volume | PIER Journals

Abstract

Digital manufacturing, or 3D printing, is a rapidly emerging technology that enables novel designs that incorporate complex geometries and even multiple materials. In electromagnetics and circuits, 3D printing allows the dielectrics to take on new and profound functionality. This paper introduces negative uniaxial metamaterials (NUMs) which are birefringent structures that can be used to manipulate electromagnetic fields at a very small scale. The NUMs presented here are composed of alternating layers of two different dielectrics. The physics of the NUMs are explained and simple analytical equations for the effective dielectric tensor are derived. Using these equations, the NUMs are optimized for strength of anisotropy and for space stretching derived from transformation optics. The analytical equations are validated through rigorous simulations and by laboratory measurements. Three NUMs where manufactured using 3D printing where each exhibited anisotropy in a different orientation for measurement purposes. All of the data from the analytical equations, simulations, and experiments are in excellent agreement confirming that the physics of the NUMs is well understood and that NUMs can be designed quickly and easily using just the analytical equations.

1. Gibson, I., D. W. Rosen, and B. Stucker, Additive Manufacturing Technologies: Rapid Prototyping to Direct Digital Manufacturing, Springer, 2010.

2. Church, K., E. MacDonald, P. Clark, R. Taylor, D. Paul, K. Stone, M. Wilhelm, F. Medina, J. Lyke, and R. Wicker, "Printed electronic processes for flexible hybrid circuits and antennas," 2009 Flexible Electronics & Displays Conference and Exhibition, 1-7, 2009.

3. Espalin, D., D. W. Muse, E. MacDonald, and R. B. Wicker, "3D Printing multifunctionality: Structures with electronics," The International Journal of Advanced Manufacturing Technology, Vol. 72, No. 5, 963-978, 2014.
doi:10.1007/s00170-014-5717-7

4. Ketterl, T. P., Y. Vega, N. C. Arnal, J. W. I. Stratton, E. A. Rojas-Nastrucci, M. F. Cordoba-Erazo, M. M. Abdin, C. W. Perkowski, P. I. Deffenbaugh, K. H. Church, and T. M. Weller, "A 2.45 GHz phased array antenna unit cell fabricated using 3-D multi-layer direct digital manufacturing," IEEE Transactions on Microwave Theory and Techniques, Vol. 63, No. 12, 4382-4394, 2015.
doi:10.1109/TMTT.2015.2496180

5. Yi, J., S. N. Burokur, G. Piau, and A. Lustrac, "3D printed broadband transformation optics based all-dielectric microwave lenses," Journal of Optics, Vol. 18, No. 4, 044010, 2016.
doi:10.1088/2040-8978/18/4/044010

6. Rumpf, R. C., J. Pazos, C. R. Garcia, L. Ochoa, and R. Wicker, "3D printed lattices with spatially variant self-collimation," Progress In Electromagnetics Research, Vol. 139, 1-14, 2013.
doi:10.2528/PIER13030507

7. Hao, J., Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, "Manipulating electromagnetic wave polarizations by anisotropic metamaterials," Phys. Rev. Lett., Vol. 99, No. 6, 063908, 2007.
doi:10.1103/PhysRevLett.99.063908

8. Pendry, J. B., D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science, Vol. 312, No. 5781, 1780-1782, 2006.
doi:10.1126/science.1125907

9. Rumpf, R. C., C. R. Garcia, H. H. Tsang, J. E. Padilla, and M. D. Irwin, "Electromagnetic isolation of a microstrip by embedding in a spatially variant anisotropic metamaterial," Progress In Electromagnetics Research, Vol. 142, 243-260, 2013.
doi:10.2528/PIER13070308

10. Garcia, C. R., J. Correa, D. Espalin, J. H. Barton, R. C. Rumpf, R. Wicker, and V. Gonzalez, "3D printing of anisotropic metamaterials," Progress In Electromagnetics Research Letters, Vol. 34, 75-82, 2012.
doi:10.2528/PIERL12070311

11. Datta, S., C. T. Chan, K. M. Ho, and C. M. Soukoulis, "Effective dielectric constant of periodic composite structures," Physical Review B, Vol. 48, 14936, 1993.
doi:10.1103/PhysRevB.48.14936

12. Lalanne, P. and J. Hugonin, "High-order effective-medium theory of subwavelength gratings in classical mounting: Application to volume holograms," J. Opt. Soc. Am. A, Vol. 15, No. 7, 1843-1851, 1998.
doi:10.1364/JOSAA.15.001843

13. Grann, E. B., M. G. Moharam, and D. A. Pommet, "Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings," J. Opt. Soc. Am. A, Vol. 11, 2695-2703, 1994.
doi:10.1364/JOSAA.11.002695

14. Berry, E. A., J. J. Gutierrez, and R. C. Rumpf, "Design and simulation of arbitrarily-shaped transformation optic devices using a simple finite-difference method," Progress In Electromagnetics Research B, Vol. 68, 1-16, 2016.
doi:10.2528/PIERB16012007

15. Kwon, D. H. and D. H. Werner, "Transformation electromagnetics: An overview of the theory and applications," IEEE Antennas and Propagation Magazine, Vol. 52, No. 1, 24-46, 2010.
doi:10.1109/MAP.2010.5466396

16. Leung, K. and Y. Liu, "Photon band structures: The plane-wave method," Physical Review B, Vol. 41, 10188, 1990.
doi:10.1103/PhysRevB.41.10188

17. Flanders, D. C., "Submicrometer periodicity gratings as artificial anisotropic dielectrics," Appl. Phys. Lett., Vol. 42, No. 6, 492-494, 1983.
doi:10.1063/1.93979

18. Lalanne, P. and D. Lemercier-Lalanne, "Depth dependence of the effective properties of subwavelength gratings," J. Opt. Soc. Am. A, Vol. 14, No. 2, 450-459, 1997.
doi:10.1364/JOSAA.14.000450

19. Kikuta, H., Y. Ohira, and K. Iwata, "Achromatic quarter-wave plates using the dispersion of form birefringence," Appl. Opt., Vol. 36, 1566-1572, 1997.
doi:10.1364/AO.36.001566

20. Van Vliet, A. H. F. and T. de Graauw, "Quarter wave plates for submillimeter wavelengths," Int. J. Infrared Millim. Waves, Vol. 2, No. 3, 465-477, 1981.
doi:10.1007/BF01007414

21. Born, M. and E. Wolf, "Light propagation in uniaxial crystals," Principles in Optics, 680, 1970.

22. Rumpf, R. C., "Chapter three --- Engineering the dispersion and anisotropy of periodic electromagnetic structures," Solid State Physics, Vol. 66, 213-300, 2015.
doi:10.1016/bs.ssp.2015.02.002

23. Nicolson, A. M. and G. F. Ross, "Measurement of the intrinsic properties of materials by time-domain techniques," IEEE Transactions on Instrumentation and Measurement, Vol. 19, No. 4, 377-382, 1970.
doi:10.1109/TIM.1970.4313932

24. Weir, W. B., "Automatic measurement of complex dielectric constant and permeability at microwave frequencies," Proceedings of the IEEE, Vol. 62, No. 1, 33-36, 1974.
doi:10.1109/PROC.1974.9382

25. Ansys, , http://www.ansys.com/Products/Electronics/, Ansys Electromagnetics.

26. Rumpf, R. C., , http://emlab.utep.edu/ee5390em21/Lecture%2015%20{%20Homogenization%20-and%20parameter%20retrieval.pdf, Homogenization and Parameter Retrieval.

27. Vicente, A. N., G. M. Dip, and C. Junqueira, "The step by step development of NRW method," 2011 SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference (IMOC 2011), 738-742, 2011.
doi:10.1109/IMOC.2011.6169318

28. Wang, S. S., G. Moharam, R. Magnusson, and J. S. Bagby, "Guided-mode resonances in planar dielectric-layer diffraction gratings," J. Opt. Soc. Am. A, Vol. 7, 1470-1474, 1990.
doi:10.1364/JOSAA.7.001470

29. Wang, S. S. and R. Magnusson, "Theory and applications of guided-mode resonance filters," Appl. Opt., Vol. 32, 2606-2613, 1993.
doi:10.1364/AO.32.002606

30. Stratasys, , http://www.stratasys.com/3d-printers/technologies/fdm-technology, Fused deposition modeling technology.

31. Steven, A., "Rapid prototyping is coming of age," Mechanical Engineering, Vol. 117, No. 7, 62, 1995.

32. Laird Technologies, , http://www.lairdtech.com, Laird HiK Powder.

Dr. Jose Avila

Dr. Cesar L. Valle

Dr. Edgar Bustamante

Professor Raymond C. Rumpf