Efficient microwave-to-optical frequency conversion (MOC) using Rydberg atoms is promising for radiometry, electrometry, and hybrid quantum networks. However, in free space, the total system efficiency can be much lower than the internal atomic conversion efficiency because of the large mismatch between microwave wavelength, optical wavelength, and atomic-ensemble size. Here, we develop a systematic theoretical framework in which the total conversion efficiency is factorized into microwave mode-matching efficiency, optical spin-wave extraction efficiency, and internal coherent conversion efficiency. In the regime ${\lambda }_{\mathrm{m}}\gg L\gg {\lambda }_{\mathrm{o}}$, the atomic ensemble couples to the microwave field as a collective dipole, whereas its coupling to the optical field is governed by a phase-matched spin-wave mode. We show that the total efficiency is primarily limited by microwave mode matching. For an ideal diffraction-limited Gaussian microwave mode coupled to this collective dipole, the microwave extraction factor is bounded by about $3/16$ under standard polarization and orientation averaging. This analysis provides a transparent benchmark for evaluating free-space Rydberg MOC and identifies microwave mode matching as the key target for experimental optimization.

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• Frequency conversion
• Rydberg atoms & molecules