Optical Möbius strips in three dimensional ellipse fields: II. Lines of linear polarization

The minor axes of, and the normals to, the polarization ellipses that surround singular lines of linear polarization in three dimensional optical ellipse fields are shown to be organized into Möbius strips (technically twisted ribbons) and into structures we call “rippled rings” (r-rings). The Möbius strips have two full twists, and can be either right- or left-handed. The major axes of the surrounding ellipses generate cone-like structures. Three orthogonal projections that give rise to 15 indices are used to characterize the different structures These indices, if independent, could generate 839,808 geometrically and topologically distinct lines; selection rules are presented that reduce the number of lines to 8248, some 5562 of which have been observed in a computer simulation. Analytical expressions are presented for 11 of the 15 indices in terms of wavefield parameters; four indices proved to be intractable. Statistical probabilities are presented for the most important index combinations in random fields. It is argued that it is presently feasible to perform experimental measurements of the Möbius strips, r-rings, and cones described here theoretically.     

Polarization singularity proliferation in three-dimensional ellipse fields

The classical singularities of elliptically polarized light are points of circular (linear) polarization, characterized by a half-integer (integer) topological index. On average, in any plane of a random ellipse field there is of the order of one each of these classical singularities per coherence area. It is shown that every ellipse in such a field is a multiple singularity characterized by nine different topological indices: Three indices characterize rotations of the principal axis system of the surrounding ellipses, and six indices characterize a one- or two-turn spiral precession of these axes. The nine indices can divide the field into 32,768 different volumes with different structures separated by singular surfaces (grain boundaries) on which an index becomes undefined. This unprecedented proliferation of singularities and structures can occur in other three-dimensional systems in which individual elements are described by unique principal axis systems, for example, liquid crystals, and should be sought in such systems.     

Quasi-one Dimensional Topological Insulator: Möbius Molecular Devices in Peierls Transition

We show that, assisted by the Peierls transition of lattice, as a quasi-one dimensional (Q1D) tight binding system, a Möbius molecular device can behave as a simple topological insulator. With the Peierls phase transition to form a domain wall, the solitonary zero modes exist as the ground state of this electron-phonon hybrid system, which is protected by the Z₂ topology of the Möbius strip. The robustness of the ground state prevents these degenerate zero modes from their energy spectrum splitting caused by any perturbation.     

Connection between complete and Möbius forms of gauge invariant operators

We study the connection between complete representations of gauge invariant operators and their Möbius representations acting in a limited space of functions. The possibility to restore the complete representations from Möbius forms in the coordinate space is proven and a method of restoration is worked out. The operators for transition from the standard BFKL kernel to the quasi-conformal one are found both in Möbius and total representations.     

Mechanisms and Möbius strips: understanding dynamic processes in annulenes

Exploratory computational studies on annulenes with planar, Möbius, and two‐twist topologies have resulted in new mechanisms to explain facile thermal configuration change (cis‐trans isomerization) for medium‐sized annulenes ([12]‐ to [16]annulene). Möbius π‐bond shifting through both aromatic and antiaromatic transition states, two‐twist π‐bond shifting, and planar nondegenerate π‐bond shifting can all be invoked to explain experimental results. Moreover, a simple bond‐shift rule, which is based on the change in number of trans C?C double bonds (Δtrans), was developed that predicts the topology of the transition state(s) necessary to effect the desired cis‐trans isomerization. The bond‐shift rule was also applied to configuration change in dehydro[12]annulene. Finally, extensive investigation of the [14]annulene hypersurface revealed that numerous Möbius minima exist within 10 kcal/mol of the global minimum. Copyright © 2012 John Wiley & Sons, Ltd.     

Atomistic study of the pressure-induced phase-transition mechanism in GaAs by Möbius inversion potentials

In this work, the phase transition from zincblende (B3) to rocksalt (B1) structure in bulk GaAs is investigated by using Möbius inversion potentials. A Cm transition path is proposed from the molecular static simulation results, even though it is different from previously proposed transition paths Imm2, R3m and P3₂. The present Cm path is quite close to the previously suggested Imm2 path according to the crystal cell geometries and activation enthalpies. By comparison, the activation enthalpies along the R3m and P3₂ path are relative high. Therefore, the Imm2 mechanism, as a simplified model of the Cm one, is suggested to describe the microscopic process of the B3-B1 phase transition of GaAs. In this way, we investigate the changes of the system features during the transition process characterized by Imm2 mechanism and obtain a concise picture for the common B3-B1 transition. All the calculated results are compared to relevant experimental observations and other calculations.     

Dimer statistics of honeycomb lattices on Klein bottle,Möbius strip and cylinder

Dimer statistics is a central problem in statistical physics. In this paper the enumerations of close-packed dimers of honeycomb lattices on Klein bottle, Möbius strip and cylinder are considered. By establishing a Pfaffian orientation or a crossing orientation, and then computing the determinants of the skew-symmetric matrices of the resulting orientation graphs, we obtain explicit expressions of the number of close-packed dimers of the Klein-bottle polyhex, the Möbius polyhex and the cylindrical polyhex.     

Intensity fluctuations and degree of polarization in three-dimensional thermal light fields

The normalized intensity fluctuations of arbitrary electromagnetic wave fields obeying Gaussian statistics are expressed in terms of the three-dimensional degree of polarization. This general formulation implies an important physical result concerning the polarization of planar fields and the dimensionality of the formalism. The results are expected to be particularly useful in intensity interferometry.     

Photoelectron angular distributions of molecules in bichromatic laser fields of circular polarization

Photoelectron angular distributions (PADs) from above-threshold ionization of O₂ and N₂ molecules irradiated by a bichromatic laser field of circular polarization are studied. The bichromatic laser field is specially modulated such that it can be used to mimic a sequence of one-cycle laser pulses. The PADs are greatly affected by the molecular alignment, the symmetry of the initial electronic distribution, and the carrier-envelope phase of the laser pulses. Generally, the PADs do not show any symmetry, and become symmetric about an axis only when the symmetric axis of laser field coincides with the symmetric axis of molecules. This study shows that the few-cycle laser pulses can be used to steer the photoelectrons and perform the selective ionization of molecules.     

Optical spectroscopy in semiconductors in high magnetic fields using polarization modulation

Differential magneto-reflection spectra in the 1.8 to 5 eV energy range are presented for GaP, Ge, GaAs, InSb, and Si. These spectra were obtained using polarization-modulated light from [111] faces of samples in the Faraday configuration. In medium strength magnetic fields, the results are similar to those obtained using other techniques, such as electric field modulation and wavelength derivative spectroscopy in the same energy range. In higher magnetic fields (B of 50 kG or larger) more detailed structure is resolved. Oscillations attributed to Landau level transitions have been seen at critical points in the visible in InSb and in GaSb in fields up to 100 kG. At the E₁ edge an unexpected anomaly has been observed in InSb. Within experimental error, the Landau levels are equally spaced for n < 5 and n > 5 but at n = 5 there is an abrupt change in the cyclotron energy. Here n is the usual magnetic quantum number. The transverse masses are measured as $\text{m}\text{μ}{}_1\text{= 18.9 ± 0.9 (n < 5)}$, and $\text{m}\text{μ}{}_2\text{= 16.0 ± 0.9 (n > 5)}$. Possible causes of this effect are discussed. In GaSb at the corresponding threshold. Landau level observations give a mass value of $\text{m}\text{μt}\text{= 21.4 ± 1.5}$.     

Arbitrary-state solutions of the Dirac equation for a Möbius square potential using the Nikiforov-Uvarov method

We inquire into spin and pseudospin symmetries of the Dirac equation under a Möbius square-type potential using the Nikiforov-Uvarov method to calculate the bound state solutions. We numerically discuss the problem and include various explanatory figures.     

Rotation spectra of the polarization plane and circular dichroism of alkaline atoms in strong radiation fields

For alkalineLi, Na, K, Rb, andCs atoms, the Faraday rotation spectra and other effects of the polarization-plane rotation in strong radiation and magnetic fields are investigated. The spectra are calculated by computer simulation of nonlinear resonance magnetooptical polarization effects for real multilevel atoms. The properties of the spectra of different atoms depend on the relationships between the field and spin-orbital interaction energies. Saratov State Technical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 25–29, May, 1999.     

Rotation of the polarization ellipse under multiple light scattering in disordered media

A study is performed of the multiple small-angle scattering of circularly polarized waves in random media with large-size transparent inhomogeneities that are less dense than the surrounding medium. In these conditions, a new effect is observed—rotation of the polarization ellipse of the multiply scattered light.     

Boundary integral method for calculating displacement fields in three-dimensional viscoelastic piecewise-homogeneous media. I. Fundamental solutions

The boundary integral method is applied to the construction of stationary fields of elastic displacements in three-dimensional viscoelastic media, consisting of homogeneous regions with curvilinear separation boundaries. As fundamental solutions we use the sum of solutions describing converging and diverging waves. It is shown that for a such selected fundamental solution it is possible to satisfy the boundary and radiation conditions of waves at infinity.Institute of Geophysics, Siberian Branch, Russian Academy of Sciences. Translated from Izvestiya Vyssikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 76–81, July, 1994.     

Pseudospin symmetry of the Dirac equation for a Möbius squareplus Mie type potential with a Coulomb-like tensor interaction via SUSYQM

We investigate the approximate solution of the Dirac equation for a combination of Möbius square and Mie type potentials under the pseudospin symmetry limit by using supersymmetry quantum mechanics. We obtain the bound-state energy equation and the corresponding spinor wave functions in an approximate analytical manner. We comment on the system via various useful figures and tables.     

Multiphoton ionization in dielectrics: comparison of circular and linear polarization

Ionization mechanisms in bulk dielectrics irradiated by single intense 50-fs-laser pulses are investigated by ultrafast time-resolved imaging interferometry. Polarization-sensitive 6-photon ionization is shown to be the dominant ionization mechanism in fused silica and sapphire at intensities around 10 TW/cm2. For both materials the cross sections of 6-photon ionization are found to be significantly higher for linear polarization than for circular. Our experimental results corroborate an earlier theoretical prediction on the dominance of linear polarization in high-order multiphoton ionization.