arXiv:2610.41656v1 Announce Type: new Abstract: Bessel beams have recently been explored as a candidate complement to focused beams in radiative near-field communications due to their non-diffracting and self-healing properties. However, recent work has shown that the practically useful range of finite-aperture Bessel beams can occupy only a fraction of the radiative near-field region, establishing the existence of a finite propagation limit. In this paper, we establish such a limitation analytically from a depth-of-field perspective for Bessel beams generated by finite circular and square apertures. To quantify the Bessel beam depth, we first derive analytical expressions for the normalized array gain and use them to establish absolute and peak-normalized $3$-dB depth-of-field criteria. These criteria reveal critical cone-angle thresholds that partition the Bessel-beam configuration space into (i) undefined, (ii) finite, and (iii) infinite depth-of-field regimes. Our analysis further reveals that the maximum usable non-diffracting range under the proposed depth-of-field criterion is limited to $\approx22\%$ and $\approx19\%$ of the Fraunhofer distance for circular and square apertures, respectively. Numerical results confirm the accuracy of the derived limits for discrete planar arrays, providing practical engineering guidelines for the design of finite-aperture Bessel beams in future near-field communications.