Angular momentum of the fields of a few-mode fiber. III. Optical Magnus effect, Berry phase, and topological birefringence

It is shown that, on the one hand, the evolution of the angular rotation of the lines of nodes of the CP₁₁ mode is a manifestation of the optical Magnus effect in a few-mode fiber with a parabolic refractive index profile, and, on the other hand, the additional phase γ _b =±δβ ₂₁ z in CV and IV vortices is the Berry topological phase, which arises as a result of the cyclic change in the orientations of the orthogonal axes of dislocations. The splitting of the propagation velocities of orthogonal circularly polarized CV⁺ and IV⁻ modes in an LV vortex in a parabolic fiber is a manifestation of the phenomenon of topological birefringence of a few-mode fiber. The azimuth of the linear polarization of a vortex undergoes continuous angular rotation. In an optical fiber with a stepped index profile the CP₁₁ mode forms circularly polarized edge dislocation over lengths which are multiples of half the beat length, and over lengths which are odd multiples of the quarter beat length it forms linearly polarized fields with a purely screw dislocation. This transformation of edge and screw dislocations can be regarded formally as conversion of the polarizational angular momentum into orbital angular momentum. The conversion of angular momentum is a reflection of the dynamical unity of the optical Magnus effect and the Berry topological phase in the fields of a few-mode fiber. Pis’ma Zh. Tekh. Fiz. 23, 59–67 (December 12, 1997)     

Angular momentum of the fields of a few-mode waveguide: Conversion of the angular momentum

An analysis is made of the transformation of the angular momentum density in the field of an unstable IV vortex of a few-mode optical fiber. It is shown that the effect of mode dispersion of IV vortices is observed as the conversion of the polarization and orbital components of the electrodynamic angular momentum. The angular momentum defect may be recorded experimentally as a mechanical twist of the optical few-mode fiber. Formally the dispersion process resembles the conversion of the signs of the orbital and polarization components of the angular momentum density. A complex pseudopotential, whose real and imaginary parts characterize the field lines and lines of equal pseudopotential, is introduced to describe the energy flux density of the fiber vortex. The conversion of field states with equivalent partial ê ⁺ F ₁(R)exp{−iφ} and ê2⁻ F ₁(R)exp{+iφ} vortices was investigated experimentally. Pis#x2019;ma Zh. Tekh. Fiz. 23, 58–65 (November 26, 1997)     

Dynamics of field dislocations and disclinations in a few-mode fiber. IV. Formation of an optical vortex

The physical mechanisms responsible for the formation of an optical vortex in the field of a few-mode fiber have been investigated experimentally and theoretically. In an optical fiber with a parabolic refractive index profile an optical vortex is formed as a result of interaction between circularly polarized rotating pure edge dislocations of circularly polarized even and odd CP₁₁ modes. In a stepped-index fiber the formation of an optical vortex is also related to the simultaneous propagation of even and odd modes. The fields of these modes alter their structure over the fiber length and are not manifested by rotating edge dislocations. It has been found experimentally that a stable vortex does not alter its degree of polarization of the field at fiber lengths greater than 10 m. An unstable vortex, for which the product of the spin and the topological charge is always less than zero, periodically decays and recovers at a beat length of 0.65 m. It is noted that a stable optical vortex cannot be formed by orthogonally polarized LP₁₁ modes. This is because an optical vortex transfers additional angular momentum like the CP₁₁ modes whereas the LP₁₁ modes do not transfer additional angular momentum of the field. Pis’ma Zh. Tekh. Fiz. 23, 70–75 (March 12, 1997)     

Vortex optical Magnus effect in multimode fibers

A theoretical and experimental analysis is made of the optical Magnus effect in multimode optical fibers excited by a laser beam whose wavefront has a pure screw dislocation and carries the topological charge ±l, where l is the azimuthal quantum number. It is found that the angular rotation of the plane of propagation of a local wave depends on the magnitude and sign of the topological charge and changes qualitatively when the circulation of the polarization is reversed. The phase mechanism is attributed to spin-orbit interaction in the photon ensemble. It is demonstrated experimentally that the optical Magnus effect in a few-mode fiber for the CP₁₁ mode at the beat length is observed as a rotation of the axis of the pure edge dislocation field through an angle proportional to the beat length. Pis’ma Zh. Tekh. Fiz. 23, 76–81 (August 26, 1997)     

Rotation of the wavefront of an optical vortex in free space

It is shown experimentally and theoretically that when an optical vortex propagates in free space, its wavefront rotates through an angle numerically equal to the Gouy phase. It is found that both the energy maximum of the optical vortex light flux and the amplitude zero of the perturbed optical vortex field propagate along the ray surface. It is shown that the ray surface, which is a consequence of the relativistic constraints on the beam group velocity, forms an unparted hyperboloid of revolution and has various properties: 1) the circulation of the Poynting vector on the surface does not depend on the longitudinal coordinate z; 2) the evolution of the light flux and a pure screw dislocation takes place along straight lines of this surface; 3) the Poynting vector on the ray surface is always perpendicular to the wavefront surface. Pis’ma Zh. Tekh. Fiz. 25, 87–94 (March 12, 1999)     

Dynamics of dislocations and disclinations of the field of a few-order optical fiber: I. Creation and annihilation of C ± disclinations

It is shown experimentally and theoretically that the interconversion dynamics of the field of the LP₁₁ mode combination of a few-mode optical fiber is determined by the interaction of circularly polarized pure edge C ⁺ and C ⁻ disclinations. The C ⁺ and C ⁻ disclinations correspond to characteristics of the field for which the right-or left-circularly polarized electric field goes to zero. During propagation the uniformly linear-polarized dislocations D _y break down into four C ⁺ disclinations travelling in opposite senses. When each pair of C ⁻ and C ⁺ disclinations meet they annihilate each other and form linear polarization. The field of the linearly polarized disclinations thus created sums up out of phase into the original field and forms a uniformly linearly polarized field with D _x dislocations. Pis’ma Zh. Tekh. Fiz. 23, 20–27 (January 26, 1997)     

On the quantum core of an optical vortex

An optical vortex is a line around which the phase increases by an integer multiple of 2π. It follows that the phase on the line itself is undefined and hence the field must have zero amplitude there. Berry and Dennis have suggested that this line of darkness is smoothed by a ‘quantum core’ with a radius proportional to ?^1/2 and have illustrated this idea by considering the competition between stimulated and spontaneous emission by an excited atom placed in the vicinity of the vortex. We show here that a similar phenomenon may be seen in absorption when the quantum state of motion of the absorbing atom is taken into consideration. There is, however, an underlying quantum singularity in which the absorption events for an atom centred on the vortex core can take place only if accompanied by a transfer of angular momentum to the atomic motion. The nature of this singularity relies on the evolution of an entangled state between the electronic and motional degrees of freedom of the trapped atom. We comment briefly on the effects of field quantisation on this quantum core of the optical vortex.     

A Single Noninterleaved Metasurface for High-Capacity and Flexible Mode Multiplexing of Higher-Order Poincaré Sphere Beams

Cylindrical vector vortex beams, a particular class of higher-order Poincaré sphere beams, are generalized forms of waves carrying orbital angular momentum with inhomogeneous states-of-polarization on their wavefronts. Conventional methods as well as the more recently proposed segmented/interleaved shared-aperture metasurfaces for vortex beam generation are either severely limited by bulky optical setups or by restricted channel capacity with low efficiency and mode number. Here, a noninterleaved vortex multiplexing approach is proposed, which utilizes superimposed scattered waves with opposite spin states emanating from all meta-atoms in a coherent manner, counter-intuitively enabling ultrahigh-capacity, high-efficiency, and flexible generation of massive vortex beams with structured state-of-polarization. A series of exemplary prototypes, implemented by sub-wavelength-thick metasurfaces, are demonstrated experimentally, achieving kaleidoscopic vector vortex beams. This methodology holds great promise for structured wavefront shaping, vortex generation, and high information-capacity planar photonics, which may have a profound impact on transformative technological advances in fields including spin-Hall photonics, optical holography, compressive imaging, electromagnetic communication, and so on.     

11B NMR Study of Pure and Lightly Carbon-Doped MgB2 Superconductors

We report a¹¹B NMR line shape and spin-lattice relaxation rate (1/(T ₁ T)) study of pure and lightly carbon-doped MgB_2−x C _x forx=0, 0.02, and 0.04, in the vortex state and in magnetic field of 23.5 kOe. We show that while pure MgB₂ exhibits the magnetic field distribution from superposition of the normal and the Abrikosov state, slight replacement of boron with carbon unveils the magnetic field distribution of the pure Abrikosov state. This indicates a considerable increase ofH _c ^2/c with carbon doping with respect to pure MgB₂. The spin-lattice relaxation rate 1/(T ₁ T) demonstrates clearly the presence of a coherence peak right belowT _c in pure MgB₂, followed by a typical BCS decrease on cooling. However, at temperatures lower than ≈10 K strong deviation from the BCS behavior is observed, probably from residual contribution of the vortex dynamics. In the carbon-doped systems both the coherence peak and the BCS temperature dependence of 1/(T ₁ T) weaken, an effect attributed to the gradual shrinking of the σ hole cylinders of the Fermi surface with electron doping.     

Commutation Rules and Eigenvalues of Spin and Orbital Angular Momentum of Radiation Fields

Abstract

We investigate the separation of the total angular momentum J of the electromagnetic field into a ‘spin’ part S and an ‘orbital’ part L. We show that both ‘spin’ and ‘orbital’ angular momentum are observables. However, the transversality of the radiation field affects the commutation relations for the associated quantum operators. This implies that neither S nor L are angular momentum operators. Moreover their eigenvalues are not discrete. We construct field modes such that each mode excitation (photon) is in a simultaneous eigenstate of S _z and L _z. We consider the interaction of such a photon with an atom and the resulting effect on the internal and external part of the atomic angular momentum.     

Self-consistent calculation of the longitudinal NMR for the Balian-Werthamer and Anderson-Brinkman-Morel states of superfluid3He

The general equations of motion for the Green's functions and correlation functions and the associated conservation laws for an anisotropic superfluid are derived. This leads to a simple commutator relation for the total angular momentum of the system and thep-wave pair amplitude. The longitudinal NMR frequencies for both the Balian-Werthamer (BW) and Anderson-Brinkman-Morel (ABM) states are calculated rigorously within the self-consistent random phase approximation scheme, taking account of all the degrees of freedom of the complex fluctuations of the order parameter (18 components) and their couplings via the dipole interactions. The results for the low-frequency resonances (ω?Δ) are in agreement with those of Leggett except in the vicinity ofT _c. In addition, in the presence of the dipole interaction, we find longitudinal resonances at ω=(8/5)^1/2Δ and ω=2^1/2Δ for the BW and ABM states, respectively.     

11B NMR Study of Pure and Lightly Carbon-Doped MgB2 Superconductors

We report a ¹¹B NMR line shape and spin-lattice relaxation rate (1/(T₁T))(1/(T_1T)) study of pure and lightly carbon-doped MgB_2-xC_x_{2-x}{\rm C}_x for x = 0,0.02x = 0,0.02, and 0.04, in the vortex state and in magnetic field of 23.5 kOe. We show that while pure MgB₂_2 exhibits the magnetic field distribution from superposition of the normal and the Abrikosov state, slight replacement of boron with carbon unveils the magnetic field distribution of the pure Abrikosov state. This indicates a considerable increase of H^c_c2H^c_{c2} with carbon doping with respect to pure MgB₂_2. The spin-lattice relaxation rate 1/(T₁T)1/(T_1T) demonstrates clearly the presence of a coherence peak right below T_cT_{\rm c} in pure MgB₂_2, followed by a typical BCS decrease on cooling. However, at temperatures lower than ?\approx 10 K strong deviation from the BCS behavior is observed, probably from residual contribution of the vortex dynamics. In the carbon-doped systems both the coherence peak and the BCS temperature dependence of 1/(T₁T)1/(T_1T) weaken, an effect attributed to the gradual shrinking of the σ hole cylinders of the Fermi surface with electron doping.     

Implementing torsional-mode Doppler ladar

Laguerre-Gaussian laser modes carry orbital angular momentum as a consequence of their helical-phase front screw dislocation. This torsional beam structure interacts with rotating targets, changing the orbital angular momentum (azimuthal Doppler) of the scattered beam because angular momentum is a conserved quantity. I show how to measure this change independently from the usual longitudinal momentum (normal Doppler shift) and derive the apropos coherent mixing efficiencies for monostatic, truncated Laguerre and Gaussian-mode ladar antenna patterns.     

Surface force spectroscopic point load measurements and viscoelastic modelling of the micromechanical properties of air flow sensitive hairs of a spider (Cupiennius salei)

The micromechanical properties of spider air flow hair sensilla (trichobothria) were characterized with nanometre resolution using surface force spectroscopy (SFS) under conditions of different constant deflection angular velocities (rad s⁻¹) for hairs 900–950 μm long prior to shortening for measurement purposes. In the range of angular velocities examined (4×10⁻⁴−2.6×10⁻¹ rad s⁻¹), the torque T (Nm) resisting hair motion and its time rate of change (Nm s⁻¹) were found to vary with deflection velocity according to power functions. In this range of angular velocities, the motion of the hair is most accurately captured by a three-parameter solid model, which numerically describes the properties of the hair suspension. A fit of the three-parameter model (3p) to the experimental data yielded the two torsional restoring parameters, S _3p=2.91×10⁻¹¹ Nm rad⁻¹ and =2.77×10⁻¹¹ Nm rad⁻¹ and the damping parameter R _3p=1.46×10⁻¹² Nm s rad⁻¹. For angular velocities larger than 0.05 rad s⁻¹, which are common under natural conditions, a more accurate angular momentum equation was found to be given by a two-parameter Kelvin solid model. For this case, the multiple regression fit yielded S _2p=4.89×10⁻¹¹ Nm rad⁻¹ and R _2p=2.83×10⁻¹⁴ Nm s rad⁻¹ for the model parameters. While the two-parameter model has been used extensively in earlier work primarily at high hair angular velocities, to correctly capture the motion of the hair at both low and high angular velocities it is necessary to employ the three-parameter model. It is suggested that the viscoelastic mechanical properties of the hair suspension work to promote the phasic response behaviour of the sensilla.     

Determination of the chemical diffusion coefficient of lithium in Li3V2(PO4)3

The chemical diffusion of lithium ion in Li₃V₂(PO₄)₃ were investigated by cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS) methods. The CV results show that there exists a linear relationship between the peak current (i_p) and the square root of the scan rate (ν^1/2). The impedance spectrum exhibits a single semicircle and a straight line in a very low frequency region. A linear behavior was observed for every curve of the real resistance as a function of the inverse square root of the angular frequency in a very low frequency region. The obtained chemical diffusion coefficient from EIS measurements varies within 10^− 9 to 10^− 8 cm²·s^− 1, in good agreement with those from CV results.     

Vortex Mutual Friction in Superfluid 3He

We give a full account of our extensive measurements of vortex mutual friction in rotating superfluid ³He, in both the A- and B-phases. The B-phase results are in qualitative agreement with a theory based on the concept of “spectral flow”; the agreement becomes quantitative if an effective energy gap of 0.63 Δ is used, but the Justification for such a substitution is not clear. The vortex core transition, at first not seen because of metastability and hysteresis, has now been observed. Detailed investigation suggests that the high temperature vortex state is a temperature dependent mixture of at least two vortex types. The A-phase mutual friction is found to be well described by two hydrodynamic coefficients, the orbital viscosity and the orbital inertia. The latter corresponds to an orbital angular momentum per Cooper pair of (0.0015 ± 0.0017 ) ħ, consistent with the prediction of the spectral flow theory. We find that the most uniform l texture is obtained by cooling through T_c while rotating, and then stopping rotation. Detailed investigation of textural memory effects shows that the uniform l-up and l-down textures are associated with opposite directions of rotation. We discuss the various types of texture that may be formed in our experiments. Finally, we compare our mutual friction results with those found in ⁴HeII.     

Engineering Co2MnAlxSi1−x Heusler Compounds as a Model System to Correlate Spin Polarization,Intrinsic Gilbert Damping,and Ultrafast Demagnetization

Engineering of magnetic materials for developing better spintronic applications relies on the control of two key parameters: the spin polarization and the Gilbert damping, responsible for the spin angular momentum dissipation. Both of them are expected to affect the ultrafast magnetization dynamics occurring on the femtosecond timescale. Here, engineered Co₂MnAl_xSi_1-x Heusler compounds are used to adjust the degree of spin polarization at the Fermi energy, P, from 60% to 100% and to investigate how they correlate with the damping. It is experimentally demonstrated that the damping decreases when increasing the spin polarization from 1.1 × 10⁻³ for Co₂MnAl with 63% spin polarization to an ultralow value of 4.6 × 10⁻⁴ for the half-metallic ferromagnet Co₂MnSi. This allows the investigation of the relation between these two parameters and the ultrafast demagnetization time characterizing the loss of magnetization occurring after femtosecond laser pulse excitation. The demagnetization time is observed to be inversely proportional to 1 – P and, as a consequence, to the magnetic damping, which can be attributed to the similarity of the spin angular momentum dissipation processes responsible for these two effects. Altogether, the high-quality Heusler compounds allow control over the band structure and therefore the channel for spin angular momentum dissipation.     

Above threshold dissociation in HD+ using frequency chirped laser pulses

We have theoretically studied the dynamics of above threshold dissociation (ATD) in molecular ions HD⁺ using frequency chirped femtosecond laser pulses from numerical solutions of the time-dependent Schrödinger equation by using the three-dimensional time-dependent quantum wave packet method. Energy-dependent distributions of ATD fragments are analyzed by an asymptotic-flow expression in momentum space. Linearly positive and negative frequency chirped laser pulses are adopted. It is found that varying frequency chirped parameters can change branching ratios of the 1sσ _g and 2pσ _u dissociations channels. The concept of a light-induced potential is used to interpret the ATD process. The angular resolved energy distributions of the photofragments are also illustrated.     

Frequency Response of AC Susceptibility in Melt Textured YBCO Superconductors

We have reviewed the scaling relations for frequency dependent AC susceptibility proposed by Lee. et al. and other contributions. Based on vortex glass analysis, we derived a scaling equation for the peak temperature of the imaginary part and ac magnetic field frequency f. The peak temperature T_p is found to obey: T_p = Cf^1/(v(z–1))+T_g, where C is a constant, and T_g is the vortex glass temperature. The scaling relationship was applied to our melt textured YBCO superconductors, which was found in good agreement with the experimental data.