Metasurfaces can manipulate optical wavefronts by locally shifting the phase of incident light with metallic or dielectric optical nanoresonators that are generally arranged on a lattice with subwavelength spacing. However, such conventional metasurfaces inevitably generate a spatially discrete multi-level phase profile due to the spacing of their building blocks. This directly leads to an efficiency reduction and thus limits their capability. Here, we propose and demonstrate highly efficient transmissive metasurfaces with the ability to form a continuous phase profile. The proposed strategy relies on the fact that high-index dielectric nanobeams with gradually modulated widths can be interpreted to be a virtually impedance-matched material with spatial variations of its refractive index. By highly utilizing such features, one-dimensionally continuous, arbitrary phase profiles can be created in a simple manner with the width profile design. Since spatial transmittance variations can be minimized due to the impedance matching feature, this approach provides a nearly ideal phase profile for spatial light modulation with phase-only filtering operations. We demonstrate that this approach has the capability to improve the performance in various metasurface-based optical components, including polarization-dependent, large-angle beam deflectors and versatile multi-beam splitters. Considering that designing optical phases even in deep-subwavelength regimes is critical for free-space optics, the proposed approach will enable new classes of optical components with complex wavefront engineering.

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