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2012-11-24
Limits of Negative Group Delay Phenomenon in Linear Causal Media
By
Progress In Electromagnetics Research, Vol. 134, 227-246, 2013
Abstract
Asymptotic limits of Negative Group Delay (NGD) in linear causal media satisfying Kramers-Kronig relations are investigated. Even though there is no limit on the NGD-bandwidth product of a linear medium, it is shown that the out-of-band to center frequency amplitude ratio, or out-of-band gain, increases with the NGD-bandwidth product, and is proportional to the amplitude of undesired transients when waveforms with defined "turn on/off" times propagate in the media. The optimal causal dispersion characteristic exhibiting NGD is obtained through Kramers-Kronig relations, which maximizes the NGD-bandwidth product as a function of the out-of-band gain. It is shown that the NGD-bandwidth product has an upper asymptotic limit proportional to the square root of the logarithm of the maximum out-of-band gain. The derived NGD-bandwidth upper asymptotic limit of the optimally engineered causal dispersion characteristic is validated with two examples of physical media, a Lorentzian dielectric medium, and an artificially fabricated loaded transmission line medium.
Citation
Miodrag Kandic, and Greg E. Bridges, "Limits of Negative Group Delay Phenomenon in Linear Causal Media," Progress In Electromagnetics Research, Vol. 134, 227-246, 2013.
doi:10.2528/PIER12082915
References

1. Mojahedi, M., E. Schamiloglu, F. Hegeler, and K. J. Malloy, "Time-domain detection of superluminal group velocity for single microwave pulses," Phys. Rev. E, Vol. 62, No. 4, 2000.
doi:10.1103/PhysRevE.62.5758

2. Wang, Y., Y. Zhang, L. He, F. Liu, H. Li, and H. Chen, "Direct observation of negative phase velocity and positive group velocity in time domain for composite right/left-handed transmission lines," Journal of Applied Physics, Vol. 100, 113503, 2006.
doi:10.1063/1.2372573

3. Ibraheem, A., J. Schoebel, and M. Koch, "Group delay characteristics in coplanar waveguide left-handed media," Journal of Applied Physics, Vol. 103, 024903, 2008.
doi:10.1063/1.2832750

4. Mojahedi, M., K. J. Malloy, G. V. Eleftheriades, J. Woodley, and R. Y. Chiao, "Abnormal wave propagation in passive media," IEEE Journal of Selected Topics in Quantum Electronics, Vol. 9, No. 1, 30-39, 2003.
doi:10.1109/JSTQE.2002.807971

5. Bolda, L., R. Y. Chiao, and J. C. Garrison, "Two theorems for the group velocity in dispersive media," Phys. Rev. A, Gen. Phys., Vol. 48, No. 5, 3890-3894, Nov. 1993.
doi:10.1103/PhysRevA.48.3890

6. Brillouin, L., Wave Propagation and Group Velocity, Academic Press, New York, 1960.

7. Stenner, 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, No. 5, 053902, 2005.
doi:10.1103/PhysRevLett.94.053902

8. 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, No. 5, 056601, 2002.
doi:10.1103/PhysRevE.66.056601

9. Kandic, M. and G. Bridges, "Asymptotic limits of negative group delay in active resonator-based distributed circuits," IEEE Trans. Circuits Syst. I, Vol. 58, No. 8, 1727-1735, Aug. 2011.
doi:10.1109/TCSI.2011.2107251

10. Lucyszyn, S., I. D. Robertson, and A. H. Aghvami, "Negative group delay synthesiser," Electronics Letters, Vol. 29, No. 9, 798-800, Apr. 29, 1993.
doi:10.1049/el:19930533

11. Siddiqui, O. F., M. Mojahedi, and G. V. Eleftheriades, "Periodically loaded transmission line with effective negative refractive index and negative group velocity," IEEE Trans. on Antennas and Propag., Vol. 51, No. 10, 2619-2625, Oct. 2003.
doi:10.1109/TAP.2003.817556

12. Noto, H., K. Yamauchi, M. Nakayama, and Y. Isota, "Negative group delay circuit for feed-forward amplifier," IEEE/MTT-S International Microwave Symposium, 1103-1106, Jun. 3-8, 2007.

13. Mitchell, M. W. and R. Y. Chiao, "Causality and negative group delays in a simple bandpass amplifier," Am. J. Phys., Vol. 66, No. 1, 14-19, Jan. 1998.
doi:10.1119/1.18813

14. Ravelo, B., A. Perennec, M. Le Roy, and Y. G. Boucher, "Active microwave circuit with negative group delay," IEEE Microwave and Wireless Components Letters, Vol. 17, No. 12, 861-863, Dec. 2007.
doi:10.1109/LMWC.2007.910489

15. Choi, H., Y. Jeong, C. D. Kim, and J. S. Kenney, "Bandwidth enhancement of an analog feedback amplifier by employing a negative group delay circuit," Progress In Electromagnetics Research, Vol. 105, 253-272, 2010.
doi:10.2528/PIER10041808

16. Nakanishi, T., K. Sugiyama, and M. Kitano, "Demonstration of negative group delays in a simple electronic circuit," Am. J. Phys., Vol. 70, No. 11, 1117-1121, Nov. 2002.
doi:10.1119/1.1503378

17. Jackson, J. D., Classical Electrodynamics, 3rd Edition, John Wiley & Sons Inc., New York, 1998.

18. Bode, H. W., Network Analysis and Feedback Amplifier Design, Van Nostrand, New York, 1945.

19. Monti, G. and L. Tarricone, "Negative group velocity in a split ring resonator-coupled microstrip line," Progress In Electromagnetics Research, Vol. 94, 33-47, 2009.
doi:10.2528/PIER09052801