Engineering Metamaterial Interface Scattering Coefficients via Quantum Graph Theory
Main Article Content
Abstract
For layered metamaterial devices, the reflection and transmission coefficients at an interface typically depend on the properties of the coupling between different layers. In this paper, we set out to engineer the reflection/transmission behaviour at boundaries to obtain desirable properties such as achieving total reflection and transmission. Based on the quantum graph formulation for modelling metamaterials developed in Sci. Rep. 12 (1), 18006 (2022), we tailor the interface reflection and transmission coefficients by patterning the boundary with resonant elements at each interface vertex. By tuning the internal lengths of the resonant elements, we demonstrate both minimization and maximization of the reflection coefficient via a scattering formulation. In addition, we present an interface set-up incorporating beyond-nearest-neighbour connections, which yields narrow-band transmission for certain angles only, creating an angular filtering interface.
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
R. Kumar, M. Kumar, J. Singh Chohan, S. Kumar, Mater. Today 56, 3016 (2022)
Y. Chen, M. Kadic, M. Wegener, Nature Commun. 12, 3278 (2021)
J.A.I. Martínez, M.F. Groß, Y. Chen, T. Frenzel, V. Laude, M. Kadic, M. Wegener, Sci. Adv. 7, eabm2189 (2021)
D.B. Moore, J.R. Sambles, A.P. Hibbins, T.A. Starkey, G.J. Chaplain, Phys. Rev. B 107, 144110 (2023)
G.J. Chaplain, I.R. Hooper, A.P. Hibbins, T.A. Starkey, Phys. Rev. Appl. 19, 044061, (2023)
Y. Chen, J.L.G. Schneider, M.F. Groß, K. Wang, S. Kalt, P. Scott, M. Kadic, M. Wegener, Adv. Funct. Mater. 33, 2302699 (2023)
A. Kazemi, K.J. Deshmukh, F. Chen, Y. Liu, B. Deng, H. Chien Fu, P. Wang, Phys. Rev. Lett. 131, 176101 (2023)
L. Brillouin, Wave Propagation and Group Velocity, Academic Press, New York 1960
T. Lawrie, G. Tanner, D. Chronopoulos, Sci. Rep. 12, 18006 (2022)
T. Kottos, U. Smilansky, Ann. Phys. 274, 76 (1999)
S. Gnutzmann, U. Smilansky, Adv. Phys. 55, 527 (2006)
G. Berkolaiko, P. Kuchment, Introduction to Quantum Graphs, Vol. 186, American Mathematical Soc., 2013
C. Brewer, S.C. Creagh, G. Tanner, J. Phys. A Math. Theor. 51, 445101 (2018)
J. Kempe, Contemp. Phys. 44, 307 (2003)
G.K. Tanner, in: Non-Linear Dynamics and Fundamental Interactions: Proceedings of the NATO Advanced Research Workshop on Non-Linear Dynamics and Fundamental Interactions, Tashkent 2004, Springer, 2006, p. 87
B. Hein, G. Tanner, Phys. Rev. Lett. 103, 260501 (2009)
T. Lawrie, S. Gnutzmann, G. Tanner, arXiv:2309.11251, 2023
P. Kuchment, J. Physics A Math. General 38, 4887 (2005)
P. Exner, S. Nakamura, Y. Tadano, Lett. Math. Phys. 112, 83 (2022)
M. Touboul, Ph.D. thesis, Aix-Marseille Université, 2021