This paper studies the difference between retro-directive beamforming technique and retro-reflective beamforming technique in the context of wireless power transmission applications. In all of our studies, a wireless power receiver broadcasts continuous-wave pilot signal; the wireless power transmitter receives and analyzes the pilot signal; finally, the wireless power transmitter transmits continuous-wave power with phase profile conjugate to that of the received pilot signal. Our study demonstrates that a linear equi-spaced array configuration employed by the wireless power transmitter behaves as a retro-directive beamformer when the wireless power receiver resides in the far-zone of the wireless power transmitter, whereas it behaves as a retro-reflective beamformer when the wireless power receiver is not in the far-zone. This paper further investigates two types of array configurations other than linear equi-spaced array when the wireless power transmitter behaves as a retro-reflective beamformer. One is a V-shaped array, which is obtained by deforming the linear equi-spaced array to a ``V'' shape. The other is termed ``perturbed array:'' on the basis of linear equi-spaced array, all the elements' locations are perturbed randomly. It is particularly interesting to compare the equi-spaced array and perturbed array. When the wireless power receiver resides 5 or 6 wavelengths away, a 6-element equi-spaced array and a 6-element perturbed array produce the same power level at the near-zone focal point, but the maximum far-zone gain associated with the perturbed array is 1 dB lower than the equi-spaced array. All the conclusions drawn in this paper are supported by numerical results as well as experimental results.
2. Visser, H. J. and R. J. M. Vullers, "RF energy harvesting and transport for wireless sensor network applications: Principles and requirements," Proceedings of the IEEE, Vol. 101, No. 6, 1410-1423, June 2013.
3. Zhai, H., H. K. Pan, and M. Lu, "A practical wireless charging system based on ultra-wideband retro-reflective beamforming," IEEE International Antennas and Propagation Symposium, Toronto, Canada, July 2010.
4. Mazurenko, O. and Y. Yakornov, "Focused arrays beamforming," Behaviour of Electromagnetic Waves in Different Media and Structures, 419-440, A. Akdagli, Ed., InTech, Rijeka, 2011.
5. Kildal, P.-S. and M. M. Davis, "Characterization of near-field focusing with application to low altitude beam focusing of the Arecibo tri-reflector system," IEE Proceedings --- Microwaves Antennas and Propagation, Vol. 143, No. 4, 284-292, August 1996.
6. Reid, D. R. and G. S. Smith, "A comparison of the focusing properties of a Fresnel zone plate with a doubly-hyperbolic lens for application in a free-space, focused beam measurement system," IEEE Transactions on Antennas and Propagation, Vol. 57, No. 2, 499-507, February 2009.
7. Chou, H.-T., T.-M. Hung, N.-N. Wang, H.-H. Chou, C. Tung, and P. Nepa, "Design of a near-field focused reflectarray antenna for 2.4 GHz RFID reader applications," IEEE Transactions on Antennas and Propagation, Vol. 59, No. 3, 1013-1018, March 2011.
8. Karimkashi, S. and A. A. Kishk, "Focusing properties of Fresnel zone plate lens antennas in the near-field region," IEEE Transactions on Antennas and Propagation, Vol. 59, No. 5, 1481-1487, May 2011.
9. Gomez-Tornero, J. L., D. Blanco, E. Rajo-Iglesias, and N. Llombart, "Holographic surface leaky-wave lenses with circularly-polarized focused near-fields --- Part I: Concept, design and analysis theory," IEEE Transactions on Antennas and Propagation, Vol. 61, No. 7, 3475-3485, July 2013.
10. Monnai, Y. and H. Shinoda, "Focus-scanning leaky-wave antenna with electronically pattern-tunable scatterers," IEEE Transactions on Antennas and Propagation, Vol. 59, No. 6, 2070-2077, June 2011.
11. Okuyama, T., Y. Monnai, and H. Shinoda, "20-GHz focusing antennas based on corrugated waveguide scattering," IEEE Antennas and Wireless Propagation Letters, Vol. 12, 1284-1286, 2013.
12. Buffi, A., P. Nepa, and G. Manara, "Design criteria for near-field-focused planar arrays," IEEE Antennas and Propagation Magazine, Vol. 54, 40-50, 2012.
13. Tuan, S.-C. and H.-T. Chou, "Analytic analysis of transient radiation from phased array antennas in the near- and far-field focus applications," IEEE Transactions on Antennas and Propagation, Vol. 61, No. 5, 2519-2531, May 2013.
14. Leon, G. and F. Las-Heras, "Fresnel-zone-based focused planar array," IEEE Antennas and Wireless Propagation Letters, Vol. 13, 165-168, 2014.
15. Stephan, K. D., J. B. Mead, D. M. Pozar, L. Wang, and J. A. Pearce, "A near field focused microstrip array for a radiometric temperature sensor," IEEE Transactions on Antennas and Propagation, Vol. 55, No. 4, 1199-1203, April 2007.
16. Bogosanovic, M. and A. G. Williamson, "Microstrip antenna array with a beam focused in the near-field zone for application in noncontact microwave industrial inspection," IEEE Transactions on Instrumentation and Measurement, Vol. 56, No. 6, 2186-2195, December 2007.
17. Buffi, A., A. A. Serra, P. Nepa, H.-T. Chou, and G. Manara, "A focused planar microstrip array for 2.4 GHz RFID readers," IEEE Transactions on Antennas and Propagation, Vol. 58, No. 5, 1536-1544, May 2010.
18. Karimkashi, S. and A. A. Kishk, "Focused microstrip array antenna using a Dolph-Chebyshev near-field design," IEEE Transactions on Antennas and Propagation, Vol. 57, No. 12, 3813-3820, December 2009.
19. Alvarez, J., R. G. Ayestaran, G. Leon, L. F. Herran, A. Arboleya, J. A. Lopez-Fernandez, and F. Las-Heras, "Near field multifocusing on antenna arrays via non-convex optimisation," IET Microwaves, Antennas & Propagation, Vol. 8, No. 10, 754-764, July 2014.
20. Siragusa, R., P. Lemaitre-Auger, and S. Tedjini, "Tunable near-field focused circular phase-array antenna for 5.8-GHz RFID applications," IEEE Antennas and Wireless Propagation Letters, Vol. 10, 33-36, 2011.
21. Wang, X., S. Sha, J. He, L. Guo, and M. Lu, "Wireless power delivery to low-power mobile devices based on retro-reflective beamforming," IEEE Antennas and Wireless Propagation Letters, Vol. 13, 919-922, 2014.
22. He, J., X. Wang, L. Guo, S. Shen, and M. Lu, "A distributed retro-reflective beamformer for wireless power transmission," Microwave and Optical Technology Letters, Vol. 57, No. 8, 1873-1876, August 2015.
23. Wang, X., X. Hou, L. Wang, and M. Lu, "Employing phase-conjugation antenna array to beam microwave power from satellite to earth," IEEE International Conference on Wireless for Space and Extreme Environments, Orlando, FL, December 2015.
24. Balanis, C. A., Antenna Theory: Analysis and Design, 3rd Ed., Wiley-Interscience, 2005.