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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 25 — Dec. 5, 2011
  • pp: 25263–25278

Total longitudinal momentum in a dispersive optical waveguide

Jianhui Yu, Chunyan Chen, Yanfang Zhai, Zhe Chen, Jun Zhang, Lijun Wu, Furong Huang, and Yi Xiao  »View Author Affiliations

Optics Express, Vol. 19, Issue 25, pp. 25263-25278 (2011)

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Using the Lorentz force law, we derived simpler expressions for the total longitudinal (conserved) momentum and the mechanical momentums associated with an optical pulse propagating along a dispersive optical waveguide. These expressions can be applied to an arbitrary non-absorptive optical waveguide having continuous translational symmetry. Our simulation using finite difference time domain (FDTD) method verified that the total momentum formula is valid in a two-dimensional infinite waveguide. We studied the conservation of the total momentum and the transfer of the momentum to the waveguide for the case when an optical pulse travels from a finite waveguide to vacuum. We found that neither the Abraham nor the Minkowski momentum expression for an electromagnetic wave in a waveguide represents the complete total (conserved) momentum. Only the total momentum as we derived for a mode propagating in a dispersive optical waveguides is the ‘true’ conserved momentum. This total momentum can be expressed as PTot = –UDie/vg + neff U/c. It has three contributions: (1) the Abraham momentum; (2) the momentum from the Abraham force, which equals to the difference between the Abraham momentum and the Minkowski momentum; and (3) the momentum from the dipole force which can be expressed as –UDie/vg. The last two contributions constitute the mechanical momentum. Compared with FDTD-Lorentz-force method, the presently derived total momentum formula provides a better method in terms of analyzing the permanent transfer of optical momentum to a waveguide.

© 2011 OSA

OCIS Codes
(000.2690) General : General physics
(230.7370) Optical devices : Waveguides
(260.2110) Physical optics : Electromagnetic optics

ToC Category:
Physical Optics

Original Manuscript: September 2, 2011
Revised Manuscript: October 3, 2011
Manuscript Accepted: November 13, 2011
Published: November 23, 2011

Jianhui Yu, Chunyan Chen, Yanfang Zhai, Zhe Chen, Jun Zhang, Lijun Wu, Furong Huang, and Yi Xiao, "Total longitudinal momentum in a dispersive optical waveguide," Opt. Express 19, 25263-25278 (2011)

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  1. R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Colloquium: momentum of an electromagnetic wave in dielectric media,” Rev. Mod. Phys. 79(4), 1197–1216 (2007). [CrossRef]
  2. I. Brevik, “Experiment in phenomenological electrodynamics and the electromagnetic energy-momentum tensor,” Phys. Rep. 52(3), 133–201 (1979). [CrossRef]
  3. H. Minkowski, ““Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegten Körpern,” Nachr. Ges. Wiss. Gottn Math.-Phys. Kl. 1908, 53–111 (1908); reprinted in Math Ann 68, 472–525 (1910).
  4. J. A. Kong, Electromagnetic Wave Theory (Wiley, 1986), Chap. VII.
  5. P. W. Milonni and R. W. Boyd, “Momentum of light in a dielectric medium,” Adv. Opt. Photonics 2(4), 519–553 (2010). [CrossRef]
  6. C. Baxter and R. Loudon, “Radiation pressure and the photon momentum in dielectrics,” J. Mod. Opt. 57(10), 830–842 (2010). [CrossRef]
  7. V. M. Abraham, “Zur Elektrodynamik bewegter Körper,” Rend. Circ. Matem. Palermo 28(1), 1–28 (1909). [CrossRef]
  8. D. F. Nelson, “Momentum, pseudomomentum, and wave momentum: Toward resolving the Minkowski-Abraham controversy,” Phys. Rev. A 44(6), 3985–3996 (1991). [CrossRef] [PubMed]
  9. A. Feigel, “Quantum vacuum contribution to the momentum of dielectric media,” Phys. Rev. Lett. 92(2), 020404 (2004). [CrossRef] [PubMed]
  10. C. Wang, “ Wave four-vector in a moving medium and the Lorentz covariance of Minkowski's photon and electromagnetic momentums,” arXiv.org, arXiv:1106.1163v11 (2011).
  11. R. Loudon, “Radiation pressure and momentum in dielectrics,” Fortschr. Phys. 52(11-12), 1134–1140 (2004). [CrossRef]
  12. R. Loudon, S. M. Barnett, and C. Baxter, “Radation pressure and momentum transfer in dielectrics: The photon drag effect,” Phys. Rev. A 71(6), 063802 (2005). [CrossRef]
  13. M. Mansuripur, “Radiation pressure and the linear momentum of the electromagnetic field,” Opt. Express 12(22), 5375–5401 (2004). [CrossRef] [PubMed]
  14. S. M. Barnett and R. Loudon, “On the electromagnetic force on a dielectric medium,” J. Phys. At. Mol. Opt. Phys. 39(15), S671–S684 (2006). [CrossRef]
  15. B. A. Kemp, T. Grzegorczyk, and J. A. Kong, “Ab initio study of the radiation pressure on dielectric and magnetic media,” Opt. Express 13(23), 9280–9291 (2005). [CrossRef] [PubMed]
  16. M. Mansuripur and A. R. Zakharian, “Maxwell’s macroscopic equations, the energy-momentum postulates, and the Lorentz law of force,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(2), 026608 (2009). [CrossRef] [PubMed]
  17. E. A. Hinds and S. M. Barnett, “Momentum exchange between light and a single atom: Abraham or Minkowski?” Phys. Rev. Lett. 102(5), 050403 (2009). [CrossRef] [PubMed]
  18. S. M. Barnett, “Resolution of the abraham-minkowski dilemma,” Phys. Rev. Lett. 104(7), 070401 (2010). [CrossRef] [PubMed]
  19. P. L. Saldanha, “Division of the momentum of electromagnetic waves in linear media into electromagnetic and material parts,” Opt. Express 18(3), 2258–2268 (2010). [CrossRef] [PubMed]
  20. A. R. Zakharian, M. Mansuripur, and J. V. Moloney, “Radiation pressure and the distribution of electromagnetic force in dielectric media,” Opt. Express 13(7), 2321–2336 (2005). [CrossRef] [PubMed]
  21. W. She, J. Yu, and R. Feng, “Observation of a push force on the end face of a nanometer silica filament exerted by outgoing light,” Phys. Rev. Lett. 101(24), 243601 (2008). [CrossRef] [PubMed]
  22. M. Mansuripur and A. R. Zakharian, “Theoretical analysis of the force on the end face of a nanofilament exerted by an outing light pulse,” Phys. Rev. A 80(2), 023823 (2009). [CrossRef]
  23. H. Yu, W. Fang, F. Gu, M. Qiu, Z. Yang, and L. Tong, “Longitudinal Lorentz force on a subwavelength-diameter optical fiber,” Phys. Rev. A 83(5), 053830 (2011). [CrossRef]
  24. I. Brevik and S. A. Ellingsen, “Transverse radiation force in a tailored optical fiber,” Phys. Rev. A 81(1), 011806 (2010). [CrossRef]
  25. I. Brevik, “Comment on “Observation of a push force on the end face of a nanometer silica filament exerted by outgoing light”,” Phys. Rev. Lett. 103(21), 219301, author reply 219302 (2009). [CrossRef] [PubMed]
  26. W. She, J. Yu, and R. Feng, “She et al. Reply,” Phys. Rev. Lett. 103(21), 219302 (2009). [CrossRef]
  27. M. Mansuripur, “Comment on “Observation of a push force on the end face of a nanometer silica filament exerted by outgoing light”,” Phys. Rev. Lett. 103(1), 019301 (2009). [CrossRef] [PubMed]
  28. J. Yu, R. Feng, and W. She, “Low-power all-optical switch based on the bend effect of a nm fiber taper driven by outgoing light,” Opt. Express 17(6), 4640–4645 (2009). [CrossRef] [PubMed]
  29. L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003). [CrossRef] [PubMed]
  30. L. Tong, J. Lou, and E. Mazur, “Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides,” Opt. Express 12(6), 1025–1035 (2004). [CrossRef] [PubMed]
  31. P. Russell, “Photonic crystal fibers,” Science 299(5605), 358–362 (2003). [CrossRef] [PubMed]
  32. B. J. Eggleton, C. Kerbage, P. S. Westbrook, R. S. Windeler, and A. Hale, “Microstructured optical fiber devices,” Opt. Express 9(13), 698–713 (2001). [CrossRef] [PubMed]
  33. V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29(11), 1209–1211 (2004). [CrossRef] [PubMed]
  34. Q. Xu, V. R. Almeida, R. R. Panepucci, and M. Lipson, “Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material,” Opt. Lett. 29(14), 1626–1628 (2004). [CrossRef] [PubMed]
  35. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, New York, 1983)
  36. A. Talflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method, 3rd ed. (Artech House, Boston, 2005)
  37. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 2.

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