To address the demand for efficient optical coupling in back-illuminated mid-infrared focal plane arrays (FPAs), this paper numerically investigates a double-concave silicon-based air-microlens operating in the 3-5 μm wavelength range. Unlike conventional convex lenses, the proposed design embeds a concave air cavity within a high-refractive-index silicon medium, leveraging the strong refractive index contrast (Δn≈2.42) to achieve tight beam focusing. Using the finite-difference time-domain (FDTD) method, we analyze the influence of the front curvature radius, rear curvature radius, and air cavity thickness on key focusing metrics.Physical mechanism analysis reveals that the double-concave architecture decouples the wavefront phase modulation process. Specifically, the front surface dominates the preliminary focusing, while the rear surface acts as a near-field phase corrector to suppress spherical aberrations and optimize the wavevector matching of high-frequency evanescent waves. For an illumination wavelength of 4 μm, the minimum focal spot size can reach 0.83 μm (approximately 71% of the effective wavelength λ_eff within the silicon medium). Based on these findings, we extract two typical design criteria to accommodate practical engineering trade-offs: a “minimum focal spot priority” design tailored for high-resolution arrays, and a “maximum depth of focus priority” design for systems requiring high thermo-mechanical assembly tolerances. The proposed “in-silicon focusing” architecture naturally fits the physical configuration of miniaturized infrared detectors, demonstrating significant potential for enhancing the fill factor of on-chip optoelectronic systems.