Transverse Angular Momentum Research Articles

Extraordinary spin density and energy back-flow under interference.

A novel phenomenon was reported recently that the "local optical spin density" based on the Poynting vector might be counter-intuitively opposite to the integrated spin orientation while the one related to the gauge-invariant canonical expression might not [Phys. Lett. B779, 385 (2018)]. However, the "local optical spin density" of the gauge-invariant canonical expression can also be counter-intuitively opposite to the integrated spin orientation under the interference of plane waves, even if all of the plane waves possess the same polarization state. Moreover, the interference fields might acquire a transverse spin density (perpendicular to the propagation plane), which can have more well-controlled relations with the polarization. Additionally, the Poynting vector shows counter-intuitive back-flow and a circular motion (vortex) in the propagation plane locally, which implies a transverse local "orbital" angular momentum density related to the polarization.

Mathematical modelling of pressure-driven micropolar biological flow due to metachronal wave propulsion of beating cilia

In this paper, we present an analytical study of pressure-driven flow of micropolar non-Newtonian physiological fluids through a channel comprising two parallel oscillating walls. The cilia are arranged at equal intervals and protrude normally from both walls of the infinitely long channel. A metachronal wave is generated due to natural beating of cilia and the direction of wave propagation is parallel to the direction of fluid flow. Appropriate expressions are presented for deformation via longitudinal and transverse velocity components induced by the ciliary beating phenomenon with cilia assumed to follow elliptic trajectories. The conservation equations for mass, longitudinal and transverse (linear) momentum and angular momentum are reduced in accordance with the long wavelength and creeping Stokesian flow approximations and then normalized with appropriate transformations. The resulting non-linear moving boundary value problem is solved analytically for constant micro-inertia density, subject to physically realistic boundary conditions. Closed-form expressions are derived for axial velocity, angular velocity, volumetric flow rate and pressure rise. The transport phenomena are shown to be dictated by several non-Newtonian parameters, including micropolar material parameter and Eringen coupling parameter, and also several geometric parameters, viz eccentricity parameter, wave number and cilia length. The influence of these parameters on streamline profiles (with a view to addressing trapping features via bolus formation and evolution), pressure gradient and other characteristics are evaluated graphically. Both axial and angular velocities are observed to be substantially modified with both micropolar rheological parameters and furthermore are significantly altered with increasing volumetric flow rate. Free pumping is also examined. An inverse relationship between pressure rise and flow rate is computed which is similar to that observed in Newtonian fluids. The study is relevant to hemodynamics in narrow capillaries and also bio-inspired micro-fluidic devices.

Transverse angular momentum in topological photonic crystals

Engineering local angular momentum of structured light fields in real space enables applications in many fields, in particular, the realization of unidirectional robust transport in topological photonic crystals with a non-trivial Berry vortex in momentum space. Here, we show transverse angular momentum modes in silicon topological photonic crystals when considering transverse electric polarization. Excited by a chiral external source with either transverse spin angular momentum or transverse phase vortex, robust light flow propagating along opposite directions is observed in several kinds of sharp-turn interfaces between two topologically-distinct silicon photonic crystals. A transverse orbital angular momentum mode with alternating phase vortex exists at the boundary of two such photonic crystals. In addition, unidirectional transport is robust to the working frequency even when the ring size or location of the pseudo-spin source varies in a certain range, leading to the superiority of the broadband photonic device. These findings enable one to make use of transverse angular momentum, a kind of degree of freedom, to achieve unidirectional robust transport in the telecom region and other potential applications in integrated photonic circuits, such as on-chip robust delay lines.

Time correlation functions in the Lebwohl-Lasher model of liquid crystals.

Time correlation functions in the Lebwohl-Lasher model of nematic liquid crystals are studied using theory and molecular dynamics simulations. In particular, the autocorrelation functions of angular momentum and nematic director fluctuations are calculated in the long-wavelength limit. The constitutive relations for the hydrodynamic currents are derived using a standard procedure based on non-negativity of the entropy production. The continuity equations are then linearized and solved to calculate the correlation functions. We find that the transverse angular momentum fluctuations are coupled to the director fluctuations and are both propagative. The propagative nature of the fluctuations suppresses the anticipated hydrodynamic long-time tails in the single-particle autocorrelation functions. The fluctuations in the isotropic phase are, however, diffusive, leading to t^{-d/2} long-time tails in d spatial dimensions. The Frank elastic constant measured using the time correlation functions are in good agreement with previously reported results.

Energy flux density and angular momentum density of radial Pearcey-Gauss vortex array beams in the far field

The longitudinal and transverse energy flux density (EFD) and angular momentum density (AMD) of the radial Pearcey-Gauss vortex array beams are studied by using the vector angular spectrum representation and stationary phase method, where the influence of topological charge, initial phase index, noncanonical strength and the number of beamlet on far-field vectorial structures of the corresponding beam is emphasized. The results show that the topological charge of center optical vortex is always equal to initial phase index for different noncanonical strength. The longitudinal EFDs exhibit different structures by varying initial phase index and the number of beamlet. For an odd-N, the topological charge of center optical vortex can be determined by distinguishing the longitudinal EFD, however for an even-N the topological charge cannot be identified due to the equivalence of longitudinal EFD in the case of positive and negative initial phase index m. The AMD tends to split more branches from the positive and negative direction with increasing the absolute value of topological charge l, The inner structures of AMD are also affected by different beamlets while the zero value of AMD is always retained.

Energy flux density and angular momentum density of Pearcey-Gauss vortex beams in the far field

The longitudinal and transverse energy flux density (EFD) and angular momentum density (AMD) of a Pearcey–Gauss vortex beam in the far field are studied using the vector angular spectrum representation and stationary phase method, where the influence of topological charge, noncanonical strength and off-axis distance of the embedded optical vortex on far-field vectorial structures of the corresponding beam is emphasized. For comparison, the EFD and AMD of the Pearcey–Gauss beam with non-vortex in the far field are also discussed. The results show that the longitudinal EFDs of the Pearcey–Gauss vortex beam exhibit parabolic patterns, and the number of parabolic dark zones equals the absolute value of topological charge of the embedded optical vortex in the input plane. While for the Pearcey–Gauss beam, the dark zones are not found owing to the non-vortex in the input plane. The motion of zero-intensity spot of whole beam appears by varying the off-axis distance. Noncanonical strength and off-axis distance both can adjust the magnitudes and directions of transverse EFD and control the spatial energy distributions of longitudinal EFD, but not change the net AMD.

Linear and angular momenta in tightly focused vortex segmented beams of light (Invited Paper)

We investigate the linear momentum density of light, which can be decomposed into spin and orbital parts, in the complex three-dimensional field distributions of tightly focused vortex segmented beams. The chosen angular spectrum exhibits two spatially separated vortices of opposite charge and orthogonal circular polarization to generate phase vortices in a meridional plane of observation. In the vicinity of those vortices, regions of negative orbital linear momentum occur. Besides these phase vortices, the occurrence of transverse orbital angular momentum manifests in a vortex charge-dependent relative shift of the energy density and linear momentum density.

Transverse multipolar light-matter couplings in evanescent waves

We present an approach to study the interaction between matter and evanescent fields. The approach is based on the decomposition of evanescent plane waves into multipoles of well-defined angular momentum transverse to both decay and propagation directions. We use the approach to identify the origin of the recently observed directional coupling of emitters into guided modes, and of the opposite Zeeman state excitation of atoms near a fiber. We explain how to rigorously quantify both effects, and show that the directionality and the difference in excitation rates grow exponentially with the multipolar order of the light-matter interaction. We also use the approach to study and maximize the transverse torque exerted by an evanescent plane wave onto a given spherical absorbing particle. The maximum occurs at the quadrupolar order of the particle, and for a particular polarization of the plane wave. All the obtained physical insights can be traced back to the two main features of the decomposition of evanescent plane waves into transverse multipolar modes: A polarization independent exponential dominance of modes with large transverse angular momentum, and a polarization controlled parity selection rule.

Cavity modes with optical orbital angular momentum in a metamaterial ring based on transformation optics

In this work, we theoretically study the cavity modes with transverse orbital angular momentum in metamaterial ring based on transformation optics. The metamaterial ring is designed to transform the straight trajectory of light into the circulating one by enlarging the azimuthal angle, effectively presenting the modes with transverse orbital angular momentum. The simulation results confirm the theoretical predictions, which state that the transverse orbital angular momentum of the mode not only depends on the frequency of the incident light, but also depends on the transformation scale of the azimuthal angle. Because energy dissipation inevitably reduces the field amplitude of the modes, the confined electromagnetic energy and the quality factor of the modes inside the ring are also studied in order to evaluate the stability of those cavity modes. The results show that the metamaterial ring can effectively confine light with a high quality factor and maintain steady modes with the orbital angular momentum, even if the dimension of the ring is much smaller than the wavelength of the incident light. This technique for exploiting the modes with optical transverse orbital angular momentum may provides a unique platform for applications related to micromanipulation.

From transverse angular momentum to photonic wheels

This Progress Article details the latest achievements and underlying principles of light carrying transverse spin.The capabilities and future applications of this young yet already advanced field are highlighted. Scientists have known for more than a century that light possesses both linear and angular momenta along the direction of propagation. However, only recent advances in optics have led to the notion of spinning electromagnetic fields capable of carrying angular momenta transverse to the direction of motion. Such fields enable numerous applications in nano-optics, biosensing and near-field microscopy, including three-dimensional control over atoms, molecules and nanostructures, and allowing for the realization of chiral nanophotonic interfaces and plasmonic devices. Here, we report on recent developments of optics with light carrying transverse spin. We present both the underlying principles and the latest achievements, and also highlight new capabilities and future applications emerging from this young yet already advanced field of research.

Testing noncontextuality inequalities that are building blocks of quantum correlations

Measurement scenarios containing events with relations of exclusivity represented by pentagons, heptagons, nonagons, etc., or their complements are the only ones in which quantum probabilities cannot be described classically. Interestingly, quantum theory predicts that the maximum values for any of these graphs cannot be achieved in Bell inequality scenarios. With the exception of the pentagon, this prediction remained experimentally unexplored. Here we test the quantum maxima for the heptagon and the complement of the heptagon using three- and five-dimensional quantum states, respectively. In both cases, we adopt two different encodings: linear transverse momentum and orbital angular momentum of single photons. Our results exclude maximally noncontextual hidden-variable theories and are in good agreement with the maxima predicted by quantum theory.

Rutherford scattering of electron vortices

By considering a cylindrically symmetric generalization of a plane wave, the first Born approximation of screened Coulomb scattering unfolds two new dimensions in the scattering problem: transverse momentum and orbital angular momentum of the incoming beam. In this paper, the elastic Coulomb scattering amplitude is calculated analytically for incoming Bessel beams. This reveals novel features occurring for wide angle scattering when the incoming beam is correctly prepared. The result successfully generalizes the well known Rutherford formula, incorporating transverse and orbital angular momentum into the formalism.

Transverse angular momentum and transverse barycenter shift of a focused light field due to nonuniform input angular momentum

We calculate the spin, intrinsic and extrinsic orbital angular momenta, as well as the barycenter of the focal field after a high-NA lens and find that, when the input beam is with nonuniform angular momentum (AM), the focal field carries both longitudinal and transverse parts of AM and the barycenter of the field has a transverse shift owing to the spin and orbital Hall effect of light. When one half of the input beam possesses spin and orbital AM, σ and l, and the other half with -σ and -l, a pure transverse AM is generated in the focal field, accompanying a shift of the field barycenter in the transverse plane that depends on σ and l.

Geometric spin Hall effect of light in tightly focused polarization-tailored light beams

Recently, it was shown that a nonzero transverse angular momentum manifests itself in a polarization-dependent intensity shift of the barycenter of a paraxial light beam [Aiello et al., Phys. Rev. Lett. 103, 100401 (2009)]. The underlying effect is phenomenologically similar to the spin Hall effect of light but does not depend on the specific light-matter interaction and can be interpreted as a purely geometric effect. Thus, it was named the geometric spin Hall effect of light. Here, we experimentally investigate the appearance of this effect in tightly focused vector beams. We use an experimental nanoprobing technique in combination with a reconstruction algorithm to verify the relative shifts of the components of the electric energy density and the shift of the intensity in the focal plane. By that, we experimentally demonstrate the geometric spin Hall effect of light in a highly nonparaxial beam.

Integrated multi vector vortex beam generator

A novel method to generate and manipulate vector vortex beams in an integrated, ring resonator based geometry is proposed. We show numerically that a ring resonator, with an appropriate grating, addressed by a vertically displaced access waveguide emits a complex optical field. The emitted beam possesses a specific polarization topology, and consequently a transverse intensity profile and orbital angular momentum. We propose a combination of several concentric ring resonators, addressed with different bus guides, to generate arbitrary orbital angular momentum qudit states, which could potentially be used for classical and quantum communications. Finally, we demonstrate numerically that this device works as an orbital angular momentum sorter with an average cross-talk of -10dB between different orbital angular momentum channels.

The photonic wheel - demonstration of a state of light with purely transverse angular momentum

In classical mechanics, a system may possess angular momentum which can be either transverse (e.g. in a spinning wheel) or longitudinal (e.g. for a spiraling seed falling from a tree) with respect to the direction of motion. However, for light, a typical massless wave system, the situation is less versatile. Photons are well-known to exhibit intrinsic angular momentum which is longitudinal only: the spin angular momentum defining the polarization and the orbital angular momentum associated with a spiraling phase front. Here we show that it is possible to generate a novel state of the light field that contains purely transverse angular momentum, the analogue of a spinning mechanical wheel. We realize this state by tight focusing of a polarization tailored light beam and measure it using an optical nano-probing technique. Such a novel state of the light field can find applications in optical tweezers and spanners where it allows for additional rotational degree of freedom not achievable in single-beam configurations so far.

New relation between transverse angular momentum and generalized parton distributions

I derive a rigorous relation between the expectation value of the transverse component of the Belinfante version of the angular momentum $⟨{J}_{T}^{\mathrm{bel}}⟩$ of a quark in a transversely polarized nucleon in terms of the generalized parton distributions $H$ and $E$, namely $⟨{J}_{T}^{\mathrm{bel}}(\mathrm{\text{quark}})⟩=[1/2M][{P}_{0}{\ensuremath{\int}}_{\ensuremath{-}1}^{1}dxx{E}_{q}(x,0,0)+M{\ensuremath{\int}}_{\ensuremath{-}1}^{1}dxx{H}_{q}(x,0,0)]$, where ${P}_{0}$ is the energy of the nucleon and where quark implies the sum of quark and antiquark of a given flavor. A similar relation holds for gluons. The result is remarkably similar to Ji's relation for the case of longitudinal polarization, whose content I spell out precisely, and which has proved extremely interesting in testing models, in comparing different definitions of quark and gluon angular momentum, and in comparing with lattice calculations. The transverse relation can offer additional insights into all of these, by extending them to the new domain of transversely polarized and moving nucleons.

Transverse angular momentum of photons

We develop the quantum theory of transverse angular momentum of light beams. The theory applies to paraxial and quasiparaxial photon beams in vacuum and reproduces the known results for classical beams when applied to coherent states of the field. Both the Poynting vector, alias the linear momentum, and the angular-momentum quantum operators of a light beam are calculated including contributions from first-order transverse derivatives. This permits a correct description of the energy flow in the beam and the natural emergence of both the spin and the angular momentum of the photons. We show that for collimated beams of light, orbital angular-momentum operators do not satisfy the standard commutation rules. Finally, we discuss the application of our theory to some concrete cases.

Transverse Angular Momentum and Geometric Spin Hall Effect of Light

We present a novel fundamental phenomenon occurring when a polarized beam of light is observed from a reference frame tilted with respect to the direction of propagation of the beam. This effect has a purely geometric nature and amounts to a polarization-dependent shift or split of the beam intensity distribution evaluated as the time-averaged flux of the Poynting vector across the plane of observation. We demonstrate that such a shift is unavoidable whenever the beam possesses a nonzero transverse angular momentum. This latter result has general validity and applies to arbitrary systems such as, e.g., electronic and atomic beams.

Coordination of leg swing, thorax rotations, and pelvis rotations during gait: The organisation of total body angular momentum

In walking faster than 3 km/h, transverse pelvic rotation lengthens the step (“pelvic step”). It is often assumed that the thorax then starts to counter rotate to limit total body angular momentum around the vertical. But the relative timing of pelvis and thorax rotation during gait is insufficiently understood. The present study aimed at analysing how transverse pelvis and thorax rotations relate to the movements of the upper leg, and how these patterns contribute to total body angular momentum. Nine healthy male volunteers walked on a treadmill at nine different velocities, ranging from 2.0 km/h to 5.2 km/h. Full body kinematics were recorded. Femur–pelvis, pelvis–thorax, and femur–thorax relative phase were calculated, as well as transverse plane angular momentum of all body segments. The shift in pelvis–thorax coordination from in-phase to out of phase with increasing velocity was found to depend on the pelvis beginning to move in-phase with the femur, while the thorax continued to counter rotate with respect to the femur. Moreover, pelvic and thoracic contributions to total body angular momentum were low (less than 10%), while contributions of the legs and arms were much larger (approximately 90%), suggesting that pelvis–thorax coordination is relatively unimportant to the organisation of total body angular momentum. Taken together, these results may imply that our understanding of the pelvic step need to be changed. Moreover, the alterations in pelvis–thorax relative phase that were reported for different locomotor pathologies may depend on different mechanisms.