Electromagnetic Momentum and Radiation pressure derived from the Fresnel relations Michael e. crenshaw AMSRD-AMR-WS-ST. USA RDECOM. Redstone ArsenaL. Alabama 35898 Abstract: Using the Fresnel relations as axioms, we derive a generalized electromagnetic momentum for a piecewise homogeneous medium and a different generalized momentum for a medium with a spatially varying re- fractive index in the Wentzel-Kramers-Brillouin(WKB)limit. Both gener- alized momenta depend linearly on the field, but the refractive index appears to different powers due to the difference in translational symmetry. For the case of the slowly varying index, it is demonstrated that there is negligible transfer of momentum from the electromagnetic field to the material Such a transfer occurs at the interface between the vacuum and a homogeneous ma- terial allowing us to derive the radiation pressure from the Fresnel reflection formula. The Lorentz volume force is shown to be nil OCIS codes: (260.2110) Electromagnetic theory; (260.2160) Energy transfer References and links I. H. Minkowski, Natches. Ges. Wiss. Gottingen 53(1908): Math. Ann. 68, 472(1910) 2. M. Abraham, Rend Circ. Mat. Palermo 28, 1(1909); 30, 33 (1910) 3. A Einstein and J. Laub, Ann. Phys. (Leipzig)26, 541(1908) 4. R Peierls, "The momentum of light in a refracting medium, "Proc R Soc. Lond. A 347, 475-491(1976). 5. M. Kranys, "The Minkowski and Abraham Tensors, and the non-uniqueness of non-closed systems. In Engng.sci20,1193-1213(1982 6. G. H. Livens, The Theory of Electricity.( Cambridge University Press, Cambridge, 1908) 7. Y. N. Obukhov and F. w. Hehl, ""Electromagnetic energy-momentum and forces in matter, "Phys. Lett. A 311 277-284(2003) 8. J C. Garrison and R. Y Chiao. "Canonical and kinetic forms of the electromagnetic momentum in quantization scheme for a dispersive dielectric, "Phys. Rev. A 70, 053826-1-8 9. S. Antoci and L. Mihich, "A forgotten argument by gordon uniquely selects momentum tensor of the electromagnetic field in homogeneous, isotropic matte Cim.B112,991-1001 10. R. V. Jones and J. C. S. Richards, "The pressure of radiation in a refracting medium. "Proc. R. Soc. London A 221,480(1954) 11. A. Ashkin and (1973) 12. A. F. Gibson, M. E. Kimmitt, A O. Koohian, D. E. Evans, and G. F D. Levy, "A Study of Radiation Pressure in a Refractive Medium by the Photon Drag Effect, "Proc. R Soc. London A 370, 303-318(1980). 13. D. G. Lahoz and G. M. Graham, ""Experimental decision on the electromagnetic momentum. "J. Phys. A 15, 303-318(1982 14. I Brevik, "Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum ten- sor”"Phys.Rep.52,133-201(1979) 15. I Brevik, "Photon-drag experiment and the electromagnetic momentum in matter, "Phys. Rev. B 33, 1058-106 (1986). H. Goldstein. Classical 17. M. E Crenshaw, "Generalized electromagnetic momentum and the Fresnel relations "Phys. Lett. A 346, 249- #77863·S1500USD Received 18 December 2006, accepted 7 January 2007 (C)2007OSA January 2007/Vol 15, No. 2/OPTICS EXPRESS 714Electromagnetic Momentum and Radiation Pressure derived from the Fresnel Relations Michael E. Crenshaw AMSRD-AMR-WS-ST, USA RDECOM, Redstone Arsenal, Alabama 35898 michael.crenshaw@us.army.mil Abstract: Using the Fresnel relations as axioms, we derive a generalized electromagnetic momentum for a piecewise homogeneous medium and a different generalized momentum for a medium with a spatially varying re￾fractive index in the Wentzel–Kramers–Brillouin (WKB) limit. Both gener￾alized momenta depend linearly on the field, but the refractive index appears to different powers due to the difference in translational symmetry. For the case of the slowly varying index, it is demonstrated that there is negligible transfer of momentum from the electromagnetic field to the material. Such a transfer occurs at the interface between the vacuum and a homogeneous ma￾terial allowing us to derive the radiation pressure from the Fresnel reflection formula. The Lorentz volume force is shown to be nil. OCIS codes: (260.2110) Electromagnetic theory; (260.2160) Energy transfer References and links 1. H. Minkowski, Natches. Ges. Wiss. Gottingen 53 (1908); Math. Ann. ¨ 68, 472 (1910). 2. M. Abraham, Rend. Circ. Mat. Palermo 28, 1 (1909); 30, 33 (1910). 3. A. Einstein and J. Laub, Ann. Phys. (Leipzig) 26, 541 (1908). 4. R. Peierls, “The momentum of light in a refracting medium,” Proc. R. Soc. Lond. A 347, 475–491 (1976). 5. M. Kranys, “The Minkowski and Abraham Tensors, and the non-uniqueness of non-closed systems,” Int. J. Engng. Sci. 20, 1193–1213 (1982). 6. G. H. Livens, The Theory of Electricity, (Cambridge University Press, Cambridge, 1908). 7. Y. N. Obukhov and F. W. Hehl, “Electromagnetic energy–momentum and forces in matter,” Phys. Lett. A 311, 277-284 (2003). 8. J. C. Garrison and R. Y. Chiao, “Canonical and kinetic forms of the electromagnetic momentum in an ad hoc quantization scheme for a dispersive dielectric,” Phys. Rev. A 70, 053826-1–8 (2004). 9. S. Antoci and L. Mihich, “A forgotten argument by Gordon uniquely selects Abraham’s tensor as the energy– momentum tensor of the electromagnetic field in homogeneous, isotropic matter,” Nuovo Cim. B112, 991–1001 (1997). 10. R. V. Jones and J. C. S. Richards, “The pressure of radiation in a refracting medium,” Proc. R. Soc. London A 221, 480 (1954). 11. A. Ashkin and J. M. Dziedzic, “Radiation Pressure on a Free Liquid Surface,” Phys. Rev. Lett. 30, 139–142 (1973). 12. A. F. Gibson, M. F. Kimmitt, A. O. Koohian, D. E. Evans, and G. F. D. Levy, “A Study of Radiation Pressure in a Refractive Medium by the Photon Drag Effect,” Proc. R. Soc. London A 370, 303–318 (1980). 13. D. G. Lahoz and G. M. Graham, “Experimental decision on the electromagnetic momentum,” J. Phys. A 15, 303–318 (1982). 14. I. Brevik, “Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum ten￾sor,” Phys. Rep. 52, 133–201 (1979). 15. I. Brevik, “Photon-drag experiment and the electromagnetic momentum in matter,” Phys. Rev. B 33, 1058–1062 (1986). 16. H. Goldstein, Classical Mechanics, 2nd Ed., (Addison-Wesley, Reading, MA, 1980). 17. M. E. Crenshaw, “Generalized electromagnetic momentum and the Fresnel relations,” Phys. Lett. A 346, 249– 254, (2005). #77863 - $15.00 USD Received 18 December 2006; accepted 7 January 2007 (C) 2007 OSA 22 January 2007 / Vol. 15, No. 2 / OPTICS EXPRESS 714