The 1.8-2.3 \(\upmu\) m band lies within the short-wavelength infrared (SWIR) region and serves as a key operational window for a wide range of applications, including quantum sensing, molecular spectroscopy, and free-space quantum and classical optical communication. Despite its significance, optical devices operating in this band still face two major challenges: chromatic aberration across the wide spectral range and the difficulty of integration due to bulky optical elements. Metalenses are composed of subwavelength nanostructures that locally control the phase and group delay of light, enabling precise wavefront shaping and broadband dispersion compensation. These capabilities make them highly promising for use in infrared optical systems, particularly in applications such as focusing and imaging for compact integrated devices. In this study, we propose a metalens design based on a CaF \(_2\) substrate, where each nanocell consists of a single-bar silicon structure. These nanocells are periodically arranged with a 900 nm period, enabling precise control of dispersion and phase. By systematically fine-tuning the bar length and width, the design enables simultaneous dispersion compensation and phase modulation, achieving stable focusing performance over a broad spectral range. Finite-Difference Time-Domain (FDTD) simulations demonstrate effective suppression of chromatic aberration across 1800–2300 nm, with simulated focal-length variation within 6% of the target value. We further analyze the polarization distribution across the focal spot and find a weak wavelength dependence of the degree of polarization (DoP), which we attribute to the spatially varying polarization state in the high-NA focal region together with the wavelength-dependent anisotropic response of the nanostructures. Meanwhile, this design offers a compact, broadband, and high-performance approach for beam collimation and wavefront shaping in the SWIR band, showing promising potential for applications in quantum communication and sensing systems.