Optical Magnus Effect Research Articles

Unusual optical phenomena inside and near a rotating sphere: the photonic hook and resonance.

Based on the optical Magnus effect, the analytical expressions of the electromagnetic field that a spinning dielectric sphere illuminated by polarized plane waves are derived according to the "instantaneous rest-frame" hypothesis and Minkowski's theory. More attention is paid to the near field. The unusual optical phenomena in mesoscale spheres without material and illumination wave asymmetry that are the photonic hook (PH) and whispering gallery mode (WGM)-like resonance caused by rotation are explored. The impact of resonance scattering on PHs is further analyzed under this framework. The influence of non-reciprocal rotating dimensionless parameter γ on PH and resonance is emphasized. The results in this paper have extensive application prospects in mesotronics, particle manipulation, resonator design, mechatronics, and planetary exploration.

Curved photonic nanojet generated by a rotating cylinder.

The curved photonic nanojet (CPNJ) produced due to the interaction between a dielectric circular cylinder rotating at a stable angular velocity and a plane wave is investigated. Based on this model, the optical Magnus effect of a dielectric circular cylinder is verified. And the analytical expression of both internal and external electric field are given based on the instantaneous rest-frame theory and the partial-wave series expansion method in cylindrical coordinates. The influence of the size parameter, the relative refractive index, and the rotating dimensionless parameter on the CPNJ are analyzed and discussed in numerical results. The "photonic nanojet curved" effect is highlighted, which can be used to generate the off-axis photonic nanojet (PNJ) controlling particles by adjusting the angular velocity of the dielectric cylinder. The results of this manuscript have promising application prospects in optical tweezers, particle manipulation, and optical trapping. Moreover, it also provides theoretical support for the particle spinning and generation of the off-axis CPNJ.

Covariant formulation of spin optics for electromagnetic waves

We develop geometric optics expansion up to the subleading order for circularly polarized electromagnetic waves on curved spacetime. This subleading order geometric optics expansion, in which the conventional eikonal function is modified by inserting a carefully chosen helicity-dependent correction, is called spin optics. We derive the propagation and polarization equations in the spin optics approximation as electromagnetic waves travel in curved spacetime. Polarization-dependent deviation of the light ray trajectory from the geodesic, describing the gravitational spin Hall effect, is observed. We also establish an analogy with the related phenomena (optical Magnus effect) of condensed matter physics.

Optical Magnus radiation force and torque on a dielectric layered cylinder with a spinning absorptive dielectric core.

A dielectric cylindrical shell material with an inner stationary absorptive core (or, equivalently, a concentric layered cylinder) illuminated by an axisymmetric wave field (in 2D) with arbitrary polarization will experience a time-averaged radiation force along the direction of wave propagation, whereas the transverse component vanishes as required by symmetry. Counterintuitively, the present analysis shows that when the inner absorptive core material rotates with an initial angular velocity Ω0 around its main geometrical axis, a transverse radiation force component arises (in addition to a longitudinal force) as well as an axial radiation torque component in plane waves. This phenomenon is the analog of the classical hydrodynamic Magnus effect. In this analysis, the instantaneous rest-frame theory and the modal series expansion method in cylindrical coordinates are utilized to formulate the EM/optical scattering from a cylindrical shell with arbitrary thickness, and to compute the optical radiation force and torque vector components. Particular emphases are given on the size parameter of the cylindrical shell, the layer thickness, the angular rotation of the inner absorptive core, and the polarization (TM or TE) of the incident plane waves. Numerical computations illustrate the analysis and explicate the behaviors of the longitudinal, transverse, and axial radiation force and torque components. Related applications for the optical Magnus effect in radiation force and torque investigations can benefit from the results of the present analysis in spin-optics, rotational Doppler shift for optical waves, optical tweezers, optical manipulation of elongated spinning objects, and particle rotation.

Optical Magnus effect in the photophoresis of a spinning absorptive dielectric circular cylinder.

When a stationary absorptive dielectric cylinder suspended in a gas (such as air) is illuminated by an axisymmetric wave field (such as plane waves), the transverse (T) photophoretic asymmetry factor (PAF) vanishes as required by geometrical symmetry [Appl. Opt.60, 7937 (2021) APOPAI0003-693510.1364/AO.435306]. Counter-intuitively, when the cylinder possesses an initial angular velocity Ω0 with a sufficiently small acceleration and spins around its main axis in the illuminating field of axisymmetric plane waves, it is shown here that the T-PAF (which is directly proportional to the T-photophoretic force vector component) is quantifiable, in analogy with the Magnus effect in hydrodynamics where a force perpendicular to the axis of the cylinder and to the propagation direction arises. Based upon the instantaneous rest-frame theory and the partial-wave series expansion method in cylindrical coordinates, the internal electric field of the spinning absorptive dielectric cylinder is determined and utilized to compute both the longitudinal (L) and T-PAFs. Particular emphases are given on the size parameter of the cylinder, its angular rotation, the light absorption inside its core material and the polarization (TM or TE) of the incident plane waves. The dimensionless intensity function (DIF) is also computed, which reveals quantitative information on the heated portions within the internal absorptive core material of the cylinder. Numerical computations illustrate the analysis and explicate the behaviors of the DIF and the L- and T-PAFs, which predict the emergence of the forward, neutral, and reverse optical/electromagnetic Magnus effect in the photophoresis of an absorptive dielectric cylinder and related applications in spin optics, optical tweezers, optical manipulation of elongated objects, and radiative transfer research.

Physical optics in a uniform gravitational field

The motion of a (quasi-)plane wave in a uniform gravitational field is studied. It is shown that the energy of an elliptically polarized wave does not propagate along a geodesic, but in a direction that is rotated with respect to the gravitational force. The similarity with the walk-off effect in anisotropic crystals or the optical Magnus effect in inhomogeneous media is pointed out.

Transformation of the vector part of the 4-momentum in the Dirac equation and in Maxwell’s equations in Majorana form for chiral media

It is suggested to extend the results obtained for Maxwell’s equations in Majorana form (spin-1 particles) for spin particles with a half-integer spin and a nonzero mass. It is shown that in an unbounded “chiral medium” (twisted media) the degeneration existing between particles of different helicities is removed. For ultrarelativistic particles, an analog to the inverse optical Magnus effect follows where the effect is determined by the chirality of the medium. From the inverse scattering problem for the transforms under consideration it follows that the amplitude of the wave function of a particle in a chiral medium can vary with time according to a linear law (for example, the process of neutrino (antineutrino) production or annihilation), and the parameters of the medium satisfy the evolution equation.

Transverse angular shift in optical Magnus effect

Starting from the plane angular spectrum theory, we establish a transmission model of beam refraction at the interface between air and glass. Based on this model, we reveal a transverse angular shift in the optical Magnus effect. For a certain linearly and elliptically polarized light beam, the field centroid of refraction beam exhibits a transverse angular shift. However, the transverse angular shift would vanish when the incident light beam is circularly polarized. At an interface between positive and negative refractive indexes, the transverse angle shift presents a reversed phenomenon which is caused by negative diffraction in the left-handed materials. Ultra-high refractive index can significantly reduce the transverse angular shift. On the contrary, the ultra-low refractive index can significantly enhance the transverse angular shift. These findings provide a new method of how to adjust and enhance the optical Magnus effect.

Role of transverse-momentum currents in the optical Magnus effect in free space

We establish a general vector field model to describe the role of transverse-momentum currents in the optical Magnus effect in free space. As an analogy of the mechanical Magnus effect, the circularly polarized wave packet in our model acts as the rotating ball, and its rotation direction depends on the polarization state. Based on this model, we demonstrate the existence of an optical polarization-dependent Magnus effect which is significantly different from the conventional optical Magnus effect in that light-matter interaction is not required. Further, we reveal the relation between transverse-momentum currents and the optical Magnus effect, and find that such a polarization-dependent rotation is unavoidable when the wave packet possesses transverse-momentum currents. The physics underlying this intriguing effect is the combined contributions of transverse spin and orbital currents. We predict that this effect may be observed experimentally even in the propagation direction. These findings provide further evidence for the optical Magnus effect in free space and can be extrapolated to other physical systems.

Metamaterials from Amorphous Ferromagnetic Microwires: Interaction between Microwires

For inhomogeneous mediums the оptical Magnus effect has been derived. The metamaterials fabricated from amorphous ferromagnet Co-Fe-Cr-B-Si microwires are shown to exhibit a negative refractive index for electromagnetic waves over wide scale of GHz frequencies. Optical properties and optical Magnus effect of such metamaterials are tunable by an external magnetic field.

Spin-orbit interaction of light

Spin-orbit interaction is a weak coupling between intrinsic (spin) and extrinsic (orbital motion) degrees of freedom of spinning particles. It implies mutual conversion between a particle’s spin and orbital angular momenta. Classical polarized light also carries spin and reveals spin-orbit coupling when propagating along a curved trajectory.1 This manifests itself in two mutual phenomena. First, the curved trajectory affects the evolution of the light’s polarization state, which is described by the Berry phase and parallel-transport law: see Figure 1(a). Second, the light trajectory also experiences a reaction from the spin, i.e., a polarization-dependent perturbation of the trajectory occurs. This can also be described in terms of the Berry phase and represents a topological spin transport of photons also known as the spin-Hall effect of light or the optical Magnus effect: see Figure 1(b). We recently reported the first direct observation of this effect.2 Remarkably, the spin-orbit coupling phenomena have a dual, geometro-dynamical nature. On the one hand, the parallel transport of the polarization and the spin-Hall effect can be attributed to the inertia of the wave field and the Coriolis effect. On the other, the spin-orbit interaction of light has an inherent geometrical origin that is described by the Berry-phase topological monopole in momentum space. Two decades ago, the Berry phase brought a geometrical beauty to the description of quantum-adiabatic evolution.3, 4 Physicists started to realize that seemingly ‘passive’ geometrical concepts, such as Berry curvature, also manifest themselves dynamically, producing a real action on physical objects. As a result, geometry-induced forces appear that affect the dynamics of quantum particles with some internal properties.5 In particular, they describe the Magnus effect of quantum vortices6 and spinHall effect of spinning particles.7, 8 This offers a novel type of quantum transport that is robust against the details of the system and is determined solely by the geometry and intrinsic properties of the particles. Figure 1. Spin-orbit interaction of light. (a) Evolution of the polarization vector (e → e′ → e′′) along a helical trajectory according to the Berry phase and parallel-transport law. Θ: Polarization rotation angle for each helix. (b) Topological spin transport of photons: Reaction of spin to the trajectory causes splitting of rightand left-hand circularly polarized beams. ∆: Splitting for each helix. (Reproduced with permission from Nature Photonics.2)

Effect of polarization on the trajectory of dissipative solitons

We show that the optical Magnus effect for dissipative solitons is determined not only by the helicity but also by the topological index, i.e., by the magnetic quantum number or by the projection of the soliton orbital moment on its trajectory. In the case of inhomogeneous media, we find a relation between the optical Magnus effect and the nonholonomy of the field of unit vectors tangent to the trajectory.

Optical Magnus effect in metamaterials fabricated from ferromagnetic microwires

In homogeneous negative phase velocity media, the Doppler and Cherenkov-Vavilov effects and the refraction and pressure of light are anomalous: they are inverse with respect to the corresponding effects in conventional media. Using the geometrical optics approximation, it is shown that the optical Magnus effect in inhomogeneous negative phase velocity media is also anomalous. The effect is demonstrated by considering a metamaterial consisting of parallel amorphous ferromagnetic microwires in a magnetic field. The metamaterial proves to be a left-handed one in the realistic region of the electromagnetic spectrum. The optical properties of such a left-handed medium can be controlled by the external magnetic field.

Non-Abelian evolution of electromagnetic waves in a weakly anisotropic inhomogeneous medium

A theory of electromagnetic wave propagation in a weakly anisotropic smoothly inhomogeneous medium is developed, based on the quantum-mechanical diagonalization procedure applied to Maxwell equations. The equations of motion for the translational (ray) and intrinsic (polarization) degrees of freedom are derived ab initio. The ray equations take into account the optical Magnus effect (spin Hall effect of photons) as well as trajectory variations owing to the medium anisotropy. Polarization evolution is described by the precession equation for the Stokes vector. In the generic case, the evolution of wave turns out to be non-Abelian: it is accompanied by mutual conversion of the normal modes and periodic oscillations of the ray trajectories analogous to electron zitterbewegung. The general theory is applied to examples of wave evolution in media with circular and linear birefringence.

Polarization effects due to the mutual influence of trajectory parameters and polarization

In the geometric optics approximation, we comparatively analyze the polarization effects resulting from the influence of polarization on the beam trajectory. We show that the beam trajectory equations describing the optical Magnus effect that are obtained from the canonical Hamilton equations, Fermat principle, and truncated vector wave equations give the same result, coincident with the result in the mode approach. We explain the reasons underlying the previously derived results.

Fermat principle for spinning light

Mimicking the description of spinning particles in General Relativity, the Fermat Principle is extended to spinning photons. Linearization of the resulting Papapetrou-Souriau type equations yields the semiclassical model used recently to derive the ``Optical Hall Effect'' for polarized light (alias the ``Optical Magnus Effect'').

Topological spin transport of photons: the optical Magnus effect and Berry phase

The Letter develops a modified geometrical optics (GO) of smoothly inhomogeneous isotropic medium, which takes into account two topological phenomena: Berry phase and the optical Magnus effect. Taking into account the correspondence between a quasi-classical motion of a quantum particle with a spin and GO of an electromagnetic wave in smoothly inhomogeneous media, we have introduced the standard gauge potential associated with the degeneracy in the wave momentum space. This potential corresponds to the magnetic-monopole-like field (Berry curvature), which causes the topological spin (polarization) transport of photons. The deviations of waves of right-hand and left-hand polarization occur in the opposite directions and orthogonally to the principal direction of motion. This produces a spin current directed across the principal motion. The situation is similar to the anomalous Hall effect for electrons. In addition, a simple scheme of the experiment allowing one to observe the topological spin splitting of photons has been suggested.

Modified geometrical optics of a smoothly inhomogeneous isotropic medium: the anisotropy, Berry phase, and the optical Magnus effect.

We present a modification of the geometrical optics method, which allows one to properly separate the complex amplitude and the phase of the wave solution. Appling this modification to a smoothly inhomogeneous isotropic medium, we show that in the first geometrical optics approximation the medium is weakly anisotropic. The refractive index, being dependent on the direction of the wave vector, contains the correction, which is proportional to the Berry geometric phase. Two independent eigenmodes of right-hand and left-hand circular polarizations exist in the medium. Their group velocities and phase velocities differ. The difference in the group velocities results in the shift of the rays of different polarizations (the optical Magnus effect). The difference in the phase velocities causes an increase of the Berry phase along with the interference of two modes leading to the familiar Rytov law about the rotation of the polarization plane of a wave. The theory developed suggests that both the optical Magnus effect and the Berry phase are accompanying nonlocal topological effects. In this paper the Hamilton ray equations giving a unified description for both of these phenomena have been derived and also a novel splitting effect for a ray of noncircular polarization has been predicted. Specific examples are also discussed.

Optical magnus effect as a consequence of Berry phase anisotropy

Presented in this work is a modified geometric optics of smoothly inhomogeneous isotropic medium, which takes into account weak anisotropy introduced by inhomogeneity. Pointed out is the common nature of two fundamental phenomena: Berry’s geometrical phase and the optical Magnus effect, that is, propagation of rays of right and left circular polarization along different trajectories. Shown is that the former phenomenon can be explained by the difference in phase velocity of waves of right-hand and left-hand polarizations, while the latter one is the result of the difference in their group velocity. This work demonstrates that the optical Magnus effect is quite a topological effect that exclusively depends on the geometry of the system’s contour in the momentum space. We predict the effect of the splitting of a ray of mixed polarization into two circularly polarized rays and propose a scheme for the experimental observation of this phenomenon.

Inverse optical magnus effect in the Majorana representation

An equation describing the effect of additional bending during photon motion along a twisted path is obtained from Maxwell’s equations in the Majorana representation. The generalized Rytov law in an arbitrary curvilinear system of coordinates forms the basis for the effect. The effect considered is inverse to the optical Magnus effect.