正在加载图片...
week ending PRL97,133902(20 PHYSICAL REVIEW LETTERS 29 SEPTEMBER 2006 Optical Momentum Transfer to absorbing Mie Particles Brandon A. Kemp, Tomasz M. Grzegorczyk, and Jin Au Kon Research laboratory of electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA (Received 12 April 2006: revised manuscript received 26 June 2006; published 26 September 2006) The momentum transfer to absorbing particles is derived from the Lorentz force density without prior assumption of the momentum of light in media. We develop a view of momentum conservation rooted in the stress tensor formalism that is based on the separation of momentum contributions to bound and free currents and charges consistent with the Lorentz force density. This is in contrast with the usual separation of material and field contributions. The theory is applied to predict a decrease in optical momentum transfer to Mie particles due to absorption, which contrasts the common intuition based on the scattering and absorption by rayleigh particles. PACS numbers: 41.20Jb The momentum of light in optically dense media has lent interpretation in terms of momentum conservation that been the center of a debate in physics for nearly a century distinguishes two processes of momentum transfer result- [1, 2]. Although the So-called Abraham- Minkowski contro- ing from the wave refiection or transmission at the bound versy originated out of relativistic formulations, the pri- ary and the attenuation in the medium. Our proposed view mary issue of the radiation pressure exerted on the renders a more direct description of experiments than the interface of a dielectric boundary can be studied indepen- usual separation of wave momentum into electromagnetic dently of material motion [3]. The momentum density and material contributions [3, 5, 12-14. The Lorentz force vector derived from the macroscopic electromagnetic density and momentum conservation are equivalently ap- ave theory [4] for a nonmagnetic medium is G=Dx plied to explain relevant experimental observations and to B= EOuOE X H+ PX uoH, where the wave momentum calculate the radiation pressure on absorbing Mie particles density is expressed as the sum of the electromagnetic In contrast to the scattering plus absorption forces derived momentum density EouoE X H and a mechanical momen- for small particles, we predict that absorption can reduce tum density resulting from the dielectric polarization P= the total optical momentum transfer to certain particles due D-EoE in the presence of a field [5]. The debate of the to the balance between the force on free currents and the of normally incident light from free force on bound currents and charg space onto a dielectric interface can be demonstrated by The Lorentz force is applied directly to bound and free momentum conservation at the interface. The difference in currents and charges, which are used to model lossy media the radiation pressure resulting from either D X B or with complex permittivity E= ER iEr and permeability ∈00E× H transmitted into the dielectric is significant;μ=R+ iui in a background of(∈0,μo). The time. an outward force results from the former, while an inward average Lorentz force density on bound currents and force results from the latter [6] charges due to harmonic excitation with e -ior dependence Recently, the pressure of light on lossless media as is [10 directly to bound currents and charges [7-9) and the b =RelEo(V B)E+ Ko(V H)h. momentum conservation theorem [4] were shown to be io(ER-E0)EXB+io(pR-uo)H×D”}.(1) in agreement [10]. Application of the Lorentz force di- rectly may be regarded as more fundamental, but it here Ref represents the real part of a complex quantity computationally expensive compared to momentum con- and denotes the complex conjugate. The leading two servation [11]. However, there still exist questions as terms in (D)contribute via a surface force density on bound to the application of momentum conservation to the radia- electric and magnetic charges, while the final two terms tion pressure in lossy materials represent the volume force density on bound electric and In this Letter, we rigorously treat the optical momentum magnetic currents [10, 11. In addition to(1), the force transfer to lossy media in the framework of the macro- ensity on free currents scopic electromagnetic theory. We apply the Lorentz force directly to bound and free currents and charges, thus fc=Re{ WEE X B”-o1H×D” avoiding a priori assumptions regarding the form of extends the recent analysis of the photon drag effect [15]to wave momentum. The separation of the total Lorentz force include magnetization, oblique incidence, and arbitrary in terms of forces on bound currents and charges(Fb) and polarization. The total time-average force on the material on free currents(Fc) provides insight into the mechanisms F= F Fb results from integration of the time-average of momentum transfer in lossy media. We show an equiva- force densities over the entire medium. 0031-9007/06/97(13)/133902(4) 133902-1 o 2006 The American Physical SocietyOptical Momentum Transfer to Absorbing Mie Particles Brandon A. Kemp,* Tomasz M. Grzegorczyk, and Jin Au Kong Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA (Received 12 April 2006; revised manuscript received 26 June 2006; published 26 September 2006) The momentum transfer to absorbing particles is derived from the Lorentz force density without prior assumption of the momentum of light in media. We develop a view of momentum conservation rooted in the stress tensor formalism that is based on the separation of momentum contributions to bound and free currents and charges consistent with the Lorentz force density. This is in contrast with the usual separation of material and field contributions. The theory is applied to predict a decrease in optical momentum transfer to Mie particles due to absorption, which contrasts the common intuition based on the scattering and absorption by Rayleigh particles. DOI: 10.1103/PhysRevLett.97.133902 PACS numbers: 41.20.Jb, 42.25.Fx The momentum of light in optically dense media has been the center of a debate in physics for nearly a century [1,2]. Although the so-called Abraham-Minkowski controversy originated out of relativistic formulations, the primary issue of the radiation pressure exerted on the interface of a dielectric boundary can be studied independently of material motion [3]. The momentum density vector derived from the macroscopic electromagnetic wave theory [4] for a nonmagnetic medium is G D B 00E H P 0H, where the wave momentum density is expressed as the sum of the electromagnetic momentum density 00E H and a mechanical momentum density resulting from the dielectric polarization P D 0E in the presence of a field [5]. The debate of the radiation pressure of normally incident light from free space onto a dielectric interface can be demonstrated by momentum conservation at the interface. The difference in the radiation pressure resulting from either D B or 00E H transmitted into the dielectric is significant; an outward force results from the former, while an inward force results from the latter [6]. Recently, the pressure of light on lossless media as calculated by both the application of the Lorentz force directly to bound currents and charges [7–9] and the momentum conservation theorem [4] were shown to be in agreement [10]. Application of the Lorentz force directly may be regarded as more fundamental, but it is computationally expensive compared to momentum conservation [11]. However, there still exist some questions as to the application of momentum conservation to the radiation pressure in lossy materials. In this Letter, we rigorously treat the optical momentum transfer to lossy media in the framework of the macroscopic electromagnetic theory. We apply the Lorentz force directly to bound and free currents and charges, thus avoiding a priori assumptions regarding the form of wave momentum. The separation of the total Lorentz force in terms of forces on bound currents and charges (Fb) and on free currents (Fc) provides insight into the mechanisms of momentum transfer in lossy media. We show an equivalent interpretation in terms of momentum conservation that distinguishes two processes of momentum transfer resulting from the wave reflection or transmission at the boundary and the attenuation in the medium. Our proposed view renders a more direct description of experiments than the usual separation of wave momentum into electromagnetic and material contributions [3,5,12–14]. The Lorentz force density and momentum conservation are equivalently applied to explain relevant experimental observations and to calculate the radiation pressure on absorbing Mie particles. In contrast to the scattering plus absorption forces derived for small particles, we predict that absorption can reduce the total optical momentum transfer to certain particles due to the balance between the force on free currents and the force on bound currents and charges. The Lorentz force is applied directly to bound and free currents and charges, which are used to model lossy media with complex permittivity R iI and permeability R iI in a background of (0, 0). The timeaverage Lorentz force density on bound currents and charges due to harmonic excitation with ei!t dependence is [10] f b 1 2Ref0r EE 0r HH i!R 0E B i!R 0H D g; (1) where Refg represents the real part of a complex quantity and denotes the complex conjugate. The leading two terms in (1) contribute via a surface force density on bound electric and magnetic charges, while the final two terms represent the volume force density on bound electric and magnetic currents [10,11]. In addition to (1), the force density on free currents, f c 1 2Ref!IE B !IH D g; (2) extends the recent analysis of the photon drag effect [15] to include magnetization, oblique incidence, and arbitrary polarization. The total time-average force on the material F F c Fb results from integration of the time-average force densities over the entire medium. PRL 97, 133902 (2006) PHYSICAL REVIEW LETTERS week ending 29 SEPTEMBER 2006 0031-9007=06=97(13)=133902(4) 133902-1 © 2006 The American Physical Society