volume | PIER Journals

Abstract

Most tunneling effects are investigated using a one-dimensional model, but such an approach fails to explain the phenomena of the propagation of wave in a system with geometric discontinuities. This work studies the tunneling characteristics in a waveguide system that consists of a middle section with a distinct cutoff frequency, which is controlled by the cross-sectional geometry. Unlike in the one-dimensional case, in which only the fundamental mode is considered, in a virtually three-dimensional system, multiple modes have to be taken into consideration. High-order modes (HOMs) modify the amplitude and the phase of the fundamental mode (TE₁₀), thus subsequently affecting the transmission and group delay of a wave. The effect of the high-order evanescent modes is calculated, and the results are compared with the simulated ones using a full-wave solver. Both oversized and undersized waveguides reveal the necessity of considering the HOMs. The underlying physics is manifested using a multiple-reflection model. This study indicates that the high-order evanescent modes are essential to the explanation of the phenomena in a tunneling system with geometrical discontinuities.

1. Landauer, R. and T. Martin, "Barrier interaction time in tunneling," Rev. Mod. Phys., Vol. 66, No. 1, 217-228, 1994.
doi:10.1103/RevModPhys.66.217 Google Scholar

2. Hauge, E. H. and J. A. Stovneng, "Tunneling time: A critical review," Rev. Mod. Phys., Vol. 61, No. 4, 917-936, 1989.
doi:10.1103/RevModPhys.61.917 Google Scholar

3. Solli, D., R. Y. Chiao, and J. M. Hickmann, "Superluminal effects and negative group delays in electronics, and their applications," Phys. Rev. E, Vol. 66, 056601, 2002.
doi:10.1103/PhysRevE.66.056601 Google Scholar

4. Jackson, A. D., A. Lande, and B. Lautrup, "Apparent superluminal behavior in wave propagation," Phys. Rev. A, Vol. 64, 044101, 2001.
doi:10.1103/PhysRevA.64.044101 Google Scholar

5. Winful, H. G., "Nature of superluminal barrier tunneling," Phys. Rev. Lett., Vol. 90, 023901, 2003.
doi:10.1103/PhysRevLett.90.023901 Google Scholar

6. Hartman, T. E., "Tunneling of a wave packet," J. Appl. Phys., Vol. 33, No. 12, 3427-3433, 1962.
doi:10.1063/1.1702424 Google Scholar

7. Winful, H. G., "Delay time and the hartman effect in quantum tunneling," Phys. Rev. Lett., Vol. 91, 260401, 2003.
doi:10.1103/PhysRevLett.91.260401 Google Scholar

8. Stenner, M. D., D. J. Gauthier, and M. A. Neifeld, "Fast causal information transmission in a medium with a slow group velocity," Phys. Rev. Lett., Vol. 94, 053902, 2005.
doi:10.1103/PhysRevLett.94.053902 Google Scholar

9. Wang, L. J., A. Kuzmich, and A. Dogariu, "Gain-assisted superluminal light propagation," Nature, Vol. 406, 277-279, 2000.
doi:10.1038/35018520 Google Scholar

10. Cui, C. L., J. K. Jia, J. W. Gao, Y. Xue, G. Wang, and J. H. Wu, "Ultraslow and superluminal light propagation in a four-level atomic system," Phys. Rev. A, Vol. 76, 033815, 2007.
doi:10.1103/PhysRevA.76.033815 Google Scholar

11. Halvorsen, T. G. and J. M. Leinaas, "Superluminal group velocity in a birefringent crystal," Phys. Rev. A, Vol. 77, 023808, 2008.
doi:10.1103/PhysRevA.77.023808 Google Scholar

12. Steinberg, A. M., P. G. Kwiat, and R. Y. Chiao, "Measurement of the single-photon tunneling time," Phys. Rev. Lett., Vol. 71, No. 5, 708-711, 1993.
doi:10.1103/PhysRevLett.71.708 Google Scholar

13. Von Freymann, G., S. John, S. Wong, V. Kitaev, and G. A. Ozin, "Measurement of group velocity dispersion for finite size three-dimensional photonic crystals in the near-infrared spectral region," Appl. Phys. Lett., Vol. 86, 053108, 2005.
doi:10.1063/1.1857076 Google Scholar

14. Vetter, R. M., A. Haibel, and G. Nimtz, "Negative phase time for scattering at quantum wells: A microwave analogy experiment," Phys. Rev. E, Vol. 63, 046701, 2001.
doi:10.1103/PhysRevE.63.046701 Google Scholar

15. Brodowsky, H. M., W. Heitmann, and G. Nimtz, "Comparison of experimental microwave tunneling data with calculations based on Maxwell's equations," Phys. Lett. A, Vol. 222, 125-129, 1996.
doi:10.1016/0375-9601(96)00646-9 Google Scholar

16. Winful, H. G., "Group delay, stored energy, and the tunneling of evanescent electromagnetic waves," Phys. Rev. E, Vol. 68, 016615, 2003.
doi:10.1103/PhysRevE.68.016615 Google Scholar

17. Wang, Z. Y. and C. D. Xiong, "Theoretical evidence for the superluminality of evanescent modes," Phys. Rev. A, Vol. 75, 042105, 2007.
doi:10.1103/PhysRevA.75.042105 Google Scholar

18. Chen, X. and C. Xiong, "Electromagnetic simulation of the evanescent mode," Ann. Phys. (Leipzig), Vol. 7, 631, 1998. Google Scholar

19. Pablo, A., L. Barbero, H. E. Hernandez-Figueroa, and E. Recami, "Propagation speed of evanescent modes," Phys. Rev. E, Vol. 62, No. 6, 8628-8635, 2000.
doi:10.1103/PhysRevE.62.8628 Google Scholar

20. Enders, A. and G. Nimtz, "Photonic-tunneling experiments," Phys. Rev. B, Vol. 47, No. 15, 9605-9609, 1993.
doi:10.1103/PhysRevB.47.9605 Google Scholar

21. Enders, A. and G. Nimtz, "Evanescent-mode propagation and quantum tunneling," Phys. Rev. E, Vol. 48, No. 1, 632-634, 1993.
doi:10.1103/PhysRevE.48.632 Google Scholar

22. Winful, H. G., "The meaning of group delay in barrier tunnelling: A re-examination of superluminal group velocities," New J. Phys., Vol. 8, 101, 2006.
doi:10.1088/1367-2630/8/6/101 Google Scholar

23. Fleming, J. G., S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, "All-metallic three-dimensional photonic crystals with a large infrared bandgap," Nature, Vol. 417, 52-55, 2002.
doi:10.1038/417052a Google Scholar

24. Capmany, J. and D. Novak, "Microwave photonics combines two worlds," Nature Photonic, Vol. 1, 319-330, 2007.
doi:10.1038/nphoton.2007.89 Google Scholar

25. Pozar, D. M., Microwave Engineering, Chap. 5, Addison-Welsey, New York, 1990.

26. Gesell, G. A. and I. R. Ciric, "Recurrence modal analysis for multiple waveguide discontinuities and its application to circular structures," IEEE Trans. Microwave Theory Tech., Vol. 41, No. 3, 484-490, 1993.
doi:10.1109/22.223749 Google Scholar

27. Rozzi, T. E. and W. F. G. Mecklenbrauker, "Wide-band network modeling of interacting inductive irises and steps," IEEE Trans. Microwave Theory Tech., Vol. 23, No. 2, 235-240, 1975.
doi:10.1109/TMTT.1975.1128532 Google Scholar

28. Davies, P. C. W., "Quantum tunneling time," Am. J. Phys., Vol. 73, No. 1, 23-27, 2004.
doi:10.1119/1.1810153 Google Scholar

Dr. Hsin-Yu Yao

Prof. Tsun-Hun Chang