PHYSICAL REVIEW E 73. 056604(2006) Radiation pressure of light pulses and conservation of linear momentum in dispersive media Michael Scalora, Giuseppe D'Aguanno, Nadia Mattiucci, Mark J. Bloemer, Marco Centim Concita Sibilia, and Joseph W. Haus Charles M. Bowden Research Center, AMSRD-AMR-WS-ST, Research, Development, and Engineering Center, Redstone arsenal. alabama 3 5898-5000. USA Time Domain Corporation, Cummings Research Park, 7057 Old Madison Pike, Huntsville, Alabama 35806, USA INFM at Dipartimento di Energetica, Universita di Roma"La Sapienza, Via A. Scarpa 16, 00161 Roma, Italy Electro-Optics Program, University of Dayton, Dayton, Ohio 45469-0245, USA (Received 12 December 2005: revised manuscript received 1 March 2006; published 16 May 2006) We derive an expression for the Minkowski momentum under conditions of dispersive susceptibility ermeability, and compare it to the abraham momentum in order to test the principle of conservation of linear momentum when matter is present. We investigate cases when an incident pulse interacts with a variety of structures, including thick substrates, resonant, free-standing, micron-sized multilayer stacks, and negative index materials. In general, we find that for media only a few wavelengths thick the Minkowski and Abraham momentum densities yield similar results. For more extended media, including substrates and Bragg mirrors embedded inside thick dielectric substrates, our calculations show dramatic differences between the minkowski and Abraham momenta. Without exception, in all cases investigated the instantaneous Lorentz force exerted on the medium is consistent only with the rate of change of the Abraham momentum. As a practical example, we use our model to predict that electromagnetic momentum and energy buildup inside a multilayer stack can lead ground for basic electromagnetic phenomena such as momentum transfer to macroscopic media W. r results to widely tunable accelerations that may easily reach and exceed 100 m/s2 for a mass of 10-s g. Our results suggest that the physics of the photonic band edge and other similar finite structures may be used as a testing DO:10.103/ PhysReve.73.056604 PACS number(s): 42.25 Bs, 42.25 Gy, 42.70.Qs, 78.20.Ci . INTRODUCTION light in fact exerts pressure, and was later experimentally For the better part of two decades photonic band gap verified by Nichols and Hull [6]. A good perspective of the (PBG) structures have been the subject of many theoretical early history of the subject is given by Mulser [7J, who also and experimental studies. Since the pioneering work of Yablonovitch [1] and John [2]. investigations have focused lated Brillouin and Raman scattering, are radiation-pressure on all kinds of geometrical arrangements, which vary from driven phenomena. More recently, Antonoyiannakis and Pen- one-dimensional, layered stacks, more amenable to analyti- dry [8] examined issues related to forces present in photonic topologies that require a full vector Maxwell approach [3]. In dielectric material, a light beam attracts the interface. The ent aspect of this particular problem, namely the interaction crystals, and the authors go on to predict an attractive force between neighboring dielectric spheres. Povinelli et al. [9] acting with pulses of finite bandwidth. Interesting questions studied the effect s of radiation pressure in omni-directional arise as incident pulses are tuned near the band edge, where reflector waveguides. They showed that as light propagates electromagnetic energy and momentum become temporarily down the guide(parallel to the dielectric mirrors),radiation stored inside the medium. When tuned near the band edge, in pressure causes the mirrors to attract, and, in the absence of the absence of meaningful absorption, a pulse of finite band. any losses, the attractive force appears to diverge near the cut width can lose forward momentum in at least two ways:() off frequency. Tucker et al. [10] have in rated effects of by tuning inside the gap, which results in mirrorlike reflec- radiation pressure and thermal jitter in a hybrid environment, tions and maximum transfer of momentum and (i) by tuning composed of a Fabry-Perot resonator as part of a microme. a minimum. and the field becomes localized inside the stack. that radiation pressur re can cause si mall changes in the sepa- It has been shown that relatively narrow-band band optical ration of movable mirrors even at room temperature, leading pulses may be transmitted without scattering losses or shape to nonlinear shifts of the Fabry-Perot resonance and hyster- changes [4] insuring that momentum and energy storage in- esis loops In MEMS lasers, the authors suggest that nonlin- porary. Therefore, a structure ear radiation pressure effects may induce changes in the not fixed to the laboratory frame naturally acquires linear characteristic low-frequency chirp of the device [10] momentum in an effort to conserve it. In what follows we The issue of how much electromagnetic momentum is attempt to answer the following question: how much and transferred to macroscopic bodies is still a matter of debate, what sort of motion results from the interaction? primarily". because what is considered electromagnetic The issue of radiation pressure on macroscopic bodies and what mechanical is to some extent arbitrary., as noted rches all the way back to Maxwell [5], who realized that by Jackson [11]. There are two well-known expressions that 1539-3755/200673(5)/056604(12) 056604-1 @2006 The American Physical SocietyRadiation pressure of light pulses and conservation of linear momentum in dispersive media Michael Scalora,1 Giuseppe D’Aguanno,1 Nadia Mattiucci,2,1 Mark J. Bloemer,1 Marco Centini,3 Concita Sibilia,3 and Joseph W. Haus4 1 Charles M. Bowden Research Center, AMSRD-AMR-WS-ST, Research, Development, and Engineering Center, Redstone Arsenal, Alabama 35898-5000, USA 2 Time Domain Corporation, Cummings Research Park, 7057 Old Madison Pike, Huntsville, Alabama 35806, USA 3 INFM at Dipartimento di Energetica, Universita di Roma “La Sapienza”, Via A. Scarpa 16, 00161 Roma, Italy 4 Electro-Optics Program, University of Dayton, Dayton, Ohio 45469-0245, USA
Received 12 December 2005; revised manuscript received 1 March 2006; published 16 May 2006 We derive an expression for the Minkowski momentum under conditions of dispersive susceptibility and permeability, and compare it to the Abraham momentum in order to test the principle of conservation of linear momentum when matter is present. We investigate cases when an incident pulse interacts with a variety of structures, including thick substrates, resonant, free-standing, micron-sized multilayer stacks, and negative index materials. In general, we find that for media only a few wavelengths thick the Minkowski and Abraham momentum densities yield similar results. For more extended media, including substrates and Bragg mirrors embedded inside thick dielectric substrates, our calculations show dramatic differences between the Minkowski and Abraham momenta. Without exception, in all cases investigated the instantaneous Lorentz force exerted on the medium is consistent only with the rate of change of the Abraham momentum. As a practical example, we use our model to predict that electromagnetic momentum and energy buildup inside a multilayer stack can lead to widely tunable accelerations that may easily reach and exceed 1010 m/s2 for a mass of 10−5 g. Our results suggest that the physics of the photonic band edge and other similar finite structures may be used as a testing ground for basic electromagnetic phenomena such as momentum transfer to macroscopic media. DOI: 10.1103/PhysRevE.73.056604 PACS number
s: 42.25.Bs, 42.25.Gy, 42.70.Qs, 78.20.Ci I. INTRODUCTION For the better part of two decades photonic band gap
PBG structures have been the subject of many theoretical and experimental studies. Since the pioneering work of Yablonovitch 1 and John 2, investigations have focused on all kinds of geometrical arrangements, which vary from one-dimensional, layered stacks, more amenable to analyti￾cal treatment, to much more complicated three-dimensional topologies that require a full vector Maxwell approach 3. In our current effort, in part we focus our attention on a differ￾ent aspect of this particular problem, namely the interaction of short pulses with free-standing, resonant structures inter￾acting with pulses of finite bandwidth. Interesting questions arise as incident pulses are tuned near the band edge, where electromagnetic energy and momentum become temporarily stored inside the medium. When tuned near the band edge, in the absence of meaningful absorption, a pulse of finite band￾width can lose forward momentum in at least two ways:
i by tuning inside the gap, which results in mirrorlike reflec￾tions and maximum transfer of momentum and
ii by tuning at a band edge resonance, where the transfer of momentum is a minimum, and the field becomes localized inside the stack. It has been shown that relatively narrow-band band optical pulses may be transmitted without scattering losses or shape changes 4, insuring that momentum and energy storage in￾side the structure is only temporary. Therefore, a structure not fixed to the laboratory frame naturally acquires linear momentum in an effort to conserve it. In what follows we attempt to answer the following question: how much and what sort of motion results from the interaction? The issue of radiation pressure on macroscopic bodies arches all the way back to Maxwell 5, who realized that light in fact exerts pressure, and was later experimentally verified by Nichols and Hull 6. A good perspective of the early history of the subject is given by Mulser 7, who also showed that resonant multiwave interactions, such as stimu￾lated Brillouin and Raman scattering, are radiation-pressure￾driven phenomena. More recently, Antonoyiannakis and Pen￾dry 8 examined issues related to forces present in photonic crystals and found that when traversing from a low to a high dielectric material, a light beam attracts the interface. The implications then extend to 3D
three-dimensional photonic crystals, and the authors go on to predict an attractive force between neighboring dielectric spheres. Povinelli et al. 9 studied the effects of radiation pressure in omni-directional reflector waveguides. They showed that as light propagates down the guide
parallel to the dielectric mirrors, radiation pressure causes the mirrors to attract, and, in the absence of any losses, the attractive force appears to diverge near the cut off frequency. Tucker et al. 10 have investigated effects of radiation pressure and thermal jitter in a hybrid environment, composed of a Fabry-Perot resonator as part of a microme￾chanical switching mechanism
MEMS. The authors found that radiation pressure can cause small changes in the sepa￾ration of movable mirrors even at room temperature, leading to nonlinear shifts of the Fabry-Perot resonance and hyster￾esis loops. In MEMS lasers, the authors suggest that nonlin￾ear radiation pressure effects may induce changes in the characteristic low-frequency chirp of the device 10. The issue of how much electromagnetic momentum is transferred to macroscopic bodies is still a matter of debate, primarily “¼because what is considered electromagnetic and what mechanical is to some extent arbitrary¼,” as noted by Jackson 11. There are two well-known expressions that PHYSICAL REVIEW E 73, 056604
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