Difference of natural waves determined in the modern and previous theories of natural gyrotropy of crystals

On the basis of exact numerical calculations, the difference of parameters of natural waves determined in the contemporary and previous theories of gyrotropy is determined. It is found that the differences correspond to the limit and, for the majority of commonly used crystals, are beyond the limits of the practically accessible accuracy of the measurement of natural-wave parameters. Because of this, experimenters are recommended to study gyrotropic crystals as before, using the previous theory of gyrotropy. The modern theory of gyrotropy, as a manifestation of spatial dispersion, should be used only in exceptional cases, for instance, in the search for the third, i.e., excitonic, natural wave.     

X-ray dichroism in biaxial gyrotropic media: Differential absorption and fluorescence excitation spectra

The differential absorption and the differential change in the polarization state of an X-ray beam propagating inside a gyrotropic crystal are described using a Müller matrix, the 16 elements of which are related to the anisotropic components of the multipolar polarizability tensors at the absorbing site. Analytical expressions are given up to third order for X-ray linear and circular dichroism, X-ray optical rotation and X-ray circular polarimetry in transmission. The same formalism is extended to discuss Fluorescence detected dichroism spectra with or without polarization analysis of the fluorescence. Fluorescence detected dichroism is strictly proportional to dichroism measured in the transmission geometry only for uniaxial crystals. In biaxial crystals, the tiny effects of X-ray gyrotropy are swamped by large linear dichroism signals due to the imperfect polarization transfer function of Bragg monochromators. Second order effects should also be taken into consideration. Our general formulation of linear and circular dichroism includes terms of odd parity with respect to the action of the time reversal operator: such terms cannot contribute to natural dichroism but can be activated by a magnetic field. The terms responsible for X-ray magnetic circular dichroism are well known but non-reciprocal X-ray gyrotropy effects are also predicted in magnetic crystals of appropriate symmetry. Received 3 March 1999     

Optical activity of γ<Subscript>1</Subscript>-(Ga<Subscript>x</Subscript>In<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>)<Subscript>2</Subscript>Se<Subscript>3</Subscript> crystals

The optical activity of uniaxial γ₁-(Ga_xIn_1?x )₂Se₃ crystals (x=0.1, 0.2, 0.3, 0.4) is studied at T=295 and 77 K in the spectral range 0.5–0.8 πm. It is found that the cationic substitution In → Ga leads to a nonlinear increase in the specific rotation of the plane of polarization ρ and the component g ₃₃ of the gyration tensor. It is shown that the gyrotropy of the crystals studied is determined by high-energy transitions whose energy exceeds the energy of the edge transitions and that the gyrotropy observed has a molecular origin.     

Conservation laws in the quantum Hall Liouvillian theory and its generalizations

It is known that the localization length scaling of noninteracting electrons near the quantum Hall plateau transition can be described in a theory of the bosonic density operators, with no reference to the underlying fermions. The resulting “Liouvillian” theory has a U(1|1) global supersymmetry as well as a hierarchy of geometric conservation laws related to the noncommutative geometry of the lowest Landau level (LLL). Approximations to the Liouvillian theory contain quite different physics from standard approximations to the underlying fermionic theory. Mean-field and large-N generalizations of the Liouvillian are shown to describe problems of noninteracting bosons that enlarge the U(1|1) supersymmetry to U(1|1)×SO(N) or U(1|1)×SU(N).These noninteracting bosonic problems are studied numerically for 2⩽N⩽8 by Monte Carlo simulation and compared to the original N=1 Liouvillian theory. The N>1 generalizations preserve the first two of the hierarchy of geometric conservation laws, leading to logarithmic corrections at order 1/N to the diffusive large-N limit, but do not preserve the remaining conservation laws. The emergence of nontrivial scaling at the plateau transition, in the Liouvillian approach, is shown to depend sensitively on the unusual geometry of Landau levels.     

Magnetogyrotropy in twisted CdS crystals

In this paper the optical activity (gyrotropy) induced by a simultaneous action of a magnetic field and a torsion in hexagonal CdS crystals has been investigated. The crystal having undergone to both external influences is placed between two crossed polarizers. The spectral course of transmittance of this system near the isotropic point of CdS (the wavelength where the birefringence changes its sign) is studied in the experiment. An explanation of the experimental results is given by using the model of elliptical birefringence in anisotropic gyrotropic crystals. Taking into account the superposition of both external influences, it has been proved that the torsion generates gyrotropy whose parameter changes its sign in the isotropic point.     

Optoacoustic interaction in uniaxial gyrotropic quartz crystals

The specific features are considered of the noncollinear optoacoustic interaction in uniaxial gyrotropic quartz crystals in an intermeadiate regime of diffraction close to the Bragg regime. A system of equations of coupled waves is presented which describes the optoacoustic interaction in uniaxial gyrotropic crystals in the Raman-Nath, intermedaite, and the Bragg regimes of diffraction. The dependences of the diffraction efficiency on the ultrasonic wave intensity, the optoacoustic interaction length, and on the incident light polarization are investigated. A multispike structure of the Bragg maximum is studied that appears in accounting for the crystal gyrotropy. A good agreement between the theoretical calculations and the known experimental results for a quartz crystal is shown. Mozyr State Pedagogical Institute, 28, Studencheskaya Str., Mozyr, 247760, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 66, No. 2, pp. 278–281, March–April, 1999.     

Features of acousto-optic interaction in uniaxial gyrotropic crystals

The features of noncollinear acousto-optic interaction in gyrotropic crystals in the intermediate diffraction regime and the regime of Bragg diffraction were investigated. The dependence of the efficiency of diffraction in gyrotropic paratellurite, tellurium, and quartz crystals on the intensity of the ultrasonic wave, acousto-optic interaction length, and incident-light polarization was investigated. It is shown that the gyrotropy of the crystal is responsible for the appearance of a multiple-peak structure of the Bragg maximum. It has been established that in the case of propagation of incident and diffracted waves in the vicinity of the optical axis of the crystal, the diffraction efficiency is independent of the polarization state of the incident light. The results of theoretical calculations are in agreement with the experimental results obtained for uniaxial crystals. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 1, pp. 105–110, January–February, 2000.     

Conformal field theory and the symmetries of string field theory

The two-dimensional conformal field theory representation of Witten's bosonic string field theory is discussed. The basic overlap equations, K_n symmetry and BRST invariance are proved directly, without the usual expansion in oscillators. The conformal field theory approach naturally provides local overlap identities which (when integrated over half the string) can be used to verify properties of the cubic action. In particular, a recently proposed diffeomorphism invariance is shown to be free of anomalies. Finally, a new class of symmetries, including generalizations of the K_n symmetries which are local in spacetime, are presented.     

Relativistic multiple scattering theory of electrons by ferromagnets

In view of investigating for 3d- and 4f-ferromagnetic crystals the elastic scattering and the emission of polarized low-energy electrons as well as the bulk electronic structure, a relativistic multiple scattering theory has been developed, in which the exchange interaction with the magnetic ground state electrons is treated in a local density functional approximation. In a layer-KKR-type approach, the Dirac equation, which contains an effective magnetic field term, is first solved for a single crystal atom and subsequently for a monoatomic layer and for a semi-infinite crystal. Spin-orbit coupling and magnetic exchange interaction are thus simultaneously taken into account.     

V.A. Shamburov’s validity criteria for the gyrotropy theory

V.A. Shamburov’s attempts to constrain the range of applicability of F.I. Fedorov’s constitutive equations in the gyrotropy theory are shown to be untenable.     

Cones of optical axes in gyrotropic crystals with scalar permittivity

A theory is constructed for the degeneracy of electromagnetic waves in gyrotropic crystals near their isotropy points (in temperature and other parameters), in which permittivity ? becomes scalar due to dispersion and optical anisotropy is entirely determined by gyrotropy. It is shown that closed lines of intersection of sheets of the refraction surface, which correspond to the cones and, in particular, planes of the optical axes, are formed for isotropic ?. The polarization characteristics of wave fields experience a jump upon a transition through such lines. The conditions for the existence and geometry of the degeneracy cones under investigation are analyzed for crystals of all symmetry classes permitting optical activity. It is shown that the degeneracy lines disappear for a small deviation of ? from isotropy, while polarization anomalies persist. Isolated (one or two) degeneracy points may retain in place of the lines in the case when the optical axes of a perturbed crystal with “switched-off” gyrotropy belong to the initial cone.     

Propagation properties of Lorentz beam in uniaxial crystals orthogonal to the optical axis

The properties of Lorentz beams propagating in uniaxial crystals orthogonal to the optical axis are studied. The diffraction field components and effective beam sizes of the Lorentz beams are derived in analytical forms. Numerical results show that, upon propagating in uniaxial crystals, a Lorentz beam loses its initial Lorentz type distribution. Also, after propagating for sufficient distances, the transverse components would finally convert into a specific four-petal profile with an axial shadow, which may find applications in the optical trapping of particles. It also shows that the Lorentz beam parameters w_0x, w_0y and the ratios of refractive indices have strong influences on the diffraction field components and on the effective beam sizes when propagating in uniaxial crystals.     

On the phenomenological theory of the linear electrooptical effect in uniaxial crystals

The linear electrooptical effect in uniaxial crystals is considered with the aid of direct tensor methods. Covariant expressions for finding biradials and ray refractive indices are developed. A general expression is derived relating the nonlinear optical polarizability parameters and the electrooptical properties of a crystal. The results are applied to cuts of uniaxial ammonium dihydrogen phosphate (ADP), potassium dihydrogen phosphate (PDP), and quartz crystals often used for light modulation. The induced phase differences between the light waves propagating in such crystals are found for the field orientations considered.     

Spectral polarization features of the macroscopic manifestation of parity violation in gaseous media

A formalism based on macroscopic Maxwell equations is developed for the case of media with violations of the space symmetry and time reversal. It is demonstrated that the parity violation in a medium is equivalent to the manifestation of spatial dispersion and natural optical activity. The proposed formalism makes it possible to uniquely calculate the macroscopic parameters of equations in terms of the microscopic theory. The parameters of gyrotropy and dichroism of a gaseous medium are determined within a model describing an interaction of resonance radiation with transitions to states that have different parities and are mixed by a weak interaction of an electron with the nucleus of the atom. It is established that, in the range of the resonance with a magnetic dipole transition, the effect of parity violation is enhanced as a result of the considerable difference between the natural broadenings of the electric and magnetic dipole transitions. This enhancement is suppressed when the dominant Doppler broadening of the atomic transitions is taken into account. It is shown that, owing to the unitarity of the weak interaction, the effects of parity violation are alternating functions of the radiation frequency and are integrally absent in the entire spectrum.     

Generation of acoustically distributed feedback lasers based on gyrotropic crystals

Oscillation conditions were determined for acoustically distributed feedback (ADFB) lasers based on gyrotropic uniaxial and cubic crystals. The lasing threshold was shown to be higher for the modes with clockwise polarization than for those with counterclockwise polarization. It is established that the regions of maximal amplification for clockwise (counterwise) waves of the gyrotropic crystal are displaced in the direction of decreased (increased) phase detuning, respectively, relative to amplification regions that correspond to the absence of crystal gyrotropy. The ADFB laser was shown to be capable of generating at the Bragg frequency. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 3, pp. 331–335, May–June, 2008.     

Effect of the domain structure on ferromagnetic resonance in easy-axis ferromagnets

The results of experimental and theoretical investigations of ferromagnetic resonance (FMR) in ferrite single crystals having hexagonal structure and magnetocrystalline anisotropy of the easy-axis type are reported. Experiments are carried out on disk-shaped samples of materials differing in anisotropy strength. The values of the effective anisotropy fields and the gyromagnetic ratios (g-factors) of the materials are determined from measured frequency dependences of the FMR field along the easy and hard magnetization directions for homogeneously magnetized samples. It is shown that if the FMR spectra are also measured for the same samples in the presence of a domain structure, then one can experimentally determine not only the above-mentioned parameters but also the saturation magnetization of uniaxial magnetic materials. It is shown that the theory of the FMR frequency spectrum of a partially magnetized sample with a simple domain structure in the form of a system of plane-parallel layers is in good agreement with the experiment.     

Birefringence and the gyrotropy of the compounds II-IV-V2

Conclusion The crystals II-IV-V₂ with the structure of chalcopyrite exhibit intense birefringence whose quantity according to the structural model is determined by the anisotropy of the local field and by the anisotropy of the polarizability of the II–V bond. Birefringence dispersion and its thermal and barometric coefficients are interpreted in the three-contribution model as boundary, E₁ and E₂-transitions and correspond to a compressed binary analog. The crystals II-IV-V₂ possess gyrotropic properties that are manifested in elliptical birefringence and exhibit peculiarities in the optical spectra near the isotropic point. The dispersion of gyrotropy is determined by the presence of linear terms in the dispersion zone. The quantity of gyrotropy is related to the deformation of the tetrahedron II-V₄. The anisotropy of the optical properties of the crystals II-IV-V₂ can be used for devices in nonlinear optics for the parametric transformation of light.Translated from Izvestiya Vysshikh. Uchebnykh Zavedenii, Fizika, No. 8, pp, 41–53, August, 1986.     

Nonassociativity,Malcev algebras and string theory

Nonassociative structures have appeared in the study of D‐branes in curved backgrounds. In recent work, string theory backgrounds involving three‐form fluxes, where such structures show up, have been studied in more detail. We point out that under certain assumptions these nonassociative structures coincide with nonassociative Malcev algebras which had appeared in the quantum mechanics of systems with non‐vanishing three‐cocycles, such as a point particle moving in the field of a magnetic charge. We generalize the corresponding Malcev algebras to include electric as well as magnetic charges. These structures find their classical counterpart in the theory of Poisson‐Malcev algebras and their generalizations. We also study their connection to Stueckelberg's generalized Poisson brackets that do not obey the Jacobi identity and point out that nonassociative string theory with a fundamental length corresponds to a realization of his goal to find a non‐linear extension of quantum mechanics with a fundamental length. Similar nonassociative structures are also known to appear in the cubic formulation of closed string field theory in terms of open string fields, leading us to conjecture a natural string‐field theoretic generalization of the AdS/CFT‐like (holographic) duality.     

Soliton supermultiplets and Kaluza-Klein theory

We show that the monopoles of five-dimensional Kaluza-Klein theory, considered as solutions of the N = 8 supergravity theory in five dimensions, fit into the same supermultiplets as the original fields in that theory. We show that there is an electric-magnetic duality between these magnetic monopoles and the electrically charged antigravitating objects anticipated by Scherk. We formulate a Bogomolny inequality for N = 8 supergravity, and we speculate on the wider significance of these monopoles.