Exact Solution for the Protected TEM Edge Mode in a PTD-Symmetric Parallel-Plate Waveguide

A parity time-reversal duality symmetric structure constituted by a perfect electric conductor and perfect magnetic conductor (PMC) parallel plate waveguide is analyzed. This waveguide supports unimodal transverse electromagnetic (TEM) edge mode propagation protected against backscattering from a certain class of deformations and defects. The TEM solution is found in analytical form by using three different methods, namely, conformal mapping, mode-matching, and Fourier-transform methods. It is shown through numerical simulations that the mode propagation is robust with respect to deformations such as 90° bends and discontinuities such as transition to free space. Implementation of the PMC boundary conditions via both a bed of nails and a mushroom structure is also successfully investigated.

[1]  Permalink.  Guiding Waves Along an Infinitesimal Line between Impedance Surfaces , 2017 .

[2]  Per-Simon Kildal,et al.  Dispersion Characteristics of a Metamaterial-Based Parallel-Plate Ridge Gap Waveguide Realized by Bed of Nails , 2011, IEEE Transactions on Antennas and Propagation.

[3]  R. King,et al.  The synthesis of surface reactance using an artificial dielectric , 1983 .

[4]  S. Fan,et al.  Controlling the flow of light using the inhomogeneous effective gauge field that emerges from dynamic modulation. , 2013, Physical review letters.

[5]  P·T·Dsymmetry-protected scattering anomaly in optics , 2016, 1610.00688.

[6]  Miss A.O. Penney.  (b) , 1974, The New Yale Book of Quotations.

[7]  Dirac-Maxwell correspondence: Spin-1 bosonic topological insulator , 2017, 2018 Conference on Lasers and Electro-Optics (CLEO).

[8]  S. Raghu,et al.  Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry. , 2008, Physical review letters.

[9]  F. Haldane,et al.  Nobel lecture: Topological quantum matter , 2017 .

[10]  M. Silveirinha.  Chern invariants for continuous media , 2015 .

[11]  J.R. Costa,et al.  Electromagnetic Characterization of Textured Surfaces Formed by Metallic Pins , 2008, IEEE Transactions on Antennas and Propagation.

[12]  $\mathbb{Z}_{2}$ Topological Index for Continuous Photonic Materials , 2016, 1601.02823.

[13]  F. D. M. Haldane,et al.  Analogs of quantum-Hall-effect edge states in photonic crystals , 2008 .

[14]  M. Segev,et al.  Photonic Floquet topological insulators , 2012, Nature.

[15]  Vito Daniele,et al.  The Wiener-Hopf Method in Electromagnetics , 2014 .

[16]  M. Lipson,et al.  Subject Areas : Optics A Viewpoint on : Electrically Driven Nonreciprocity Induced by Interband Photonic Transition on a Silicon Chip , 2012 .

[17]  Zheng Wang,et al.  Observation of unidirectional backscattering-immune topological electromagnetic states , 2009, Nature.

[18]  Camille Jouvaud,et al.  Robust reconfigurable electromagnetic pathways within a photonic topological insulator. , 2016, Nature materials.

[19]  R. Collin.  Field theory of guided waves , 1960 .

[20]  D. Sievenpiper,et al.  High-impedance electromagnetic surfaces with a forbidden frequency band , 1999 .

[21]  E. Rajo-Iglesias,et al.  Local Metamaterial-Based Waveguides in Gaps Between Parallel Metal Plates , 2009, IEEE Antennas and Wireless Propagation Letters.

[22]  Yuri S. Kivshar,et al.  Three-dimensional all-dielectric photonic topological insulator , 2017 .

[23]  Eva Rajo-Iglesias,et al.  Design and experimental verification of ridge gap waveguide in bed of nails for parallel-plate mode suppression , 2011 .

[24]  Jensen Li,et al.  Gauge field optics with anisotropic media. , 2014, Physical review letters.

[25]  Raj Mittra,et al.  Analytical techniques in the theory of guided waves , 1971 .

[26]  Gennady Shvets,et al.  Photonic topological insulators. , 2013, Nature materials.

[27]  C. T. Chan,et al.  Symmetry-protected transport in a pseudospin-polarized waveguide , 2015, Nature Communications.

[28]  Fengzhou Fang,et al.  Topological photonic phase in chiral hyperbolic metamaterials. , 2015, Physical review letters.