Depth of focus (DOF) and transverse resolution define the longitudinal range and definition of the focusing lens. Although metasurface axilenses and light-sword metalenses with radial and angular modulations can elongate the DOF, these approaches have inherent limitations in being reliable only for small numerical aperture (NA) cases, which in turn compromises the transverse resolution for the given aperture dimension. To conquer this limitation, we propose and experimentally demonstrate a birefringent metalens, achieving an ultradeep DOF of $41\lambda$ in terms of the total scattered field, corresponding to a record-breaking wide NA range from 0.14 to 0.7. Meanwhile, the diffraction limited focal spot size in this NA range can guarantee acquisition of images with high resolution. A hybrid methodology is proposed that utilizes both the accuracy of holography in electromagnetic field reconstruction and the polarization multiplexing to double the DOF. A stratified transmissive meta-atom is utilized to encode a pair of independent phase profiles in two orthogonal polarization channels. Furthermore, we combine the generalized scattering matrix with the multipole expansion theory for the first time to elucidate the mechanism of maintaining high transmittance and widening the transmission phase coverage by using the multilayered structure. The proposed metalens provides a competitive platform for devising high-resolution deep DOF systems for imaging and detection applications.

中文翻译：

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具有超深聚焦深度和高分辨率的双折射透射金属

聚焦深度（DOF）和横向分辨率定义了聚焦透镜的纵向范围和清晰度。尽管具有径向和角度调制的超表面轴突和轻剑金属质感可以拉长自由度，但这些方法固有的局限性在于仅对小数值孔径（NA）情况可靠，这反过来又损害了给定孔径尺寸的横向分辨率。为了克服这一局限性，我们提出并通过实验证明了双折射金属元素，可实现超深自由度。$41\lambda$就总散射场而言，相当于创纪录的宽广NA范围从0.14到0.7。同时，在该NA范围内的衍射受限制的焦点尺寸可以确保获得高分辨率的图像。提出了一种混合方法，该方法既利用全息图在电磁场重建中的准确性，又利用偏振复用将DOF加倍。利用分层的透射形亚原子在两个正交极化通道中对一对独立的相位分布进行编码。此外，我们首次将广义散射矩阵与多极扩展理论相结合，以阐明使用多层结构保持高透射率并扩大透射相覆盖范围的机理。