Quantized Energy Momentum and Wave for an Electromagnetic Pulse—A Single Photon inside Negative Refractive Indexed Media
Shantanu Das
DOI: 10.4236/jmp.2011.212183   PDF    HTML   XML   5,904 Downloads   9,759 Views   Citations


An Electromagnetic (EM) radiation in dispersion less free space vacuum is represented by a photon, with corpuscular and wave nature. The discussions, for the past century aimed at the nature of photon inside a media having dispersion in the refraction property, other than free space. What about its nature if the space be of refractive index which is negative, is discussed in this paper. We call mechanical momentum, wave-momentum, and try to match our present theories with intriguing property of this ‘photon’ or pulse carrying EM energy packet, and more so we try to find its property energy, momentum inside a media a positive refractive media, and if the media show a negative refractive index behavior, then these queries are profound, and suitable explanations to these classical concepts of corpuscular-wave nature of photon inside these media are quest for the scientists dealing with these materials having negative index of refraction. Here some of this counterintuitive nature of corpuscular-wave nature of photon inside negative indexed material is brought out, with possible ‘new definition’ of its ‘wave-momentum’, the concept of ‘reactive energy’ inside negative indexed material, along with possible ‘new wave equation’. These definitions and expressions of ‘wave-momentum’ and ‘reactive energy’ pertaining to negative indexed material are new and discussed and derived by classical means.

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S. Das, "Quantized Energy Momentum and Wave for an Electromagnetic Pulse—A Single Photon inside Negative Refractive Indexed Media," Journal of Modern Physics, Vol. 2 No. 12, 2011, pp. 1507-1522. doi: 10.4236/jmp.2011.212183.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] R. W. Ziolkowski and E. Heyman, “Wave Propagation in Media Having Negative Permittivity and Permeability,” Physical Review E, Vol. 64, No. 5, 2001, p. 056625.
[2] R. Shelby, D. R. Smith and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science, Vol. 292, No. 5514, 2001, pp. 77-79. doi:10.1126/science.1058847
[3] V. Lindell, S. Tretyakov, K. I. Nikoskinen and S. IIvonen, “BW Media with Negative Parameters, Capable of Sup- porting Backward Waves,” Microwave and Optical Tech- nology Letters, Vol. 31, No. 2, 2001, pp. 129-133. doi:10.1002/mop.1378
[4] A. Grbic and G. V. Eleftheriades, “Experimental Verifi- cation of Backward Wave Radiation from a Negative Re- fractive Index Meta-Material,” Journal of Applied Phys- ics, Vol. 92, No. 10, 2002, pp. 5930-5935. doi:10.1063/1.1513194
[5] D. R. Smith, S. Schultz, P. Markos and C. M. Soukoulis, “Determination of Effective Permittivity and Permeability of Meta-Materials from Reflection and Transmission Coefficients,” Physical Review B, Vol. 65, No. 19, 2002, pp. 195104-19109.
[6] S. Das, “Lectures: Parts 1-8 Left Handed Maxwell Sys- tems,” Class Room Lectures for the Reversed Electrodynamics.
[7] S. A. Ramakrisna, “Physics of Negative Refractive Indexed Material,” Reports on Progress in Physics, Vol. 68, No. 2, 2005, p. 449. doi:10.1088/0034-4885/68/2/R06
[8] U. Leonhardt, “Momentum in an Uncertain Light,” Nature, Vol. 444, 2006, pp. 823-824. doi:10.1038/444823a
[9] R. N. Pfeifer, T. A. Nieminen, N. R Heckenberg Halina Rubinsztein-Dunlop, “Momentum of an Electromagnetic Wave in Dielectric Media,” Reviews of Modern Physics, Vol. 79, No. 4, 2006, pp. 1197-1216. doi:10.1103/RevModPhys.79.1197
[10] S. Setiawan, T. G Mackay and A. Lakhtakia, “A Comparison of Super Radiance and Negative Phase Velocity Phenomena in Ergo Sphere of Rotating Black Hole” Physics Letters A, Vol. 341, No. 1-4, 2005, pp. 15-21. doi:10.1016/j.physleta.2005.04.064
[11] P. W. Milonni, “Field Quantization and Radiative Processes in Dispersive Di-Electric Media,” Journal of Modern Optics, Vol. 42, No. 10, 1995, pp. 1991-2004.
[12] H. Minkowski, “Die Graddglaichugen fur die Electroma- gnetischen Vorgange in bewegten Korpern,” Nachrichten von der Gesellschaft der Wissenschaften zu G?ttingen, Mathematisch-Physikalische Klasse, Weidmannsche Bu- chhandlung, Berlin, 1908, pp. 53-111.
[13] M. Abraham, “Zur Electrodynamik bewegten Korpern,” Rendiconti del Circolo Matematico, Palermo, 1909, pp. 1-28.
[14] V. G. Veselago “Electrodynamics of Materials with Ne- gative Index of Refraction,” Physicsa Uspekhi, Vol. 46, No. 7, 2003, pp. 764-768.
[15] D. Felbacq and A.Moreau, “Direct Evidence of Negative Refraction at Media with Negative Epsilon and mu,” Journal of Optics: Pure and Applied Optics, Vol. 5, 2003, pp. L9-L11.
[16] V. G. Veselago, “The Electrodynamics of Substances with Simultaneously Negative Values of ε and μ,” Soviet Physics Uspekhi, Vol. 10, No. 4, 1968, pp. 509-514. doi:10.1070/PU1968v010n04ABEH003699
[17] V. Veselago, L. Braginsky, V. Shklover and C. Hafner, “Negative Refractive Index Materials,” Journal of Computation and Theoretical Nanoscience, Vol. 3, 2006, pp. 1-30.
[18] A. Kamli, et al. “Coherent Control of Low Loss Surface Polaritons,” Physical Review Letters, Vol. 101, No. 26, 2008, pp. 263601-263605. doi:10.1103/PhysRevLett.101.263601
[19] H. Kogelnik, “Theory of Optical-Waveguides in Guided Wave Optoelectronics,” Springer-Verlag, Berlin, 1988, pp. 7-88.
[20] A. A. Barybin and V. A. Dmitriev, “Modern Electrody- namics and Coupled-Mode Theory: Application to Guided- Wave Optics,” Rinton Press, Princeton, 2002.
[21] J. B. Pendry, J. Holden, W. J. Stewart and I. Youngs, “Extremely Low Frequency Plasmons in Metallic Meso- Structures,” Physical Review Letters, Vol. 76, No. 25, 1996, pp. 4773-4776. doi:10.1103/PhysRevLett.76.4773
[22] J. B. Pendry, J. Holden, D. J. Robbins and W. J. Stewart, “Low Frequency Plasmons in Thin Wire Structures,” Jour- nal of Physics Condensed Matter, Vol. 10, No. 22, 1998, pp. 4785-4808. doi:10.1088/0953-8984/10/22/007
[23] J. B. Pendry, J. Holden, D. J. Robbins and W. J. Stewart, “Magnetism from Conductors and Enhanced Non Linear Phenomena,” IEEE Transactions on Microwave Theory and Techniques, Vol. 47, No. 11, 1999, pp. 2075-2084. doi:10.1109/22.798002
[24] D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat Nasser and S. Schultz, “Composite Medium with Simultaneously Negative Permeability and Permittivity,” Physical Review Letters, Vol. 84, No. 18, 2000, pp. 4184-4187. doi:10.1103/PhysRevLett.84.4184
[25] D. R .Smith and N. Kroll, “Negative Refractive Index in Left Handed Materials,” Physical Review Letters, Vol. 85, No. 14, 2000, pp. 2933-2936. doi:10.1103/PhysRevLett.85.2933
[26] J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Physical Review Letters, Vol. 85, No. 18, 2000, pp. 3966-3969. doi:10.1103/PhysRevLett.85.3966
[27] J. D. Jackson, “Classical Electrodynamics,” 3rd Edition, Willey, New-York, 1999.

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