In this work, we show how we can improve the image resolution capabilities of a Phase Conjugating (PC) lens as well as the angular resolution of Luneburg lens antennas by employing signal processing techniques, such as the Correlation Method (CM), the Minimum Residual Power Search Method (MRPSM), the sparse reconstruction method, and the Singular-Value-Decomposition (SVD)-based basis matrix method. In the first part, we apply these techniques for sub-wavelength imaging in the microwave regime by combining them with the well-known phase conjugation principle. We begin by considering a one-dimensional microwave sub-wavelength imaging problem handled by using three signal processing methods, and then we move on to two- or three-dimensional problems by using the SVD-based basis matrix method. Numerical simulation results show that we can enhance the resolution significantly by using these methods, even if the measurement plane is not located in the very near-field region of the source. We describe these proposed algorithms in detail and study their abilities to resolve at the sub-wavelength level. Next, we investigate the sparse reconstruction method for a normal Luneburg lens antenna, and the Correlation Method and the SVD-based basis matrix method for a flat-base Luneburg lens antenna to estimate the Direction-of-Arrival (DOA). Numerical simulation results show that the signal processing techniques are capable of enhancing the angular resolution of the Luneburg lens antenna, enabling the lens to locate multiple targets with different scattering cross-sections, and achieving higher angular resolution.
2. Pendry, J. B., "Negative refraction makes a perfect lens," Phys. Rev. Lett., Vol. 85, No. 18, 3966-3969, 2000.
3. Maslovski, S. and S. Tretyakov, "Phase conjugation and perfect lensing," J. Appl. Phys., Vol. 94, No. 7, 4241-4243, 2003.
4. Rosny, J. de, G. Lerosey, and M. Fink, "Theory of electromagnetic time-reversal mirrors," IEEE Trans. Antennas Propag., Vol. 58, No. 10, 3139-3149, 2010.
5. Shiroma, G. S., R. Y. Miyamoto, J. D. Roque, J. M. Cardenas, and W. A. Shiroma, "A high-directivity combined self-beam/null-steering array for secure point-to-point communications," IEEE Trans. Microw. Theory Tech., Vol. 55, No. 5, 838-844, 2007.
6. Gaikovich, K. P., "Subsurface near-field scanning tomography," Phys. Rev. Lett., Vol. 98, No. 18, 183902-183902, 2007.
7. Aliferis, I., T. Savelyev, M. J. Yedlin, J.-Y. Dauvignac, A. Yarovoy, C. Pichot, and L. Ligfhart, "Comparison of the diffraction stack and time-reversal imaging algorithms applied to short-range UWB scattering data," IEEE Int. Conf. Ultra-Wideband (ICUWB 2007), Singapore, Sep. 24-26, 2007.
8. Katko, A. R., S. Gu, J. P. Barrett, B.-I. Popa, G. Shvets, and S. A. Cummer, "Phase conjugation and negative refraction using nonlinear active metamaterials," Phys. Rev. Lett., Vol. 105, No. 12, 123905-123905, 2010.
9. Belov, P. A. and Y. Hao, "Sub-wavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime," Phys. Rev. B, Vol. 73, No. 11, 113110-113110, 2006.
10. Eleftheriades, G. and A. Wong, "Holography-inspired screens for sub-wavelength focusing in the near field," IEEE Microw. Wireless Compon. Lett., Vol. 18, No. 4, 236-238, 2008.
11. Merlin, R., "Radiationless electromagnetic interference: evanescent-field lenses and perfect focusing," Science, Vol. 317, No. 5840, 927-929, 2007.
12. Malyuskin, O. and V. Fusco, "Far field subwavelength source resolution using phase conjugating lens assisted with evanescent-to-propagating spectrum conversion," IEEE Trans. Antennas Propag., Vol. 58, No. 2, 459-468, 2010.
13. Memarian, M. and G. V. Eleftheriades, "Evanescent-to-propagating wave conversion in sub-wavelength metal-strip gratings," IEEE Trans. Microw. Theory Tech., Vol. 60, No. 12, 3893-3907, 2012.
14. Ge, G.-D., B.-Z. Wang, D. Wang, D. Zhao, and S. Ding, "Subwavelength array of planar monopoles with complementary split rings based on far-field time reversal," IEEE Trans. Antennas Propag., Vol. 59, No. 1, 4345-4350, 2011.
15. Katko, A. R., G. Shvets, and S. A. Cummer, "Phase conjugation metamaterials: Particle design and imaging experiments," Journal of Optics, Vol. 14, No. 11, 114003-114003, 2012.
16. Park, Y. K., "Subwavelength light focusing and imaging via wavefront shaping in complex media," Progress In Electromagnetics Research Symposium Abstracts, Guangzhou, China, August 25-28, 2014.
17. Sidorenko, P., Y. Shechtman, Y. C. Eldar, O. Cohen, and M. Segev, "Sparsity-based sub-wavelength imaging and super-resolution in time-resolved and spectroscopic instruments," Progress In Electromagnetics Research Symposium Abstracts, Guangzhou, China, August 25-28, 2014.
18. Mittra, R. (Ed.), Computational Electromagnetics --- Recent Advances and Engineering Applications, Chapter 16, 553-574, Springer, New York, 2013.
19. Gu, X., C. Pelletti, R. Mittra, and Y. Zhang, "Resolution enhancement of phase-conjugating lenses by using signal processing algorithms," IEEE Antennas Wireless Propag. Lett., Vol. 13, 511-514, 2014.
20. Gu, X., C. Pelletti, R. Mittra, and Y. Zhang, "Signal processing approach to electromagnetic sub-wavelength imaging," IEEE Antennas and Propagation Society International Symposium (APS/URSI 2013), Orlando, Florida, July 7-13, 2013.
21. Gu, X., R. Mittra, and Y. Zhang, "Electromagnetic sub-wavelength imaging using the basis matrix method in conjunction with singular value decomposition (SVD) algorithm," IEEE Antennas and Propagation Society International Symposium (APS/URSI 2014), Memphis, TN, July 6-11, 2014.
22. Mittra, R., X. Gu, and Y. Zhang, "Signal processing approach to realizing enhanced resolution from imaging systems such as lenses," XXXIth URSI General Assembly and Scientific Symposium (URSI/GASS 2014), Beijing, China, August 17-23, 2014.
23. Balanis, C. A., Modern Antenna Handbook, Wiley, 2008.
24. Lafond, O., M. Himdi, H. Merlet, and P. Lebars, "An active reconfigurable antenna at 60 GHz based on plate inhomogeneous lens and feeders," IEEE Trans. Antennas Propag., Vol. 61, No. 4, 1672-1678, 2013.
25. Luneburg, R. K., Mathematical Theory of Optics, University of California Press, 1964.
26. James, G., A. Parfitt, J. Kot, and P. Hall, "A case for the Luneburg lens as the antenna element for the square kilometre array radio telescope," Radio Science Bulletin, No. 293, 32-37, June 2000.
27. Hua, C., X. Wu, N. Yang, and W. Wu, "Air-filled parallel-plate cylindrical modified Luneberg lens antenna for multiple-beam scanning at millimeter-wave frequencies ," IEEE Trans. Microw. Theory Tech., Vol. 61, No. 1, 436-443, 2013.
28. Liang, M., X. Yu, S.-G., Rafael, W.-R. Ng, M. E. Gehm, and H. Xin, "Direction of arrival estimation using Luneburg lens," IEEE International Microwave Symposium (IMS) Digest (MTT), Vol. 1, No. 3, June 17-22 2012.
29. Jain, S. and R. Mittra, "Flat-base broadband multibeam Luneburg lens for wide angle scan," IEEE Antennas and Propagation Society International Symposium (APS/URSI 2014), Memphis, TN, July 6-11, 2014.
30. Gu, X., S. Jain, R. Mittra, and Y. Zhang, "Enhancement of angular resolution of a flat-base Luneburg lens antenna by using correlation method," Progress In Electromagnetics Research M, Vol. 37, 203-211, 2014.
31. Mittra, R., C. Pelletti, N. L. Tsitsas, and G. Bianconi, "A new technique for efficient and accurate analysis of FSSs, EBGs and metamaterials," Microw. Opt. Techn. Lett., Vol. 54, No. 4, 1108-1116, 2011.
32. Pelletti, C., G. Bianconi, R. Mittra, A. Monorchio, and K. Panayappan, "Numerically efficient method-of-moments formulation valid over a wide frequency band including very low frequencies," IET Microw. Antennas Propag., Vol. 6, No. 1, 46-51, 2012.
33. FEKO Suite 6.2 [Online], , Available: www.feko.info.
34. Donoho, D. L., "Compressed sensing," IEEE Trans. Inf. Theory, Vol. 52, No. 4, 1289-1306, 2006.
35. Balanis, C. A., Antenna Theory --- Analysis and Design, 2nd Ed., John Wiley & Sons, 1982.
36. Mohimani, H., M. Babaie-Zadeh, and C. Jutten, "A fast approach for overcomplete sparse decomposition based on smoothed L0 norm," IEEE Trans. Signal Process., Vol. 57, No. 1, 289-301, 2009.
37. Berg, E. V. D. and M. P. Friedlander, "Sparse optimization with least-squares constraints," SIAM J. OPTIM., Vol. 21, No. 4, 1201-1229, 2011.
38. Yu, W., X. Yang, Y. Liu, R. Mittra, and A. Muto, Advanced FDTD Methods: Parallelization, Acceleration, and Engineering Applications, Artech House, Norwood, MA, USA, March 2011.
39. Guru, B. and H. Hiziroglu, Electromagnetic Field Theory Fundamentals, 2nd Ed., Cambridge University Press, 2004.