Abstract

Current experimental investigations about time reversal (TR) electromagnetic (EM) fields always depended on TR mirror (TRM). However, EM fields can perform reversal operation invariance in four domains connected by Fourier Transform. A multiplication table and an appropriate operating figure about EM fields’ invariance are derived to describe a series of dual combined operations in the four domains, in which there are at least 10 dual-combination operations different from current TRM operations which can equivalently actualize TR symmetry. Theoretically, centrosymmetric operations of spatial position vector and spatial spectrum vector may have the potential to promote different reversal mirrors.

© 2013 Optical Society of America

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    [CrossRef] [PubMed]
  2. R. Carminati, R. Pierrat, J. de Rosny, and M. Fink, “Theory of the time reversal cavity for electromagnetic fields,” Opt. Lett.32(21), 3107–3109 (2007).
    [CrossRef] [PubMed]
  3. D. H. Chambers and J. G. Berryman, “Time-reversal analysis for scatterer characterization,” Phys. Rev. Lett.92(2), 023902 (2004).
    [CrossRef] [PubMed]
  4. P. Sundaralingam, V. Fusco, D. Zelenchuk, and R. Appleby, “Detection of an object in a reverberant environment using direct and differential time reversal,” 6th European Conference on Antennas and Propagation (2012).
    [CrossRef]
  5. P. Sundaralingam and V. Fusco, “Effect of quantisation and under sampling on time reversal spatial and temporal focusing in highly reverberant environment,” Proceedings of the 41st European Microwave Conference (2011).
  6. Y. M. Chen and B.-Z. Wang, “Seeing time-reversal transmission characteristics through kinetic anti-ferromagnetic Ising chain,” Chinese Phys. B21(2), 026401 (2012).
    [CrossRef]
  7. V. Dmitriev, “Space-time reversal symmetry properties of electromagnetic green’s tensors for complex and bianisotropic media,” PIER48, 145–184 (2004).
    [CrossRef]
  8. T. Strohmer, M. Emami, J. Hansen, G. Papanicolaou, and A. J. Paulraj, “Application of time-reversal with MMSE equalizer to UWB communications,” IEEE Global Telecommunications Conferenc5, 3123–3127 (2004).
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    [CrossRef] [PubMed]
  10. G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, “Focusing beyond the diffraction limit with far-Field time reversal,” Science315(5815), 1120–1122 (2007).
    [CrossRef] [PubMed]
  11. I. H. Naqvi, G. E. Zein, G. Lerosey, J. de Rosny, P. Besnier, A. Tourin, and M. Fink, “Experimental validation of time reversal ultra wide-band communication system for high data rates,” IET Microw. J. Antenna Propag.4(5), 643–650 (2010).
    [CrossRef]
  12. C. Zhou, N. Guo, and R. C. Qiu, “Time reversed ultra-wideband (UWB) multiple-input multiple-output (MIMO) based on measured spatial channels,” IEEE Trans. Vehicular Technol.58(6), 2884–2898 (2009).
    [CrossRef]
  13. R. C. Qiu, C. Zhou, N. Guo, and J. Q. Zhang, “Time reversal with MISO for ultra-wideband communications: experimental results,” IEEE Antennas Wirel. Propag. Lett.5(1), 269–273 (2006).
    [CrossRef]
  14. P. Sundaralingam, V. Fusco, and N. B. Buchanan, “Spatial field localisation and data transfer in a reverberant environment using analog real time phase conjugation,” Proceedings of the 40th European Microwave Conference (Paris, 2010), pp. 565–568.
  15. Y. Zhang, X. Z. Zhu, and Z. Q. Zhao, “Application of TRM in detection of metal buried in wall,” International Conference on Computational Problem-Solving (2012), pp. 287–290.
  16. J. Feng, C. Liao, L. L. Chen, and H. J. Zhou, “Amplification of electromagnetic waves by time reversal mirror in a leaky reverberation chamber,” International Conference on Microwave and Millimeter Wave Technology (5, 2012), pp. 1–4.
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    [CrossRef] [PubMed]
  19. O. Kuzucu, Y. Okawachi, R. Salem, M. A. Foster, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Spectral phase conjugation via temporal imaging,” Opt. Express17(22), 20605–20614 (2009).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  22. A. Yu. Butrym, O. V. Kazanskiy, and N. N. Kolchigin, “Van Atta’s array consist of tapered slot antennas for wideband pulse signals,” 5th International Conference on Antenna Theory and Techniques (Ukraine, 2005), pp. 221–223.
  23. K. W. Wong, L. Chiu, and Q. Xue, “A 2-D Van Atta Array Using Star-Shaped Antenna Elements,” IEEE Trans. Antenn. Propag.55(4), 1204–1206 (2007).
    [CrossRef]
  24. D. D. Ivanchenko, O. V. Kazansky, and N. N. Kolchigin, “About influence of mutual coupling on pattern and wave form of pulse reradiated by Van Atta's array of tapered slot antennas,” 6th International Conference on Ultrawideband and Ultrashort Impulse Signals (Sevastopol, Ukraine, 2012), pp. 81–82.
    [CrossRef]
  25. A. Khaleghi, “Measurement and analysis of ultra-wideband time reversal for indoor propagation channels,” Wirel. Pers. Commun.54(2), 307–320 (2010).
    [CrossRef]

2012

Y. M. Chen and B.-Z. Wang, “Seeing time-reversal transmission characteristics through kinetic anti-ferromagnetic Ising chain,” Chinese Phys. B21(2), 026401 (2012).
[CrossRef]

2011

2010

A. Khaleghi, “Measurement and analysis of ultra-wideband time reversal for indoor propagation channels,” Wirel. Pers. Commun.54(2), 307–320 (2010).
[CrossRef]

I. H. Naqvi, G. E. Zein, G. Lerosey, J. de Rosny, P. Besnier, A. Tourin, and M. Fink, “Experimental validation of time reversal ultra wide-band communication system for high data rates,” IET Microw. J. Antenna Propag.4(5), 643–650 (2010).
[CrossRef]

2009

C. Zhou, N. Guo, and R. C. Qiu, “Time reversed ultra-wideband (UWB) multiple-input multiple-output (MIMO) based on measured spatial channels,” IEEE Trans. Vehicular Technol.58(6), 2884–2898 (2009).
[CrossRef]

O. Kuzucu, Y. Okawachi, R. Salem, M. A. Foster, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Spectral phase conjugation via temporal imaging,” Opt. Express17(22), 20605–20614 (2009).
[CrossRef] [PubMed]

2007

K. W. Wong, L. Chiu, and Q. Xue, “A 2-D Van Atta Array Using Star-Shaped Antenna Elements,” IEEE Trans. Antenn. Propag.55(4), 1204–1206 (2007).
[CrossRef]

G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, “Focusing beyond the diffraction limit with far-Field time reversal,” Science315(5815), 1120–1122 (2007).
[CrossRef] [PubMed]

R. Carminati, R. Pierrat, J. de Rosny, and M. Fink, “Theory of the time reversal cavity for electromagnetic fields,” Opt. Lett.32(21), 3107–3109 (2007).
[CrossRef] [PubMed]

2006

R. C. Qiu, C. Zhou, N. Guo, and J. Q. Zhang, “Time reversal with MISO for ultra-wideband communications: experimental results,” IEEE Antennas Wirel. Propag. Lett.5(1), 269–273 (2006).
[CrossRef]

2004

D. H. Chambers and J. G. Berryman, “Time-reversal analysis for scatterer characterization,” Phys. Rev. Lett.92(2), 023902 (2004).
[CrossRef] [PubMed]

V. Dmitriev, “Space-time reversal symmetry properties of electromagnetic green’s tensors for complex and bianisotropic media,” PIER48, 145–184 (2004).
[CrossRef]

T. Strohmer, M. Emami, J. Hansen, G. Papanicolaou, and A. J. Paulraj, “Application of time-reversal with MMSE equalizer to UWB communications,” IEEE Global Telecommunications Conferenc5, 3123–3127 (2004).

G. Lerosey, J. de Rosny, A. Tourin, A. Derode, G. Montaldo, and M. Fink, “Time reversal of electromagnetic waves,” Phys. Rev. Lett.92(19), 193904 (2004).
[CrossRef] [PubMed]

2000

1980

Alrubaiee, M.

Appleby, R.

P. Sundaralingam, V. Fusco, D. Zelenchuk, and R. Appleby, “Detection of an object in a reverberant environment using direct and differential time reversal,” 6th European Conference on Antennas and Propagation (2012).
[CrossRef]

Berryman, J. G.

D. H. Chambers and J. G. Berryman, “Time-reversal analysis for scatterer characterization,” Phys. Rev. Lett.92(2), 023902 (2004).
[CrossRef] [PubMed]

Besnier, P.

I. H. Naqvi, G. E. Zein, G. Lerosey, J. de Rosny, P. Besnier, A. Tourin, and M. Fink, “Experimental validation of time reversal ultra wide-band communication system for high data rates,” IET Microw. J. Antenna Propag.4(5), 643–650 (2010).
[CrossRef]

Buchanan, N. B.

P. Sundaralingam, V. Fusco, and N. B. Buchanan, “Spatial field localisation and data transfer in a reverberant environment using analog real time phase conjugation,” Proceedings of the 40th European Microwave Conference (Paris, 2010), pp. 565–568.

Cai, W.

Carminati, R.

Chambers, D. H.

D. H. Chambers and J. G. Berryman, “Time-reversal analysis for scatterer characterization,” Phys. Rev. Lett.92(2), 023902 (2004).
[CrossRef] [PubMed]

Chen, L. L.

J. Feng, C. Liao, L. L. Chen, and H. J. Zhou, “Amplification of electromagnetic waves by time reversal mirror in a leaky reverberation chamber,” International Conference on Microwave and Millimeter Wave Technology (5, 2012), pp. 1–4.

Chen, Y. M.

Y. M. Chen and B.-Z. Wang, “Seeing time-reversal transmission characteristics through kinetic anti-ferromagnetic Ising chain,” Chinese Phys. B21(2), 026401 (2012).
[CrossRef]

Chiu, L.

K. W. Wong, L. Chiu, and Q. Xue, “A 2-D Van Atta Array Using Star-Shaped Antenna Elements,” IEEE Trans. Antenn. Propag.55(4), 1204–1206 (2007).
[CrossRef]

de Rosny, J.

I. H. Naqvi, G. E. Zein, G. Lerosey, J. de Rosny, P. Besnier, A. Tourin, and M. Fink, “Experimental validation of time reversal ultra wide-band communication system for high data rates,” IET Microw. J. Antenna Propag.4(5), 643–650 (2010).
[CrossRef]

R. Carminati, R. Pierrat, J. de Rosny, and M. Fink, “Theory of the time reversal cavity for electromagnetic fields,” Opt. Lett.32(21), 3107–3109 (2007).
[CrossRef] [PubMed]

G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, “Focusing beyond the diffraction limit with far-Field time reversal,” Science315(5815), 1120–1122 (2007).
[CrossRef] [PubMed]

G. Lerosey, J. de Rosny, A. Tourin, A. Derode, G. Montaldo, and M. Fink, “Time reversal of electromagnetic waves,” Phys. Rev. Lett.92(19), 193904 (2004).
[CrossRef] [PubMed]

Derode, A.

G. Lerosey, J. de Rosny, A. Tourin, A. Derode, G. Montaldo, and M. Fink, “Time reversal of electromagnetic waves,” Phys. Rev. Lett.92(19), 193904 (2004).
[CrossRef] [PubMed]

Dmitriev, V.

V. Dmitriev, “Space-time reversal symmetry properties of electromagnetic green’s tensors for complex and bianisotropic media,” PIER48, 145–184 (2004).
[CrossRef]

Emami, M.

T. Strohmer, M. Emami, J. Hansen, G. Papanicolaou, and A. J. Paulraj, “Application of time-reversal with MMSE equalizer to UWB communications,” IEEE Global Telecommunications Conferenc5, 3123–3127 (2004).

Fainman, Y.

Feng, J.

J. Feng, C. Liao, L. L. Chen, and H. J. Zhou, “Amplification of electromagnetic waves by time reversal mirror in a leaky reverberation chamber,” International Conference on Microwave and Millimeter Wave Technology (5, 2012), pp. 1–4.

Fink, M.

I. H. Naqvi, G. E. Zein, G. Lerosey, J. de Rosny, P. Besnier, A. Tourin, and M. Fink, “Experimental validation of time reversal ultra wide-band communication system for high data rates,” IET Microw. J. Antenna Propag.4(5), 643–650 (2010).
[CrossRef]

R. Carminati, R. Pierrat, J. de Rosny, and M. Fink, “Theory of the time reversal cavity for electromagnetic fields,” Opt. Lett.32(21), 3107–3109 (2007).
[CrossRef] [PubMed]

G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, “Focusing beyond the diffraction limit with far-Field time reversal,” Science315(5815), 1120–1122 (2007).
[CrossRef] [PubMed]

G. Lerosey, J. de Rosny, A. Tourin, A. Derode, G. Montaldo, and M. Fink, “Time reversal of electromagnetic waves,” Phys. Rev. Lett.92(19), 193904 (2004).
[CrossRef] [PubMed]

Foster, M. A.

Fusco, V.

P. Sundaralingam and V. Fusco, “Effect of quantisation and under sampling on time reversal spatial and temporal focusing in highly reverberant environment,” Proceedings of the 41st European Microwave Conference (2011).

P. Sundaralingam, V. Fusco, D. Zelenchuk, and R. Appleby, “Detection of an object in a reverberant environment using direct and differential time reversal,” 6th European Conference on Antennas and Propagation (2012).
[CrossRef]

P. Sundaralingam, V. Fusco, and N. B. Buchanan, “Spatial field localisation and data transfer in a reverberant environment using analog real time phase conjugation,” Proceedings of the 40th European Microwave Conference (Paris, 2010), pp. 565–568.

Gaeta, A. L.

Gayen, S. K.

Guo, N.

C. Zhou, N. Guo, and R. C. Qiu, “Time reversed ultra-wideband (UWB) multiple-input multiple-output (MIMO) based on measured spatial channels,” IEEE Trans. Vehicular Technol.58(6), 2884–2898 (2009).
[CrossRef]

R. C. Qiu, C. Zhou, N. Guo, and J. Q. Zhang, “Time reversal with MISO for ultra-wideband communications: experimental results,” IEEE Antennas Wirel. Propag. Lett.5(1), 269–273 (2006).
[CrossRef]

Hansen, J.

T. Strohmer, M. Emami, J. Hansen, G. Papanicolaou, and A. J. Paulraj, “Application of time-reversal with MMSE equalizer to UWB communications,” IEEE Global Telecommunications Conferenc5, 3123–3127 (2004).

Khaleghi, A.

A. Khaleghi, “Measurement and analysis of ultra-wideband time reversal for indoor propagation channels,” Wirel. Pers. Commun.54(2), 307–320 (2010).
[CrossRef]

Kuzucu, O.

Lerosey, G.

I. H. Naqvi, G. E. Zein, G. Lerosey, J. de Rosny, P. Besnier, A. Tourin, and M. Fink, “Experimental validation of time reversal ultra wide-band communication system for high data rates,” IET Microw. J. Antenna Propag.4(5), 643–650 (2010).
[CrossRef]

G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, “Focusing beyond the diffraction limit with far-Field time reversal,” Science315(5815), 1120–1122 (2007).
[CrossRef] [PubMed]

G. Lerosey, J. de Rosny, A. Tourin, A. Derode, G. Montaldo, and M. Fink, “Time reversal of electromagnetic waves,” Phys. Rev. Lett.92(19), 193904 (2004).
[CrossRef] [PubMed]

Liao, C.

J. Feng, C. Liao, L. L. Chen, and H. J. Zhou, “Amplification of electromagnetic waves by time reversal mirror in a leaky reverberation chamber,” International Conference on Microwave and Millimeter Wave Technology (5, 2012), pp. 1–4.

Lipson, M.

Marom, D.

Miller, D. A. B.

Montaldo, G.

G. Lerosey, J. de Rosny, A. Tourin, A. Derode, G. Montaldo, and M. Fink, “Time reversal of electromagnetic waves,” Phys. Rev. Lett.92(19), 193904 (2004).
[CrossRef] [PubMed]

Naqvi, I. H.

I. H. Naqvi, G. E. Zein, G. Lerosey, J. de Rosny, P. Besnier, A. Tourin, and M. Fink, “Experimental validation of time reversal ultra wide-band communication system for high data rates,” IET Microw. J. Antenna Propag.4(5), 643–650 (2010).
[CrossRef]

Okawachi, Y.

Panasenko, D.

Papanicolaou, G.

T. Strohmer, M. Emami, J. Hansen, G. Papanicolaou, and A. J. Paulraj, “Application of time-reversal with MMSE equalizer to UWB communications,” IEEE Global Telecommunications Conferenc5, 3123–3127 (2004).

Paulraj, A. J.

T. Strohmer, M. Emami, J. Hansen, G. Papanicolaou, and A. J. Paulraj, “Application of time-reversal with MMSE equalizer to UWB communications,” IEEE Global Telecommunications Conferenc5, 3123–3127 (2004).

Pendry, J. B.

Pierrat, R.

Qiu, R. C.

C. Zhou, N. Guo, and R. C. Qiu, “Time reversed ultra-wideband (UWB) multiple-input multiple-output (MIMO) based on measured spatial channels,” IEEE Trans. Vehicular Technol.58(6), 2884–2898 (2009).
[CrossRef]

R. C. Qiu, C. Zhou, N. Guo, and J. Q. Zhang, “Time reversal with MISO for ultra-wideband communications: experimental results,” IEEE Antennas Wirel. Propag. Lett.5(1), 269–273 (2006).
[CrossRef]

Rokitski, R.

Salem, R.

Sivan, Y.

Strohmer, T.

T. Strohmer, M. Emami, J. Hansen, G. Papanicolaou, and A. J. Paulraj, “Application of time-reversal with MMSE equalizer to UWB communications,” IEEE Global Telecommunications Conferenc5, 3123–3127 (2004).

Sun, P.-C.

Sundaralingam, P.

P. Sundaralingam, V. Fusco, and N. B. Buchanan, “Spatial field localisation and data transfer in a reverberant environment using analog real time phase conjugation,” Proceedings of the 40th European Microwave Conference (Paris, 2010), pp. 565–568.

P. Sundaralingam, V. Fusco, D. Zelenchuk, and R. Appleby, “Detection of an object in a reverberant environment using direct and differential time reversal,” 6th European Conference on Antennas and Propagation (2012).
[CrossRef]

P. Sundaralingam and V. Fusco, “Effect of quantisation and under sampling on time reversal spatial and temporal focusing in highly reverberant environment,” Proceedings of the 41st European Microwave Conference (2011).

Tourin, A.

I. H. Naqvi, G. E. Zein, G. Lerosey, J. de Rosny, P. Besnier, A. Tourin, and M. Fink, “Experimental validation of time reversal ultra wide-band communication system for high data rates,” IET Microw. J. Antenna Propag.4(5), 643–650 (2010).
[CrossRef]

G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, “Focusing beyond the diffraction limit with far-Field time reversal,” Science315(5815), 1120–1122 (2007).
[CrossRef] [PubMed]

G. Lerosey, J. de Rosny, A. Tourin, A. Derode, G. Montaldo, and M. Fink, “Time reversal of electromagnetic waves,” Phys. Rev. Lett.92(19), 193904 (2004).
[CrossRef] [PubMed]

Turner-Foster, A. C.

Wang, B.-Z.

Y. M. Chen and B.-Z. Wang, “Seeing time-reversal transmission characteristics through kinetic anti-ferromagnetic Ising chain,” Chinese Phys. B21(2), 026401 (2012).
[CrossRef]

Wong, K. W.

K. W. Wong, L. Chiu, and Q. Xue, “A 2-D Van Atta Array Using Star-Shaped Antenna Elements,” IEEE Trans. Antenn. Propag.55(4), 1204–1206 (2007).
[CrossRef]

Wu, B.

Xu, M.

Xue, Q.

K. W. Wong, L. Chiu, and Q. Xue, “A 2-D Van Atta Array Using Star-Shaped Antenna Elements,” IEEE Trans. Antenn. Propag.55(4), 1204–1206 (2007).
[CrossRef]

Zein, G. E.

I. H. Naqvi, G. E. Zein, G. Lerosey, J. de Rosny, P. Besnier, A. Tourin, and M. Fink, “Experimental validation of time reversal ultra wide-band communication system for high data rates,” IET Microw. J. Antenna Propag.4(5), 643–650 (2010).
[CrossRef]

Zelenchuk, D.

P. Sundaralingam, V. Fusco, D. Zelenchuk, and R. Appleby, “Detection of an object in a reverberant environment using direct and differential time reversal,” 6th European Conference on Antennas and Propagation (2012).
[CrossRef]

Zhang, J. Q.

R. C. Qiu, C. Zhou, N. Guo, and J. Q. Zhang, “Time reversal with MISO for ultra-wideband communications: experimental results,” IEEE Antennas Wirel. Propag. Lett.5(1), 269–273 (2006).
[CrossRef]

Zhang, Y.

Y. Zhang, X. Z. Zhu, and Z. Q. Zhao, “Application of TRM in detection of metal buried in wall,” International Conference on Computational Problem-Solving (2012), pp. 287–290.

Zhao, Z. Q.

Y. Zhang, X. Z. Zhu, and Z. Q. Zhao, “Application of TRM in detection of metal buried in wall,” International Conference on Computational Problem-Solving (2012), pp. 287–290.

Zhou, C.

C. Zhou, N. Guo, and R. C. Qiu, “Time reversed ultra-wideband (UWB) multiple-input multiple-output (MIMO) based on measured spatial channels,” IEEE Trans. Vehicular Technol.58(6), 2884–2898 (2009).
[CrossRef]

R. C. Qiu, C. Zhou, N. Guo, and J. Q. Zhang, “Time reversal with MISO for ultra-wideband communications: experimental results,” IEEE Antennas Wirel. Propag. Lett.5(1), 269–273 (2006).
[CrossRef]

Zhou, H. J.

J. Feng, C. Liao, L. L. Chen, and H. J. Zhou, “Amplification of electromagnetic waves by time reversal mirror in a leaky reverberation chamber,” International Conference on Microwave and Millimeter Wave Technology (5, 2012), pp. 1–4.

Zhu, X. Z.

Y. Zhang, X. Z. Zhu, and Z. Q. Zhao, “Application of TRM in detection of metal buried in wall,” International Conference on Computational Problem-Solving (2012), pp. 287–290.

Chinese Phys. B

Y. M. Chen and B.-Z. Wang, “Seeing time-reversal transmission characteristics through kinetic anti-ferromagnetic Ising chain,” Chinese Phys. B21(2), 026401 (2012).
[CrossRef]

IEEE Antennas Wirel. Propag. Lett.

R. C. Qiu, C. Zhou, N. Guo, and J. Q. Zhang, “Time reversal with MISO for ultra-wideband communications: experimental results,” IEEE Antennas Wirel. Propag. Lett.5(1), 269–273 (2006).
[CrossRef]

IEEE Global Telecommunications Conferenc

T. Strohmer, M. Emami, J. Hansen, G. Papanicolaou, and A. J. Paulraj, “Application of time-reversal with MMSE equalizer to UWB communications,” IEEE Global Telecommunications Conferenc5, 3123–3127 (2004).

IEEE Trans. Antenn. Propag.

K. W. Wong, L. Chiu, and Q. Xue, “A 2-D Van Atta Array Using Star-Shaped Antenna Elements,” IEEE Trans. Antenn. Propag.55(4), 1204–1206 (2007).
[CrossRef]

IEEE Trans. Vehicular Technol.

C. Zhou, N. Guo, and R. C. Qiu, “Time reversed ultra-wideband (UWB) multiple-input multiple-output (MIMO) based on measured spatial channels,” IEEE Trans. Vehicular Technol.58(6), 2884–2898 (2009).
[CrossRef]

IET Microw. J. Antenna Propag.

I. H. Naqvi, G. E. Zein, G. Lerosey, J. de Rosny, P. Besnier, A. Tourin, and M. Fink, “Experimental validation of time reversal ultra wide-band communication system for high data rates,” IET Microw. J. Antenna Propag.4(5), 643–650 (2010).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

D. H. Chambers and J. G. Berryman, “Time-reversal analysis for scatterer characterization,” Phys. Rev. Lett.92(2), 023902 (2004).
[CrossRef] [PubMed]

G. Lerosey, J. de Rosny, A. Tourin, A. Derode, G. Montaldo, and M. Fink, “Time reversal of electromagnetic waves,” Phys. Rev. Lett.92(19), 193904 (2004).
[CrossRef] [PubMed]

PIER

V. Dmitriev, “Space-time reversal symmetry properties of electromagnetic green’s tensors for complex and bianisotropic media,” PIER48, 145–184 (2004).
[CrossRef]

Science

G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, “Focusing beyond the diffraction limit with far-Field time reversal,” Science315(5815), 1120–1122 (2007).
[CrossRef] [PubMed]

Wirel. Pers. Commun.

A. Khaleghi, “Measurement and analysis of ultra-wideband time reversal for indoor propagation channels,” Wirel. Pers. Commun.54(2), 307–320 (2010).
[CrossRef]

Other

P. Sundaralingam, V. Fusco, D. Zelenchuk, and R. Appleby, “Detection of an object in a reverberant environment using direct and differential time reversal,” 6th European Conference on Antennas and Propagation (2012).
[CrossRef]

P. Sundaralingam and V. Fusco, “Effect of quantisation and under sampling on time reversal spatial and temporal focusing in highly reverberant environment,” Proceedings of the 41st European Microwave Conference (2011).

P. Sundaralingam, V. Fusco, and N. B. Buchanan, “Spatial field localisation and data transfer in a reverberant environment using analog real time phase conjugation,” Proceedings of the 40th European Microwave Conference (Paris, 2010), pp. 565–568.

Y. Zhang, X. Z. Zhu, and Z. Q. Zhao, “Application of TRM in detection of metal buried in wall,” International Conference on Computational Problem-Solving (2012), pp. 287–290.

J. Feng, C. Liao, L. L. Chen, and H. J. Zhou, “Amplification of electromagnetic waves by time reversal mirror in a leaky reverberation chamber,” International Conference on Microwave and Millimeter Wave Technology (5, 2012), pp. 1–4.

D. D. Ivanchenko, O. V. Kazansky, and N. N. Kolchigin, “About influence of mutual coupling on pattern and wave form of pulse reradiated by Van Atta's array of tapered slot antennas,” 6th International Conference on Ultrawideband and Ultrashort Impulse Signals (Sevastopol, Ukraine, 2012), pp. 81–82.
[CrossRef]

E. P. Wigner, Group Theory and its Application to the Quantum Mechanics of Atomic Spectra (Academic Press, 1959), Chap. 26.

A. Yu. Butrym, O. V. Kazanskiy, and N. N. Kolchigin, “Van Atta’s array consist of tapered slot antennas for wideband pulse signals,” 5th International Conference on Antenna Theory and Techniques (Ukraine, 2005), pp. 221–223.

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Figures (1)

Fig. 1
Fig. 1

The invariance of seven undetermined operations in appropriate operating domains.

Tables (1)

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Table 1 Dual Multiplication Table Induced on the Operator Set Ο

Equations (17)

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{ ×E( r,t )= B( r,t ) t ×H( r,t )= D( r,t ) t ·D( r,t )=0 ·B( r,t )=0
{ E( r,t ) = + E( r,ω ) e jωt dω H( r,t ) = + H( r,ω ) e jωt dω ε ¯ ¯ ( r,ω )= ε ¯ ¯ ( r,ω ) μ ¯ ¯ ( r,ω )= μ ¯ ¯ ( r,ω ) }Lossless&Satic D( r,t )= + ε ¯ ¯ ( r,ω )·E( r,ω ) e jωt dω B( r,t )= + μ ¯ ¯ ( r,ω )·H( r,ω ) e jωt dω }Linear
{ ×E( r,ω )=jωB( r,ω ) ×H( r,ω )=jωD( r,ω ) ·D( r,ω )=0 ·B( r,ω )=0
{ ε ¯ ¯ ( r,ω )= ε ¯ ¯ ( r,ω ) μ ¯ ¯ ( r,ω )= μ ¯ ¯ ( r,ω ) }Lossless&Satic D( r,ω )= ε ¯ ¯ ( r,ω )·E( r,ω ) B( r,ω )= μ ¯ ¯ ( r,ω )·H( r,ω ) }Linear
{ e n ×( E 2 E 1 )=0 e n ×( H 2 H 1 )= α 1 e n ·( D 2 D 1 )= β 1 e n ·( B 2 B 1 )=0
{ L E( r,t )·dl = t S B( r,t )·dS L H( r,t )·dl = t S D( r,t )·dS D( r,t )·d S ˜ =0 B( r,t )·d S ˜ =0
{ L E( r,ω )·dl =jω S B( r,ω )·dS L H( r,ω )·dl =jω S D( r,ω )·dS D( r,ω )·d S ˜ =0 B( r,ω )·d S ˜ =0
{ [ E( k,t ),H( k,t ) ]= [ E( r,t ),H( r,t ) ] e jk·r dr [ E( k,ω ),H( k,ω ) ]= [ E( k,t ),H( k,t ) ] e jωt dt
{ L e jk·r E( k,t )·dl = t S e jk·r B( k,t )·dS L e jk·r H( k,t )·dl = t S e jk·r D( k,t )·dS e jk·r D( k,t )·d S ˜ =0 e jk·r B( k,t )·d S ˜ =0
{ L e jk·r E( k,ω )·dl =jω S e jk·r B( k,ω )·dS L e jk·r H( k,ω )·dl =jω S e jk·r D( k,ω )·dS e jk·r D( k,ω )·d S ˜ =0 e jk·r B( k,ω )·d S ˜ =0
{ L E( r,t )·dl = t S B( r,t )·dS L H( r,t )·dl = t S D( r,t )·dS D( r,t )·d S ˜ =0 B( r,t )·d S ˜ =0
{ L E( r,ω )·dl =jω S B( r,ω )·dS L H( r,ω )·dl =jω S D( r,ω )·dS D( r,ω )·d S ˜ =0 B( r,ω )·d S ˜ =0
C ¯ ¯ [ E,H ]=[ E,H ], C ¯ ¯ 2 = I ¯ ¯
{ P ¯ ¯ [ E,H ]=[ E , H ] T ¯ ¯ ( t )=( t ), T ¯ ¯ 2 = I ¯ ¯ N ¯ ¯ ( ω )=( ω ), N ¯ ¯ 2 = I ¯ ¯ Χ ¯ ¯ ( r )=( r ), Χ ¯ ¯ 2 = I ¯ ¯ K ¯ ¯ ( k )=( k ), K ¯ ¯ 2 = I ¯ ¯
{ [ E( r,t ),H( r,t ) ]= T ¯ ¯ ( r,t ) C ¯ ¯ ( r,t ) [ E( r,t ),H( r,t ) ] [ E ( r,ω ), H ( r,ω ) ]= P ¯ ¯ ( r,ω ) C ¯ ¯ ( r,ω ) [ E( r,ω ),H( r,ω ) ] [ E( k,t ),H( k,t ) ]= T ¯ ¯ ( k,t ) C ¯ ¯ ( k,t ) [ E( k,t ),H( k,t ) ] [ E ( k,ω ), H ( k,ω ) ]= P ¯ ¯ ( k,ω ) C ¯ ¯ ( k,ω ) [ E( k,ω ),H( k,ω ) ]
{ L e jk·r E ( k,ω )·dl =jω S e jk·r B ( k,ω )·dS L e jk·r H ( k,ω )·dl =jω S e jk·r D ( k,ω )·dS e jk·r D ( k,ω )·d S ˜ =0 e jk·r B ( k,ω )·d S ˜ =0
P ¯ ¯ ( r,ω ) X ¯ ¯ ( r,t ) + + + + [ E( k,ω ),H( k,ω ) ] e jk·r e jωt dk dω = + { P ¯ ¯ ( r,ω ) + + + [ E( k,ω ),H( k,ω ) ] e jk·r dk } e jωt dω = + + + + { P ¯ ¯ ( k,ω ) [ E( k,ω ),H( k,ω ) ] } e jk·r e jωt dk dω

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