Autonomous wireless body-implanted devices for biotelemetry, telemedicine, and neural interfacing constitute an emerging technology providing powerful capabilities for medicine and clinical research. We study the through-tissue electromagnetic propagation mechanisms, derive the optimal frequency range, and obtain the maximum achievable efficiency for radiative energy transfer from inside a body to free space. We analyze how polarization affects the efficiency by exciting TM and TE modes using a magnetic dipole and a magnetic current source, respectively. Four problem formulations are considered with increasing complexity and realism of anatomy. The results indicate that the optimal operating frequency f for deep implantation (with a depth d greater than or similar to 3 cm) lies in the (10(8)-10(9))-Hz range and can be approximated as f = 2.2 x 10(7)/d. For a subcutaneous case (d less than or similar to 3 cm), the surface-wave-induced interference is significant: within the range of peak radiation efficiency (about 2 x 10(8) to 3 x 10(9) Hz), the max-to-min ratio can reach a value of 6.5. For the studied frequency range, 80%-99% of radiation efficiency is lost due to the tissue-air wave-impedance mismatch. Parallel polarization reduces the losses by a few percent; this effect is inversely proportional to the frequency and depth. Considering the implantation depth, the operating frequency, the polarization, and the directivity, we show that about an order-of-magnitude efficiency improvement is achievable compared to existing devices.