Raymond C. Rumpf, Ph.D. Pioneering 21 st Century Electromagnetics and Photonics Forum for Electromagnetic Research Methods and Application Technologies (FERMAT) Spatially-Variant Periodic Structures in Electromagnetics Noel Martinez 1, Cesar L. Valle 1, Stephen M. Kuebler 2, Javier J. Pazos 3, Cesar R. Garcia 4, Eric A. Berry 5, and Raymond C. Rumpf 1 1 University of Texas at El Paso, El Paso, Texas, USA 2 University of Central Florida, Orlando, Florida, USA 3 SpaceX, Hawthorne, California, USA 4 Lockheed Martin Corporation, Palmdale, California, USA 5 XL Scientific, Albuquerque, New Mexico, USA Abstract: Periodic structures, or lattices, have proven to be one of the most enabling technologies of the 21st century. They allowed us to make objects invisible, to manipulate light and sound like we do electricity in computer chips, to dramatically reduce size and weight of structures while maintaining mechanical strength, and appear to break fundamental laws of physics. Despite these accomplishments, profound physical mechanisms still remain hidden inside the lattices that have yet to be effectively utilized. Electromagnetic fields cannot be manipulated inside homogeneous media. There must exist an interface, a gradient, or some form of inhomogeneity. Uniform lattices can be compared to homogeneous media that have limited usefulness. To unlock the hidden physics, lattices must be made macroscopically inhomogeneous without also unintentionally deforming the unit cells. Bending, twisting, and otherwise spatially varying a periodic structure in this manner requires impossible geometries, so until recently it has only been accomplished in simple and canonical configurations. A breakthrough by the EM Lab at the University of Texas at El Paso has led to a method for generating spatially-variant lattices (SVLs) without unintentionally deforming the unit cells, thus preserving their electromagnetic properties. Using this tool, the EM Lab is exploring new physics enabled by SVLs. In collaboration with the Kuebler Lab at the University of Central Florida, a spatially-variant photonic crystal (SVPC) was designed that achieved the tightest bend of optical beam ever reported in the literature. This was accomplished using an inexpensive material with low refractive index (n = 1.59). In other work, the EM Lab showed that a spatially-variant anisotropic metamaterial (SVAM) can be used to electromagnetically decouple two electrical components placed in close proximity. This talk will discuss the algorithm for generating SVLs as well as some of the new device concepts it has enabled so far. Keywords: Metamaterials, metasurfaces, photonic crystals, functionally graded, spatially-variant
Raymond C. Rumpf, Ph.D. Pioneering 21 st Century Electromagnetics and Photonics Subject Literature: 1. R. C. Rumpf, J. J. Pazos, J. L. Digaum, S. M. Kuebler, "Spatially-Variant Periodic Structures in Electromagnetics," Phil. Trans. R. Soc. A, Vol. 373, 2014.0359, July 2015. 2. J. L. Digaum, J. J. Pazos, J. Chiles, J. D'Archangel, G. Padilla, A. Tatulian, R. C. Rumpf, S. Fathpour, G. D. Boreman, and S. M. Kuebler, "Tight Control of Light Beams in Photonic Crystals with Spatially-Variant Lattice Orientation," Optics Express, Vol. 22, Issue 21, pp. 25788-25804, 2014. 3. R. C. Rumpf, C. R. Garcia, H. H. Tsang, J. E. Padilla, M. D. Irwin, "Electromagnetic Isolation of a Microstrip by Embedding in a Spatially Variant Anisotropic Metamaterial," PIER, Vol. 142, pp. 243-260, 2013. 4. Indumathi R. Srimathi, Aaron J. Pung, Yuan Li, Raymond C. Rumpf, and Eric G. Johnson, "Fabrication of metal-oxide nano-hairs for effective index optical elements," Optics Express, Vol. 21, No. 16, pp. 18733-18741, 2013. 5. R. C. Rumpf, M. Gates, C. L. Kozikowski, W. A. Davis, "Guided-Mode Resonance Filter Compensated to Operate on a Curved Surface," PIER C, Vol. 40, pp. 93-103, 2013. 6. R. C. Rumpf, J. Pazos, C. R. Garcia, L. Ochoa, and R. Wicker, "3D Printed Lattices with Spatially Variant Self-Collimation," PIER, Vol. 139, pp. 1-14, 2013. 7. C. R. Garcia, J. Correa, D. Espalin, J. H. Barton, R. C. Rumpf, R. Wicker, V. Gonzalez, "3D Printing of Anisotropic Metamaterials," PIER Lett, Vol. 34, pp. 75-82, 2012. 8. R. C. Rumpf, J. Pazos, "Synthesis of Spatially Variant Lattices," Opt. Express, Vol. 20, Issue 14, pp. 15263-15274 (2012). Dr. Raymond C. Rumpf is an Associate Professor of Electrical and Computer Engineering at the University of Texas at El Paso (UTEP), and has a joint appointment in the Computational Science program. In Fall 2010, Raymond formed the EM Lab at UTEP with a mission to develop revolutionary technologies enabled by digital manufacturing. Prior to joining UTEP, Raymond was the Chief Technology Officer for Prime Photonics where he helped transform the company s technology portfolio from exclusively fiber optic sensors to an array of technologies for extreme applications. Before Prime Photonics, Raymond was a Principle Investigator for Harris Corporation where he researched and developed a wide range of technologies to radically miniaturize communications systems. Raymond earned his BS and MS in Electrical Engineering from the Florida Institute of Technology in 1995 and 1997 respectively. He earned his PhD in Optics in 2006 from the University of Central Florida. In 2015, Raymond was awarded the highly prestigious University of Texas Regents Outstanding Teaching Award. Raymond has been awarded over a dozen United States patents and has authored dozens of peerreviewed journal articles. He is an Associate Editor for SPIE Optical Engineering, Program Chair for Advanced Fabrication Technologies at Photonics West, and a Senior Member of SPIE. He is also a member of IEEE, OSA, and ARRL. Raymond is active in outreach with local grade schools in El Paso as well as mentoring students in third-world countries. *This use of this work is restricted solely for academic purposes. The author of this work owns the copyright and no reproduction in any form is permitted without permission by the author.*
Dr. Raymond C. Rumpf Director, EM Lab Associate Professor of Electrical and Computer Engineering University of Texas at El Paso, El Paso, Texas 79968 rcrumpf@utep.edu (202) 64-EMLAB http://emlab.utep.edu
Presentation Outline Spatially variant lattices (SVLs) SVL Algorithm Applications of SVLs Cloaking and invisibility Spatially variant photonic crystals Spatially variant anisotropic metamaterials Conclusion Slide 2
Journey to SVLs EM Lab Revolutionary technologies enabled by digital manufacturing 3 rd Dimension EM & photonics stuck in two dimensions. How do we utilize the 3 rd dimension? Spatially-Variant Lattices Functionally grade Preserve properties Slide 4
What is a Spatially Variant Lattice? Slide 5
What Can Be Spatially Varied? Orientation of unit cells Lattice spacing Fill factor Pattern within the unit cell Material composition Symmetry Square hexagonal Everything!!! Slide 6
Spatially-Variant Planar Gratings Spatially-Variant Orientation Spatially-Variant Fill Fraction Spatially-Variant Period Spatially-Variant Everything Slide 8
Synthesis Procedure for Planar Gratings Step 1 of 5: Define Spatial Variance C Spatially-Variant Lattice Orientation Spatially-Variant Lattice Spacing Spatially-Variant Threshold r r r Slide 9
Synthesis Procedure for Planar Gratings Step 2 of 5: Calculate Spatially-Variant K-Function cos r 2 K r cos r aˆ sin ˆ x r a K r y Grating Vector K Slide 10
Synthesis Procedure for Planar Gratings Step 3 of 5: Calculate Grating Phase r K r best fit r Slide 11
Synthesis Procedure for Planar Gratings Step 4 of 5: Calculate Analog PSV Grating a r cos r Slide 12
Synthesis Procedure for Planar Gratings Step 5 of 5: Calculate Binary PSV Grating b r r r r1 a r2 a r r Slide 13
Generalization to Arbitrary Lattices (1 of 2) FFT Slide 14
Generalization to Arbitrary Lattices (2 of 2) Slide 15
Arrays of Discontinuous Metallic Elements + = R. C. Rumpf, et al "Spatially-Variant Periodic Structures in Electromagnetics," Phil. Trans. R. Soc. A 373, 2014.0359, July 2015. Slide 16
Arrays on Curved Surfaces top view perspective view R. C. Rumpf, et al "Spatially-Variant Periodic Structures in Electromagnetics," Phil. Trans. R. Soc. A 373, 2014.0359, July 2015. Slide 17
Common Spatial Variance From the Literature Minatti, Gabriele, et al. "A circularly-polarized isoflux antenna based on anisotropic metasurface." IEEE Transactions on Antennas and Propagation 60.11 (2012): 4998-5009. Vasić, Borislav, et al. "Controlling electromagnetic fields with graded photonic crystals in metamaterial regime." Optics express 18.19 (2010): 20321-20333. Slide 18
Cloak Example Spatial Transform Slide 20
Cloak Example Transformation Optics & Slide 21
Cloak Example Diagonalize Tensors Slide 22
Cloak Example Design Metamaterials Slide 23
Cloak Example Spatial Variance Slide 24
Cloak Example Place Elements Slide 25
Arbitrarily Shaped Cloak Benefits of Spatial Variance: Accommodates any shaped device Greater density of elements Prevents element overlap Minimizes deformations to the unit cells Slide 26
Normalized Frequency w n = l 0 / a Self-Collimation Vs. Graded-Index y y Power x x a x 0 0 a a a y Slide 28
Bending a Self-Collimating Lattice Slide 29
Beams Through an SVPC Uniform Lattice Bent Lattice Match between input and output faces US Provisional Patent 62,351,565 Slide 30
World s Tightest Unguided Bend 30 m Bend radius was 6.7l 0. Low refractive index (SU-8, n 1.59). Operated at l 0 = 2.94 m. Recently demonstrated l 0 = 1.55 m. J. L. Digaum et al "Tight Control of Light Beams in Photonic Crystals with Spatially- Variant Lattice Orientation," Optics Express, Vol. 22, Issue 21, pp. 25788-25804, 2014. Slide 31
1550 nm SVPC 25 m Slide 32
A Sharp Double Bend r 3 l 0 Slide 33
Optical High-Speed Interconnects Circuit Board BGA w VCSELs Sharp Waveguide Bends SVPC Funnel US Provisional Patent 62,351,565 Slide 34
What is a 3D Circuit? Conventional 2D Circuit 3D Circuit Slide 36
Field Sculpting Raymond C. Rumpf "Engineering the Dispersion and Anisotropy of Periodic Electromagnetic Structures," Solid State Physics, Vol. 66, pp. 213-300, 2015. Slide 37
All-Dielectric Anisotropic Metamaterials All-dielectric Very low loss Ultra broadband Strong anisotropy C. R. Garcia, J. Correa, D. Espalin, J. H. Barton, R. C. Rumpf, R. Wicker, V. Gonzalez, "3D Printing of Anisotropic Metamaterials," PIER Lett, Vol. 34, pp. 75-82, 2012. Slide 38
Microstrip Decoupled From Metal Object in Close Proximity R. C. Rumpf, C. R. Garcia, H. H. Tsang, J. E. Padilla, M. D. Irwin, "Electromagnetic Isolation of a Microstrip by Embedding in a Spatially Variant Anisotropic Metamaterial," PIER, Vol. 142, pp. 243-260, 2013. Slide 39
Two Antennas Decoupled in 3D Printed Mobile Phone US Provisional Patent 62,016,478 Slide 40
Space Stretching Coordinate Transform x x y y z z a Output From TO a 0 0 0 a 0 0 0 a x z y US Provisional Patent 62,160,374 Slide 41
Space Stretching Negative Uniaxial Metamaterial Output From TO a 0 0 0 a 0 0 0 a x z y US Provisional Patent 62,160,374 Slide 42
Vision for 3D Printed Circuits and Electromagnetic Systems US Provisional Patent 62,016,478 Slide 43
Vision for 3D Printed Circuits and Electromagnetic Systems SVAM infill US Provisional Patent 62,016,478 Slide 44
Conclusion Spatially-variant lattices preserve electromagnetic properties SVLs enable many device concepts Periodic structures on curved surfaces Cloaking and invisibility Spatially variant photonic crystals Spatially variant anisotropic metamaterials Acknowledgements Dr. Raj Mittra DARPA YFA N66001-11-1-415 W.M. Keck Center for 3D Innovation University of Central Florida nscrypt DSM Somos Entire EM Lab team! Slide 45