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2021-09-07
Wave Propagation in Electric Periodic Structure in Space with Modulation in Time (2D+1)
By
Progress In Electromagnetics Research M, Vol. 104, 145-158, 2021
Abstract
We studied electromagnetic wave propagation in a system that is periodic in both space and time, namely a discrete 2D transmission line (TL) with capacitors modulated in tandem externally. Kirchhoff's laws lead to an eigenvalue equation whose solutions yield a band structure (BS) for the circular frequency ω as function of the phase advances kxa and kya in the plane of the TL. The surfaces ω(kxa, kya) display exotic behavior like forbidden ω bands, forbidden k bands, both, or neither. Certain critical combinations of the modulation strength mc and the modulation frequency Ω mark transitions from ω stopbands to forbidden k bands, corresponding to phase transitions from no propagation to propagation of waves. Such behavior is found invariably at the high symmetry X and M points of the spatial Brillouin zone (BZ) and at the boundary ω = (1/2)Ω of the temporal BZ. At such boundaries the ω(kxa, kya) surfaces in neighboring BZs assume conical forms that just touch, resembling a South American toy ``diábolo''; the point of contact is thus called a ``diabolic point''. Our investigation reveals interesting interplay among geometry, critical points, and phase transitions.
Citation
Jose Salazar-Arrieta Peter Halevi , "Wave Propagation in Electric Periodic Structure in Space with Modulation in Time (2D+1)," Progress In Electromagnetics Research M, Vol. 104, 145-158, 2021.
doi:10.2528/PIERM21061707
http://www.jpier.org/PIERM/pier.php?paper=21061707
References

1. Brillouin, L., Wave Propagation in Periodic Structures: Electric Filters and Crystal Lattices, Dover Publications, 1953.

2. Kittel, C., Introduction to Solid State Physics, 8th Ed., Wiley, 2005.

3. Joannopoulos, J. D., S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals, Princeton University Press, 2008.

4. Caloz, C. and T. Itoh, Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications, Wiley, 2006.

5. Pozar, D. M., Microwave Engineering, Wiley, 2012.

6. Momeni, O. and E. Afshari, "Electrical prism: A high quality factor filter for millimeter-wave and terahertz frequencies," IEEE Trans. Microw. Theory Techn., Vol. 57, No. 11, 2790-2799, 2009.
doi:10.1109/TMTT.2009.2032343

7. Afshari, E., H. S. Bhat, A. Hajimiri, and J. E. Marsden, "Extremely wideband signal shaping using one- and two-dimensional nonuniform nonlinear transmission lines," J. Appl. Phys., Vol. 99, 054901, 2006.
doi:10.1063/1.2174126

8. Lilis, G. N., J. Park, W. Lee, G. Li, H. S. Bhat, and E. Afshari, "Harmonic generation using nonlinear LC lattices," IEEE Trans. Microw. Theory Techn., Vol. 588, 1713-1723, 2010.
doi:10.1109/TMTT.2010.2049678

9. Bhat, H. S. and E. Afshari, "Nonlinear constructive interference in electrical lattices," Phys. Rev. E, Vol. 77, 066602, 2008.
doi:10.1103/PhysRevE.77.066602

10. Tousi, Y. M. and E. Afshari, "2-D electrical interferometer: A novel high-speed quantizer," IEEE Trans. Microw. Theory Techn., Vol. 58, 2549-2561, 2010.
doi:10.1109/TMTT.2010.2063830

11. Lee, W., M. Adnan, O. Momeni, and E. Afshari, "A nonlinear lattice for high-amplitude picosecond pulse generation in CMOS," IEEE Trans. Microw. Theory Techn., Vol. 60, 370-380, 2012.
doi:10.1109/TMTT.2011.2178255

12. Iyer, A. K. and G. V. Eleftheriades, "Negative refractive index metamaterials supporting 2-D waves," 2002 IEEE MTT-S International Microwave Symposium Digest, 1067-1070, 2002.

13. Eleftheriades, G. V., A. K. Iyer, P. C. Kremer, and , "Planar negative refractive index media using periodically L-C loaded transmission lines," IEEE Trans. Microw. Theory Techn., Vol. 50, 2702-2712, 2002.
doi:10.1109/TMTT.2002.805197

14. Milford, G. N. and G. V. Eleftheriades, "2D multiplier with left-handed focusing lens for terahertz signal generation," 2013 IEEE Antennas and Propagation Society International Symposium, 1182-1183, 2013.

15. Algredo-Badillo, U. and P. Halevi, "Negative refraction and focusing in magnetically coupled L-C loaded transmission lines," J. Appl. Phys., Vol. 102, 086104, 2007.
doi:10.1063/1.2794558

16. Eleftheriades, G. V. and O. F. Siddiqui, "Negative refraction and focusing in hyperbolic transmission-line periodic grids," IEEE Trans. Microw. Theory Techn., Vol. 53, 396-403, 2005.
doi:10.1109/TMTT.2004.839944

17. Zurita-Sánchez, J. R., P. Halevi, and J. C. Cervantes-González, "Reflection and transmission of a wave incident on a slab with a time-periodic dielectric function ϵ(t)," Phys. Rev. A, Vol. 79, 053821, 2009.
doi:10.1103/PhysRevA.79.053821

18. Zurita-Sánchez, J. R. and P. Halevi, "Resonances in the optical response of a slab with time-periodic dielectric function ϵ(t)," Phys. Rev. A, Vol. 81, 053834, 2010.
doi:10.1103/PhysRevA.81.053834

19. Martínez-Romero, J. S., O. M. Becerra-Fuentes, and P. Halevi, "Temporal photonic crystals with modulations of both permittivity and permeability," Phys. Rev. A, Vol. 93, 063813, 2016.
doi:10.1103/PhysRevA.93.063813

20. Martínez-Romero, J. S. and P. Halevi, "Parametric resonances in a temporal photonic crystal slab," Phys. Rev. A, Vol. 98, 053852, 2018.
doi:10.1103/PhysRevA.98.053852

21. Reyes-Ayona, J. R. and P. Halevi, "Observation of genuine wave vector (k or β) gap in a dynamic transmission line and temporal photonic crystals," Appl. Phys. Lett., Vol. 107, 2015.

22. Reyes-Ayona, J. R. and P. Halevi, "Electromagnetic wave propagation in an externally modulated low-pass transmission line," IEEE Trans. Microw. Theory Techn., Vol. 64, 3449-3459, 2016.
doi:10.1109/TMTT.2016.2604319

23. Halevi, P., U. Algredo-Badillo, and J. R. Zurita-Sánchez, "Optical response of a slab with time-periodic dielectric function ε(t): Towards a dynamic metamaterial," Active Photonic Materials IV, 61-75, 2011.

24. Mohammad-Ali, M. and A. Alù, "Exceptional points in optics and photonics," Science, Vol. 363, No. 6422, 2019.
doi:10.1126/science.aat3158

25. Marsden, J. E. and A. J. Tromba, Vector Calculus, Pearson, 2004.

26. Yakovlev, A. B. and G. W. Hanson, "On the nature of critical points in leakage regimes of a conductor-backed coplanar strip line," IEEE Trans. Microw. Theory Techn., Vol. 45, No. 1, 87-94, 1997.
doi:10.1109/22.552036

27. Miller, J. L., "Exceptional points make for exceptional sensors," Phys. Today, Vol. 70, No. 10, 23-26, 2017.
doi:10.1063/PT.3.3717

28. Seyranian, A. P., O. N. Kirillov, and A. A. Mailybaev, "Coupling of eigenvalues of complex matrices at diabolic and exceptional points," J. Phys. A, Vol. 38, 1723-1740, 2005.
doi:10.1088/0305-4470/38/8/009

29. Heiss, W. D., "The physics of exceptional points," J. Phys. A, Vol. 45, 444016, 2012.
doi:10.1088/1751-8113/45/44/444016

30. Chen, W., S. Kaya Özdemir, G. Zhao, J. Wiersig, and L. Yang, "Exceptional points enhance sensing in an optical microcavity," Nature, Vol. 548, 192-196, 2017.
doi:10.1038/nature23281

31. Hodaei, H., A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, "Enhanced sensitivity at higher-order exceptional points," Nature, Vol. 548, 1476-4687, 2017.

32. El-Ganainy, R., K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, "Non-Hermitian physics and PT symmetry," Nat. Phys., Vol. 14, 1745-2481, 2018.

33. Kazemi, H., Y. N. Mohamed, M. Tarek, F. Ahmed, and C. Filippo, "Exceptional points of degeneracy induced by linear time-periodic variation," Phys. Rev. Applied, Vol. 11, 14007, 2019.
doi:10.1103/PhysRevApplied.11.014007

34. Berry, M. V. and M. Wilkinson, "Diabolical points in the spectra of triangles," Proc. R. Soc. A, Vol. 392, 15-43, 1984.

35. Dubbers, D. and H.-J. Stöckmann, Quantum Physics: The Bottom-up Approach, Springer, 2013.
doi:10.1007/978-3-642-31060-7