths, the focal field energy increases with the height (Fig. 3). When the number of blazed structures changes, more of them cause the diffracted beams to interact with each other, offset part of the phase difference, and reduce focal shift, with improved focusing energy efficiency (Fig. 4). The incident light distribution can also manipulate the focal field. By controlling the beam parameters to adjust the energy distribution of incident light in various regions of the grating, different diffraction efficiencies of regions are obtained, and the focusing field intensity is controlled (Fig. 5). According to the analysis of lens structural profile characteristics and diffraction mechanisms, when the proportion of incident light energy contributing to the first grating area of the lens is more than that of the second grating area, the grating diffraction efficiency is high and the electric field intensity increases with w₀. When the contribution of incident light energy to the second grating area exceeds the first grating area, the grating diffraction efficiency decreases, and the electric field intensity becomes stable or even weakens with the rising w₀ (Fig. 5). By utilizing the polarization independence of subwavelength grating lenses and adjusting the polarization composition of the incident field, solid single focus, "donut" shaped, "rocket" shaped, and "spindle" shaped focal fields can be obtained (Table 2).

The amplitude and polarization of cylindrical vector beams (CVBs) are distributed cylindrically and symmetrically, and the tight CVBs focusing plays an important role in optical micromanipulation, optical storage, laser micromachining, super-resolution imaging, particle acceleration, and other fields. At present, various focusing methods have been developed, such as traditional lenses, plasmonic lenses, negative refractive photonic crystal lenses, parabolic mirrors, and meta-lenses. However, there are limitations including diffraction limit, polarization dependence, and complex preparation. Subwavelength grating lens based on -1st order diffraction can achieve tight focusing of radial and azimuthal polarized lights spontaneously, breaking through the diffraction limit and realizing flexible focal field manipulation. Despite these advantages, the energy efficiency of its focal field still deserves further improvement. Therefore, we explore and propose a structural optimization scheme for a blazed subwavelength grating lens that can increase the energy ratio of -1st order diffracted light energy to enhance the focal field energy.

We employ the full vector calculation of electromagnetic field (COMSOL Multiphysics software) based on the finite element method (FEM) to carry out specific research. The blazed structure is located on each grating step with a consistent height, and the overall lens structure is a uniform dielectric GaN. Firstly, an equivalent triangular prism model is built to verify the enhancement effect of the blazed structure on -1st order diffraction. Next, the energy and morphology changes of the focal field before and after modifying the blazed structure are compared, and the influence of the height, number, and location of blazed structures on the focal field is analyzed. Finally, the dynamic manipulation effect of the incident light amplitude distribution and polarization components on the focal field energy and morphology is studied.

We propose a blazed subwavelength grating lens that can improve the diffraction efficiency of -1st order diffracted light and enhance the focal field energy of the negative refractive grating lens. As the preset focal length increases, the height of the blazed structure that satisfies the maximum diffraction efficiency of the lens also rises. The increasing number of blazed structures leads to more balanced energy of the outgoing beams in different regions and higher energy of the focal field. Meanwhile, the ability of the focal field to suppress the secondary focus is stronger, and the focal position is more accurate. By adjusting incident Gaussian radially polarized light, the dynamic control of the focal field energy is realized. Changing the polarization components of CVBs can also achieve lateral focusing modulation and obtain focal fields with diverse morphology. Finally, our study provides ideas for optimizing the focusing performance of subwavelength grating lenses and has potential applications in optical micromanipulation, super-resolution imaging, and other fields.