On the Use of Electromagnetic Inversion for Metasurface Design

We show that the use of the electromagnetic inverse source framework offers great flexibility in the design of metasurfaces. In particular, this approach is advantageous for antenna design applications where the goal is often to satisfy a set of performance criteria such as half power beamwidths and null directions, rather than satisfying a fully known complex field. In addition, the inverse source formulation allows the metasurface and the region over which the desired field specifications are provided to be of arbitrary shape. Some of the main challenges in solving this inverse source problem, such as formulating and optimizing a nonlinear cost functional, are addressed. Lastly, some 2-D and 3-D simulated examples are presented to demonstrate the method, followed by a discussion of the method’s current limitations.

[1]  Natalia K. Nikolova.  Introduction to Microwave Imaging: Contents , 2017 .

[2]  Per Christian Hansen,et al.  Analysis of Discrete Ill-Posed Problems by Means of the L-Curve , 1992, SIAM Rev..

[3]  Aria Abubakar,et al.  2.5D forward and inverse modeling for interpreting low-frequency electromagnetic measurements , 2008 .

[4]  Christophe Caloz,et al.  General Metasurface Synthesis Based on Susceptibility Tensors , 2014, IEEE Transactions on Antennas and Propagation.

[5]  A. Devaney,et al.  Nonuniqueness in inverse source and scattering problems , 1982 .

[6]  Giuseppe D'Elia,et al.  Antenna pattern synthesis: a new general approach , 1994, Proc. IEEE.

[7]  P. Hansen,et al.  Iterative regularization with minimum-residual methods , 2007 .

[8]  G. Eleftheriades,et al.  Discontinuous electromagnetic fields using orthogonal electric and magnetic currents for wavefront manipulation. , 2013, Optics express.

[9]  David R. Smith,et al.  An Overview of the Theory and Applications of Metasurfaces: The Two-Dimensional Equivalents of Metamaterials , 2012, IEEE Antennas and Propagation Magazine.

[10]  Tommaso Isernia,et al.  Volumetric Invisibility Cloaks Design Through Spectral Coverage Optimization , 2019, IEEE Access.

[11]  Metasurface Design Using Electromagnetic Inversion , 2019, 2019 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting.

[12]  D. González-Ovejero,et al.  Modulated Metasurface Antennas for Space: Synthesis, Analysis and Realizations , 2015, IEEE Transactions on Antennas and Propagation.

[13]  T. K. Sarkar,et al.  Differences Between Modal Expansion and Intergral Equation Methods for Planar Near-Field to Far-Field Transformation , 1996 .

[14]  A. Abubakar,et al.  Optical microscopy imaging using the contrast source inversion method , 2010 .

[15]  Puyan Mojabi,et al.  Multiplicatively Regularized Source Reconstruction Method for Phaseless Planar Near-Field Antenna Measurements , 2017, IEEE Transactions on Antennas and Propagation.

[16]  Christophe Caloz,et al.  Simulation of Metasurfaces in Finite Difference Techniques , 2016, IEEE Transactions on Antennas and Propagation.

[17]  P. Hansen.  Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion , 1987 .

[18]  Tapan K. Sarkar,et al.  Differences between modal expansion and integral equation methods for planar near-field to far-field transformation (Summary) , 1996 .

[19]  J. Lovetri,et al.  Overview and Classification of Some Regularization Techniques for the Gauss-Newton Inversion Method Applied to Inverse Scattering Problems , 2009, IEEE Transactions on Antennas and Propagation.

[20]  Sergei A. Tretyakov,et al.  Susceptibility Derivation and Experimental Demonstration of Refracting Metasurfaces Without Spurious Diffraction , 2018, IEEE Transactions on Antennas and Propagation.

[21]  G. Vecchi,et al.  Improved-Accuracy Source Reconstruction on Arbitrary 3-D Surfaces , 2009, IEEE Antennas and Wireless Propagation Letters.

[22]  P. Hansen.  Discrete Inverse Problems: Insight and Algorithms , 2010 .

[23]  T. Isernia,et al.  Design of Artificial-Material-Based Antennas Using Inverse Scattering Techniques , 2018, IEEE Transactions on Antennas and Propagation.

[24]  Paul M. Meaney,et al.  Fast 3-D Tomographic Microwave Imaging for Breast Cancer Detection , 2012, IEEE Transactions on Medical Imaging.

[25]  C. Pfeiffer,et al.  Metamaterial Huygens' surfaces: tailoring wave fronts with reflectionless sheets. , 2013, Physical review letters.

[26]  T. Isernia,et al.  Towards Printable Natural Dielectric Cloaks via Inverse Scattering Techniques , 2017, Scientific Reports.

[27]  Amir H. Golnabi,et al.  3-D Microwave Tomography Using the Soft Prior Regularization Technique: Evaluation in Anatomically Realistic MRI-Derived Numerical Breast Phantoms , 2019, IEEE Transactions on Biomedical Engineering.

[29]  C. Caloz,et al.  A guided tour in metasurface land: Discontinuity conditions, design and applications , 2017, 2017 IEEE International Conference on Computational Electromagnetics (ICCEM).

[30]  F. Las-Heras,et al.  Reconstruction of Equivalent Currents Distribution Over Arbitrary Three-Dimensional Surfaces Based on Integral Equation Algorithms , 2007, IEEE Transactions on Antennas and Propagation.

[31]  M. Chen,et al.  Theory, design, and experimental verification of a reflectionless bianisotropic Huygens' metasurface for wide-angle refraction. , 2018, 1812.05084.

[32]  M. Dehmollaian,et al.  Wave Scattering by a Cylindrical Metasurface Cavity of Arbitrary Cross Section: Theory and Applications , 2018, IEEE Transactions on Antennas and Propagation.

[33]  Andrea Massa,et al.  Synthesis of Shaped Beam Reflectarrays With Constrained Geometry by Exploiting Nonradiating Surface Currents , 2018, IEEE Transactions on Antennas and Propagation.

[34]  Christophe Caloz,et al.  Design, concepts, and applications of electromagnetic metasurfaces , 2017, Nanophotonics.

[35]  Per Christian Hansen,et al.  Rank-Deficient and Discrete Ill-Posed Problems , 1996 .

[36]  C. Holloway,et al.  Averaged transition conditions for electromagnetic fields at a metafilm , 2003 .

[37]  Per Christian Hansen,et al.  REGULARIZATION TOOLS: A Matlab package for analysis and solution of discrete ill-posed problems , 1994, Numerical Algorithms.

[38]  D. Wilton,et al.  Electromagnetic scattering by surfaces of arbitrary shape , 1980 .

[39]  Yahya Rahmat-Samii,et al.  The field equivalence principle: illustration of the establishment of the non-intuitive null fields , 2000 .

[40]  Trevor Brown,et al.  On the Use of Electromagnetic Inversion for Near-Field Antenna Measurements: A Review , 2018, 2018 IEEE Conference on Antenna Measurements & Applications (CAMA).

[41]  Janse van Rensburg,et al.  Theory and Practice of Modern Antenna Range Measurements , 2014 .

[42]  Tapan K. Sarkar,et al.  An Improved Super-Resolution Source Reconstruction Method , 2009, IEEE Transactions on Instrumentation and Measurement.

[43]  C. M. Reeves,et al.  Function minimization by conjugate gradients , 1964, Comput. J..

[44]  T. Isernia,et al.  Synthesis of new variable dielectric profile antennas via inverse scattering techniques: a feasibility study , 2005, IEEE Transactions on Antennas and Propagation.

[45]  S. Hum,et al.  Augmented Huygens’ Metasurfaces Employing Baffles for Precise Control of Wave Transformations , 2019, IEEE Transactions on Antennas and Propagation.

[46]  J. LoVetri,et al.  A Prescaled Multiplicative Regularized Gauss-Newton Inversion , 2011, IEEE Transactions on Antennas and Propagation.

[47]  George V. Eleftheriades,et al.  Circuit Modeling of Huygens Surfaces , 2013, IEEE Antennas and Wireless Propagation Letters.

[48]  Trevor Brown,et al.  On the Use of the Source Reconstruction Method for Metasurface Design , 2018 .

[49]  P. Hansen.  Numerical tools for analysis and solution of Fredholm integral equations of the first kind , 1992 .

[50]  S A Tretyakov,et al.  Metasurfaces for general transformations of electromagnetic fields , 2015, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[51]  Yu-Hong Dai,et al.  Conjugate Gradient Methods with Armijo-type Line Searches , 2002 .

[52]  George V. Eleftheriades,et al.  Huygens' metasurfaces via the equivalence principle: design and applications , 2016 .