Radiation Pressure on Submerged Mirrors: Implications for the momentum of light in dielectric media College ofOptical Sciences, The University of Arizona, Tucson, Arizona 85721 Abstract: Radiation pressure measurements on mirrors submerged in dielectric liquids have consistently shown an effective Minkowski momentum for the photons within the liquid. USing an exact theoretical alculation based on Maxwells equations and the lorentz law of force, we demonstrate that this result is a consequence of the fact that conventional mirrors impart, upon reflection, a 180 phase shift to the incident beam of light. If the mirror is designed to impart a different phase, then the effective momentum will turn out to be anywhere between the two extremes of the Minkowski and abraham momenta. since all values in the range between these two extremes are equally likely to be found in experiments, we argue that the photon momentum inside a dielectric host has the arithmetic mean value of the abraham and minkowski momenta o 2007 Optical Society of America OCIS codes:(2602110)Electromagnetic theory; (1407010)Trapping. References R. VJones and J. C.S. Richards, Proc. Roy. Soc. 4 221, 480(1954). R. V Jones and B. Leslie, ""The measurement of optical radiation pressure in dispersive media, "Proc. Roy. Soc London, Series a,360,347-363(1978) 3. A. Ashkin and J Dziedzic, "Radiation pressure on a free liquid surface, "Phys. Rev. Lett. 30, 139-142(1973) 4. J. P. Gordon, "Radiation forces and momenta in dielectric media, Phys. Rev. A8, 14-21(1973) 6. L Landau, E Lifshitz, Electrodynamics of Contimuous Media, Pergamon, New York, 1960. Mansuripur, Radiation pressure and the linear momentum of the electromagnetic field, Optics Express 12, 5375-5401(200 8. R. Loudon, "Theory of the radiation pressure on dielectric sur faces, "J Mod. Opt. 49, 821-838(2002) 9. R Loudon, "Radiation pressure and momentum in dielectrics, Fortschr. Phys. 52, 1134-1140(2004 ). 10. S. M. Barnett and R. Loudon, "On the electromagnetic force on a dielectric medium, "J. Phys. B: 4t. Mol. Opt. Phys.39,S671-S684(2006) 11. M. Mansuripur, "Radiation pressure and the linear momentum of light in dispersive dielectric media, Optics Express 13,2245-2250(2005) 1 Introduction The 1953 experiments of Jones and Richards on submerged mirrors [11 followed by the refined 1977 experiments of Jones and Leslie [2], have shown beyond a doubt the dependence of the radiation pressure on the refractive index no of the submerging liquid. Such findings, in turn, have been used to support the argument that the photons inside the liquid have the Minkowski momentum noho/c, where h is Planck's constant, f o is the lights frequency, and c is the speed of light in vacuum [3, 4]. We show that the above result is a consequence of the fact that. for most mirrors. the Fresnel reflection coefficient at normal incidence p=lplexp(io ) has a phase o= 180. If, however, o is allowed to have other values, the radiation pressure on the submerged mirror will be reduced and, in particular, when o approaches zero, the effective photon momentum will be found to reach the Abraham value of hfo/(noc). Our analysis thus suggests that, depending on the chosen value of o for the mirror,the measured radiation pressure inside a dielectric medium would favor a photon momentum anywhere in the range between the abraham and minkowski values #79094s1500USD Received 17 January 2007, accepted 22 February 2007 (C)2007OSA 5 March 2007/ VoL 15. No 5/ OPTICS EXPRESS 2677Radiation Pressure on Submerged Mirrors: Implications for the Momentum of Light in Dielectric Media Masud Mansuripur College of Optical Sciences, The University of Arizona, Tucson, Arizona 85721 masud@optics.arizona.edu Abstract: Radiation pressure measurements on mirrors submerged in dielectric liquids have consistently shown an effective Minkowski momentum for the photons within the liquid. Using an exact theoretical calculation based on Maxwell’s equations and the Lorentz law of force, we demonstrate that this result is a consequence of the fact that conventional mirrors impart, upon reflection, a 180° phase shift to the incident beam of light. If the mirror is designed to impart a different phase, then the effective momentum will turn out to be anywhere between the two extremes of the Minkowski and Abraham momenta. Since all values in the range between these two extremes are equally likely to be found in experiments, we argue that the photon momentum inside a dielectric host has the arithmetic mean value of the Abraham and Minkowski momenta. © 2007 Optical Society of America OCIS codes: (260.2110) Electromagnetic theory; (140.7010) Trapping. References 1. R. V. Jones and J. C. S. Richards, Proc. Roy. Soc. A 221, 480 (1954). 2. R. V. Jones and B. Leslie, “The measurement of optical radiation pressure in dispersive media,” Proc. Roy. Soc. London, Series A, 360, 347-363 (1978). 3. A. Ashkin and J. Dziedzic, “Radiation pressure on a free liquid surface,” Phys. Rev. Lett. 30, 139-142 (1973). 4. J. P. Gordon, “Radiation forces and momenta in dielectric media,” Phys. Rev. A 8, 14-21 (1973). 5. J. D. Jackson, Classical Electrodynamics, 2nd edition, Wiley, New York, 1975. 6. L. Landau, E. Lifshitz, Electrodynamics of Continuous Media, Pergamon, New York, 1960. 7. M. Mansuripur, “Radiation pressure and the linear momentum of the electromagnetic field,” Optics Express 12, 5375-5401 (2004). 8. R. Loudon, “Theory of the radiation pressure on dielectric surfaces,” J. Mod. Opt. 49, 821-838 (2002). 9. R. Loudon, “Radiation pressure and momentum in dielectrics,” Fortschr. Phys. 52, 1134-1140 (2004). 10. S. M. Barnett and R. Loudon, “On the electromagnetic force on a dielectric medium,” J. Phys. B: At. Mol. Opt. Phys. 39, S671-S684 (2006). 11. M. Mansuripur, “Radiation pressure and the linear momentum of light in dispersive dielectric media,” Optics Express 13, 2245-2250 (2005). 1. Introduction The 1953 experiments of Jones and Richards on submerged mirrors [1], followed by the refined 1977 experiments of Jones and Leslie [2], have shown beyond a doubt the dependence of the radiation pressure on the refractive index no of the submerging liquid. Such findings, in turn, have been used to support the argument that the photons inside the liquid have the Minkowski momentum nohfo/c, where h is Planck’s constant, fo is the light’s frequency, and c is the speed of light in vacuum [3, 4]. We show that the above result is a consequence of the fact that, for most mirrors, the Fresnel reflection coefficient at normal incidence, ρ = | ρ | exp (iφ ), has a phase φ ≈ 180°. If, however, φ is allowed to have other values, the radiation pressure on the submerged mirror will be reduced and, in particular, when φ approaches zero, the effective photon momentum will be found to reach the Abraham value of hfo/(noc). Our analysis thus suggests that, depending on the chosen value of φ for the mirror, the measured radiation pressure inside a dielectric medium would favor a photon momentum anywhere in the range between the Abraham and Minkowski values. #79094 - $15.00 USD Received 17 January 2007; accepted 22 February 2007 (C) 2007 OSA 5 March 2007 / Vol. 15, No. 5 / OPTICS EXPRESS 2677