The enigma of optical momentum in a medium

Momentum, angular momentum, and spin of waves in an isotropic collisionless plasma

We examine the momentum and angular momentum (including spin) properties of linear waves, both longitudinal (Langmuir) and transverse (electromagnetic), in an isotropic nonrelativistic collisionless electron plasma. We focus on conserved quantities associated with the translational and rotational invariance of the wave fields with respect to the homogeneous medium; these are sometimes called pseudomomenta. There are two types of the momentum and angular momentum densities: (i) the kinetic ones associated with the energy flux density and the symmetrized (Belinfante) energy-momentum tensor and (ii) the canonical ones associated with the conserved Noether currents and canonical energy-momentum tensor. We find that the canonical momentum and spin densities of Langmuir waves are similar to those of sound waves in fluids or gases; they are naturally expressed via the electron velocity field. In turn, the momentum and spin densities of electromagnetic waves can be written either in the forms known for free-space electromagnetic fields, involving only the electric field, or in the dual-symmetric forms involving both electric and magnetic fields, as well as the effective permittivity of plasma. We derive these properties both within the phenomenological macroscopic approach and microscopic Lagrangian field theory for the coupled electromagnetic fields and electrons. Finally, we explore implications of the canonical momentum and spin densities in transport and electrodynamic phenomena: the Stokes drift, the wave-induced magnetization (inverse Faraday effect), etc.

Momentum considerations inside near-zero index materials

Near-zero index (NZI) materials, i.e., materials having a phase refractive index close to zero, are known to enhance or inhibit light-matter interactions. Most theoretical derivations of fundamental radiative processes rely on energetic considerations and detailed balance equations, but not on momentum considerations. Because momentum exchange should also be incorporated into theoretical models, we investigate momentum inside the three categories of NZI materials, i.e., inside epsilon-and-mu-near-zero (EMNZ), epsilon-near-zero (ENZ) and mu-near-zero (MNZ) materials. In the context of Abraham-Minkowski debate in dispersive materials, we show that Minkowski-canonical momentum of light is zero inside all categories of NZI materials while Abraham-kinetic momentum of light is zero in ENZ and MNZ materials but nonzero inside EMNZ materials. We theoretically demonstrate that momentum recoil, transfer momentum from the field to the atom and Doppler shift are inhibited in NZI materials. Fundamental radiative processes inhibition is also explained due to those momentum considerations inside three-dimensional NZI materials. Absence of diffraction pattern in slits experiments is seen as a consequence of zero Minkowski momentum. Lastly, consequence on Heisenberg inequality, microscopy applications and on the canonical momentum as generator of translations are discussed. Those findings are appealing for a better understanding of fundamental light-matter interactions at the nanoscale as well as for lasing applications.

Light emission by free electrons in photonic time-crystals

Photonic time-crystals (PTCs) are spatially homogeneous media whose electromagnetic susceptibility varies periodically in time, causing temporal reflections and refractions for any wave propagating within the medium. The time-reflected and time-refracted waves interfere, giving rise to Floquet modes with momentum bands separated by momentum gaps (rather than energy bands and energy gaps, as in photonic crystals). Here, we present a study on the emission of radiation by free electrons in PTCs. We show that a free electron moving in a PTC spontaneously emits radiation, and when associated with momentum-gap modes, the electron emission process is exponentially amplified by the modulation of the refractive index. Moreover, under strong electron–photon coupling, the quantum formulation reveals that the spontaneous emission into the PTC bandgap experiences destructive quantum interference with the emission of the electron into the PTC band modes, leading to suppression of the interdependent emission. Free-electron physics in PTCs offers a platform for studying a plethora of exciting phenomena, such as radiating dipoles moving at relativistic speeds and highly efficient quantum interactions with free electrons.

Energy and momentum conservation upon reflection of a solitary pulse in a bounded magnetized plasma

When the nature of a magnetosonic pulse propagating in a bounded magnetized plasma slab is successively transformed from compression to rarefaction and vice versa upon reflection at a plasma-vacuum interface, both the energy and the longitudinal electromagnetic (EM) momentum of the plasma-pulse system are found to oscillate between two states. Simple analytical models and particle-in-cell simulations show that these oscillations are associated with EM radiation to and from the surrounding magnetized vacuum. For partial reflection supplemental losses in total pulse energy and mechanical momentum are identified and shown to follow, respectively, Fresnel's transmission coefficients for the energy and the magnetic perturbation. This mechanical momentum loss upon partial reflection is traced to the momentarily nonzero volume-integrated Lorentz force, which in turn supports that mechanical and EM momentum transfers are, respectively, associated with the magnetic and electric parts of the momentum flux density.

Isolated detection of elastic waves driven by the momentum of light

Electromagnetic momentum carried by light is observable through the mechanical effects radiation pressure exerts on illuminated objects. Momentum conversion from electromagnetic fields to elastic waves within a solid object proceeds through a string of electrodynamic and elastodynamic phenomena, collectively bound by momentum and energy continuity. The details of this conversion predicted by theory have yet to be validated by experiments, as it is difficult to distinguish displacements driven by momentum from those driven by heating due to light absorption. Here, we have measured temporal variations of the surface displacements induced by laser pulses reflected from a solid dielectric mirror. Ab initio modelling of momentum flow describes the transfer of momentum from the electromagnetic field to the dielectric mirror, with subsequent creation/propagation of multicomponent elastic waves. Complete consistency between predictions and absolute measurements of surface displacements offers compelling evidence of elastic transients driven predominantly by the momentum of light.

The exact mechanism of momentum conversion from light to an object has varied descriptions in the literature and experimental verifications are difficult. Here the authors do an in-depth experimental and numerical study of the momentum dynamics of elastic waves in a dielectric mirror hit by a pulsed laser beam.

Light-driven mass density wave dynamics in optical fibers

We have recently developed the mass-polariton (MP) theory of light to describe the light propagation in transparent bulk materials [Phys. Rev. A 95, 063850 (2017)]. The MP theory is general as it is based on the covariance principle and the fundamental conservation laws of nature. Therefore, it can be applied also to nonhomogeneous and dispersive materials. In this work, we apply the MP theory of light to describe propagation of light in step-index circular waveguides. We study the eigenmodes of the electric and magnetic fields in a waveguide and use these modes to calculate the optical force density, which is used in the optoelastic continuum dynamics (OCD) to simulate the dynamics of medium atoms in the waveguide. We show that the total momentum and angular momentum in the waveguide are carried by a coupled state of the field and the medium. In particular, we focus in the dynamics of atoms, which has not been covered in previous theories that consider only field dynamics in waveguides. We also study the elastic waves generated in the waveguide during the relaxation following from atomic displacements in the waveguide.

Optical Chirality in Dispersive and Lossy Media

Several dynamical properties of electromagnetic waves such as energy, momentum, angular momentum, and optical helicity have been recently reexamined in dispersive and lossless media. Here, we address an alternative derivation for the optical chirality, extending it so as to include dissipative effects as well. To this end, we first elaborate on the most complete form of the conservation law for the optical chirality, without any restrictions on the nature of the medium. As a result we find a general expression for the optical chirality density both in lossless and lossy dispersive media. Our definition is perfectly consistent with that originally introduced for electromagnetic fields in free space, and is applicable to any material system, including dielectrics, plasmonic nanostructures, and left-handed metamaterials.

Electromagnetic Helicity in Complex Media

Optical helicity density is usually discussed for monochromatic electromagnetic fields in free space. It plays an important role in the interaction with chiral molecules or nanoparticles. Here we introduce the optical helicity density in a dispersive isotropic medium. Our definition is consistent with biorthogonal Maxwell electromagnetism in optical media and the Brillouin energy density as well as with the recently introduced canonical momentum and spin of light in dispersive media. We consider a number of examples, including electromagnetic waves in dielectrics, negative-index materials, and metals, as well as interactions of light in a medium with chiral and magnetoelectric molecules.

Non-conservative optical forces

Undoubtedly, laser tweezers are the most recognized application of optically induced mechanical action. Their operation is usually described in terms of conservative forces originating from intensity gradients. However, the fundamental optical action on matter is non-conservative. We will review different manifestations of non-conservative optical forces (NCF) and discuss their dependence on the specific spatial properties of optical fields that generate them. New developments relevant to the NCF such as tractor beams and transversal forces are also discussed.

Optical Momentum, Spin, and Angular Momentum in Dispersive Media

We examine the momentum, spin, and orbital angular momentum of structured monochromatic optical fields in dispersive inhomogeneous isotropic media. There are two bifurcations in this general problem: the Abraham-Minkowski dilemma and the kinetic (Poynting-like) versus canonical (spin-orbital) pictures. We show that the kinetic Abraham momentum describes the energy flux and group velocity of the wave in the medium. At the same time, we introduce novel canonical Minkowski-type momentum, spin, and orbital angular momentum densities of the field. These quantities exhibit fairly natural forms, analogous to the Brillouin energy density, as well as multiple advantages as compared with previously considered formalisms. As an example, we apply this general theory to inhomogeneous surface plasmon-polariton (SPP) waves at a metal-vacuum interface and show that SPPs carry a "supermomentum," proportional to the wave vector k_{p}>ω/c, and a transverse spin, which can change its sign depending on the frequency ω.

Will a Decaying Atom Feel a Friction Force?

We show how a simple calculation leads to the surprising result that an excited two-level atom moving through a vacuum sees a tiny friction force of first order in v/c. At first sight this seems to be in obvious contradiction to other calculations showing that the interaction with the vacuum does not change the velocity of an atom. It is even more surprising that this change in the atom's momentum turns out to be a necessary result of energy and momentum conservation in special relativity.

Optomechanical measurement of photon spin angular momentum and optical torque in integrated photonic devices

Photons carry linear momentum and spin angular momentum when circularly or elliptically polarized. During light-matter interaction, transfer of linear momentum leads to optical forces, whereas transfer of angular momentum induces optical torque. Optical forces including radiation pressure and gradient forces have long been used in optical tweezers and laser cooling. In nanophotonic devices, optical forces can be significantly enhanced, leading to unprecedented optomechanical effects in both classical and quantum regimes. In contrast, to date, the angular momentum of light and the optical torque effect have only been used in optical tweezers but remain unexplored in integrated photonics. We demonstrate the measurement of the spin angular momentum of photons propagating in a birefringent waveguide and the use of optical torque to actuate rotational motion of an optomechanical device. We show that the sign and magnitude of the optical torque are determined by the photon polarization states that are synthesized on the chip. Our study reveals the mechanical effect of photon's polarization degree of freedom and demonstrates its control in integrated photonic devices. Exploiting optical torque and optomechanical interaction with photon angular momentum can lead to torsional cavity optomechanics and optomechanical photon spin-orbit coupling, as well as applications such as optomechanical gyroscopes and torsional magnetometry.

Reflection and extinction of light by self-assembled monolayers of a quinque-thiophene derivative: A coherent scattering approach

Scattering matrix theory is used to describe resonant optical properties of molecular monolayers. Three types of coupling are included: exciton-exciton, exciton-photon, and exciton-phonon coupling. We use the K-matrix formalism, developed originally to describe neutron scattering spectra in nuclear physics to compute the scattering of polaritons by phonons. This perturbation approach takes into account the three couplings and allows one to go beyond molecular exciton theory without the need of introducing additional boundary conditions for the polariton. We demonstrate that reflection, absorption, and extinction of light by 2D self-assembled monolayers of molecules containing quinque-thiophene chromophoric groups can be calculated. The extracted coherence length of the Frenkel exciton is discussed.

Quantitative assessment of radiation force effect at the dielectric air-liquid interface

We induce nanometer-scale surface deformation by exploiting momentum conservation of the interaction between laser light and dielectric liquids. The effect of radiation force at the air-liquid interface is quantitatively assessed for fluids with different density, viscosity and surface tension. The imparted pressure on the liquids by continuous or pulsed laser light excitation is fully described by the Helmholtz electromagnetic force density.

Laser propulsion of nanobullets by adiabatic compression of surface plasmon polaritons

Laser propulsion and guide of nanosized objects is fundamental for a wide number of applications. These applications are often limited by the fact that the optical forces acting on nanoparticles are almost negligible even in the favorable case of metallic particles and hence large laser powers are needed to accelerate and guide nanosize devices in practical applications. Furthermore, metallic nanoparticles exhibit strong absorption bands and scattering and this makes more difficult controlling nanopropulsion. Thus, finding some mechanism enhancing the optomechanical interaction at the nanoscale controlled by laser is specifically challenging and pivotal. Here, we demonstrate a novel physical effect where the well-known adiabatic localization of the enhanced plasmonic surface field on the apex of metallic nanocones produces a significant optical pressure employable as a propulsive mechanism. The proposed method gives the possibility to develop new photonics devices to accelerate metallic nanobullets over long distances for a variety of applications.

Simulations of radiation pressure experiments narrow down the energy and momentum of light in matter

Consensus on a single electrodynamic theory has yet to be reached. Discord was seeded over a century ago when Abraham and Minkowski proposed different forms of electromagnetic momentum density and has since expanded in scope with the gradual introduction of other forms of momentum and force densities. Although degenerate sets of electrodynamic postulates can be fashioned to comply with global energy and momentum conservation, hope remains to isolate a single theory based on detailed comparison between force density predictions and radiation pressure experiments. This comparison is two-fold challenging because there are just a handful of quantitative radiation pressure measurements over the past century and the solutions developed from different postulates, which consist of approximate expressions and inferential deductions, are scattered throughout the literature. For these reasons, it is appropriate to conduct a consolidated and comprehensive re-analysis of past experiments under the assumption that the momentum and energy of light in matter are degenerate. We create a combined electrodynamic/fluid dynamic simulation testbed that uses five historically significant sets of electrodynamic postulates, including those by Abraham and Minkowski, to model radiation pressure under diverse configurations with minimal assumptions. This leads to new interpretations of landmark investigations of light momentum, including the Balazs thought experiment, the Jones-Richards and Jones-Leslie measurements of radiation pressure on submerged mirrors, observations of laser-deformed fluid surfaces, and experiments on optical trapping and tractor beaming of dielectric particles. We discuss the merits and demerits of each set of postulates when compared to available experimental evidence and fundamental conservation laws. Of the five sets of postulates, the Abraham and Einstein-Laub postulates provide the greatest consistency with observations and the most physically plausible descriptions of electrodynamic interactions. Force density predictions made by these two postulates are unique under many conditions and their experimental isolation is potentially within reach.

Magnesium-catalyzed hydrosilylation of α,β-unsaturated esters

ToMMgHB(C6F5)3 (1, ToM = tris(4,4-dimethyl-2-oxazolinyl)phenylborate) catalyzes the 1,4-hydrosilylation of α,β-unsaturated esters. This magnesium hydridoborate compound is synthesized by the reaction of ToMMgMe, PhSiH3, and B(C6F5)3. Unlike the transient ToMMgH formed from the reaction of ToMMgMe and PhSiH3, the borate adduct 1 persists in solution and in the solid state. Crystallographic characterization reveals tripodal coordination of the HB(C6F5)3 moiety to the six-coordinate magnesium center with a ∠Mg-H-B of 141(3)°. The pathway for formation of 1 is proposed to involve the reaction of ToMMgMe and a PhSiH3/B(C6F5)3 adduct because the other possible intermediates, ToMMgH and ToMMgMeB(C6F5)3, react to give an intractable black solid and ToMMgC6F5, respectively. Under catalytic conditions, silyl ketene acetals are isolated in high yield from the addition of hydrosilanes to α,β-unsaturated esters with 1 as the catalyst.

Spin angular momentum of surface modes from the perspective of optical power flow

We show that the spin angular momentum (SAM) carried by a surface mode can be linked to the expectation value, with respect to the distribution of optical power flow, of its decay constant by itself or divided by the product of permittivity and permeability of the medium. Rewriting the formulas for the SAM of a surface mode using the relation between the SAM density and the Poynting vector and then normalizing the light field so that the surface mode carries unit power, we derive novel formulas that show the linear relation between the SAM and those expectation values. The effect of propagation loss is also discussed briefly.

Measurement of small light absorption in microparticles by means of optically induced rotation

The absorption parameters of micro-particles have been associated with the induced spin exerted upon the particle, when embedded in a circularly polarized coherent field. The induced rotational speed is theoretically analyzed, showing the influence of the beam parameters, the parameters of the particle and the tribological parameters of the surrounding fluid. The theoretical findings have been adequately confirmed in experiments.

Is the angular momentum of an electron conserved in a uniform magnetic field?

We show that an electron moving in a uniform magnetic field possesses a time-varying "diamagnetic" angular momentum. Surprisingly this means that the kinetic angular momentum of the electron may vary with time, despite the rotational symmetry of the system. This apparent violation of angular momentum conservation is resolved by including the angular momentum of the surrounding fields.

Unravelling the effects of radiation forces in water

The effect of radiation forces at the interface between dielectric materials has been a long-standing debate for over a century. Yet there has been so far only limited experimental verification in complete accordance with the theory. Here we measure the surface deformation at the air-water interface induced by continuous and pulsed laser excitation and match this to rigorous theory of radiation forces. We demonstrate that the experimental results are quantitatively described by the numerical calculations of radiation forces. The Helmholtz force is used for the surface radiation pressure. The resulting surface pressure obtained is consistent with the momentum conservation using the Minkowski momentum density expression assuming that the averaged momentum per photon is given by the Minkowski momentum. Considering the total momentum as a sum of that propagating with the electromagnetic wave and that deposited locally in the material, the Abraham momentum interpretation also appears to be appropriate.

Relativistic Lagrangian model of a nematic liquid crystal interacting with an electromagnetic field

We develop a relativistic variational model for a nematic liquid crystal interacting with an electromagnetic field. The constitutive relation for a general anisotropic uniaxial diamagnetic and dielectric medium is analyzed. We discuss light wave propagation in this moving uniaxial medium, for which the corresponding optical metrics are identified explicitly. A Lagrangian for the coupled system of a nematic liquid crystal and the electromagnetic field is constructed, from which a complete set of equations of motion for the system is derived. The canonical energy-momentum and spin tensors are systematically obtained. We compare our results with those within the nonrelativistic models. As an application of our general formalism, we discuss the so-called Abraham-Minkowski controversy on the momentum of light in a medium.

Contributions of John Henry Poynting to the understanding of radiation pressure

The name of Poynting is universally recognized for his development of the well-known expression for the flow of electromagnetic energy. Not so well known is Poynting's series of papers on radiation pressure, with 2011 marking the centenary of the last of his 15 publications on this topic. This paper reviews and assesses his radiation-pressure work, with a level of coverage aimed at the reader familiar with the Maxwell electromagnetic theory and interested in the current understanding of radiation pressure. We begin with brief details of Poynting's life, followed by accounts of the relevant publications by others before and during his period of activity in the field from 1903 to 1911. His contributions to the understanding of radiation-pressure effects in the solar system, and the linear and angular momenta of light are discussed, with evaluations from a modern perspective.

Observation of the intrinsic Abraham force in time-varying magnetic and electric fields

The Abraham force exerted by a time-dependent electromagnetic field on neutral, polarizable matter has two contributions. The one induced by a time-varying magnetic field and a static electric field is reported here for the first time. We discuss our results in the context of the radiative momentum in matter. Our observations are consistent with Abraham's and Nelson's versions for radiative momentum.

Negative radiation pressure and negative effective refractive index via dielectric birefringence

We show that light guided in a planar dielectric slab geometry incorporating a biaxial medium has lossless modes with group and phase velocities in opposite directions. Particles in a vacuum gap inserted into the structure experience negative radiation pressure: the particles are pulled by light rather than pushed by it. This effectively one-dimensional dielectric structure represents a new geometry for achieving negative radiation pressure in a wide range of frequencies with minimal loss. Moreover, this geometry provides a straightforward platform for experimentally resolving the Abrahams-Minkowski dilemma.

Electromagnetic forces and internal stresses in dielectric media

The macroscopic electromagnetic force on dielectric bodies and the related problem of the momentum conservation are discussed. It is argued that different forms of the momentum conservation and, respectively, different forms of the force density, correspond to the different ordering in the macroscopic averaging procedure. Different averaging procedures and averaging length scale assumptions result in expressions for the force density with vastly different force density profiles which can potentially be detected experimentally by measuring the profiles of the internal stresses in the medium. The expressions for the Helmholtz force is generalized for the dissipative case. It is shown that the net (integrated) force on the body in vacuum is the same for Lorentz and Helmholtz expressions in all configuration. The case of a semi-infinite medium is analyzed and it is shown that explicit assumptions on the boundary conditions at infinity remove ambiguity in the force on the semi-infinite dielectric.

Measurement of the Abraham force and its predicted QED corrections in crossed electric and magnetic fields

We report the observation by a new method of mechanical momentum transferred to gas phase atoms and molecules upon application of crossed oscillating electric and static magnetic fields. We identify this momentum as the microscopic analogue of the classical Abraham force. Two QED predictions of additional magnetoelectrically induced mechanical momentum are addressed. One of them is experimentally refuted; the other is found to be currently below our experimental detection.

The observable pressure of light in dielectric fluids

By considering a perfect reflector submerged in a dielectric fluid, we show that the Minkowski formulation describes the optical momentum transfer to submerged objects. This result is required by global energy conservation, regardless of the phase of the reflected wave. While the electromagnetic pressure on a submerged reflector can vary with phase of the mirror reflection coefficient between twice the Abraham momentum and twice the Minkowski momentum, the Minkowski momentum is always restored due to the additional pressure on the dielectric surface. This analysis also gives further evidence for use of the Minkowski stress tensor at the boundary of a dielectric interface, which has been the subject of a long-standing debate in physics and the source of uncertainty in the modeling of optical forces on submerged particles.

Resolution of the abraham-minkowski dilemma

The dilemma of identifying the correct form for the momentum of light in a medium has run for a century and has been informed by many distinguished contributions, both theoretical and experimental. We show that both the Abraham and Minkowski forms of the momentum density are correct, with the former being the kinetic momentum and the latter the canonical momentum. This identification allows us to explain why the experiments supporting each of the rival momenta gave the results that they did. The inclusion of dispersion and absorption provides an interesting subtlety, but does not change our conclusion.