Cotton-Mouton Effect Research Articles

Superposition rule for the magneto-optic effects in isotropic media

The two well-known magneto-optic phenomena: the Faraday and Cotton-Mouton effects describe behavior of optically isotropic medium in the external magnetic field which is parallel or perpendicular to the wave propagation direction, respectively. In this paper a superposition rule for both magneto-optic effects as a generalization of Faraday and Cotton-Mouton effects for any orientation of external magnetic field with regard to the wave propagation direction is presented.

Jones birefringence in gases: Ab initio electron correlated results for atoms and linear molecules

The results of an ab initio investigation of the Jones birefringence (JB) of noble gases (He, Ne, Ar, Kr) and of a few linear molecules—both centrosymmetric (H2,N2,C2H2) and dipolar (CO)—carried out employing coupled cluster response techniques and rather extended correlation-consistent basis sets are presented. The relationships existing between the appropriate linear, quadratic, and cubic frequency-dependent response functions and the tensors introduced in the theoretical derivation of the anisotropy by Graham and Raab in 1983 [Proc. R. Soc. London, Ser. A, 390, 73 (1983)] are introduced. The magnitude of the effect is determined and comparison is made with that of the Cotton–Mouton effect (CME), which, together with the Kerr effect, is closely related to Jones birefringence and superimposed to it in actual measurements, and of electric field gradient induced birefringence (EFGB). CME yields anisotropies of the refractive index ≈100 to ≈3500 larger than those predicted for JB in the eight systems studied, whereas EFGB and JB are shown to be of comparable strength.

Measurement of the Cotton–Mouton constants of noble atoms

Magnetically induced birefringence (the Cotton–Mouton effect) of argon, neon, and helium atoms was measured with a high-sensitivity ellipsometer with a 790-nm GaAlAs diode laser. The detection limit of the change in ellipticity was attained to a shot-noise-limited value of 10-10 rad. We determined the absolute values of the ellipticity changes caused by noble atoms using the light extinction ratio of the ellipsometer as an absolute standard, with this ratio measured by a method based on Malus’s law. The measured values of the Cotton–Mouton constant were (7.1±2.5)×10-10 T-2 m-1 for He atoms, (1.3±0.5)×10-9 T-2 m-1 for Ne atoms, and (1.1±0.2)×10-8 T-2 m-1 for Ar atoms at a gas pressure of 1.52×105 Pa and a gas temperature of 285–293 K.

The Cotton–Mouton effect of furan and its homologues in the gas phase, for the pure liquids and in solution

The tensor components of the electric dipole polarizability at a wavelength of 632.8 nm, those of the magnetizability and the anisotropy of the static hypermagnetizability of furan, thiophene, and selenophene are computed using density functional theory (DFT). The polarizable continuum model (PCM) is employed to describe the system in the condensed phase. We can thus compare the temperature dependence of the Cotton–Mouton constant for the three molecules, both in the gas and in the condensed phase, pure liquids, and solutions, with the results of experiment performed using a 17 T radial access Bitter magnet at the Grenoble High Magnetic Field Laboratory. This allows to analyze, in a direct interaction of theory and experiment, the performance of DFT and PCM in describing high order nonlinear mixed electric and magnetic effects in condensed phase.

Magneto-optics of Ferritin

Measurements of Rayleigh light scattering, nonlinear light scattering in DC magnetic fields, and the Cotton–Mouton effect were carried out for 15 mM NaCl and water solutions of ferritin at room temperature. The spherical geometry of the molecule implies that it is optically isotropic. Such a macromolecule should not manifest magnetic anisotropy; however, in solution it shows induced magnetic birefringence (Cotton–Mouton effect) and changes in the intensity of the scattered light components. The analysis of the obtained results indicates the deformation of linear optical polarizability induced in the ferritin by a magnetic field as the main source of the magneto-optical phenomena observed. Light scattering and the CM effects theoretically depend on the linear magneto-optical polarizability, χ, and the nonlinear magneto-optical polarizability, η. Using the theory describing the phenomena as well as the experimental data, the values of the anisotropy of linear magneto-optical polarizability components, χ ‖−χ ⊥=−(1.3±0.7)×10 −22 [cm 3] (in SI units χ ‖−χ ⊥=−(2.0±1.2)×10 −33 [m 3]), the linear optical polarizability, α=(α ‖+2α ⊥)/3=(3.9±1.0)×10 −20 [cm 3] (in SI units α=(3.52±0.09)×10 −4 [Cm 2V −1]), and its anisotropy, κ α=(α ‖−α ⊥)/3α=−(0.06±0.03), nonlinear magneto-optical polarizability, η=(η ‖+2η ⊥)/3=−(4.7±0.9)×10 −30 [cm 3Oe −2] (in SI units η=−(6.7±1.3)×10 −18 [Cm 4V −1A −2]) and its anisotropy, κ η=(η ‖−η ⊥)/3η=−(0.15±0.10), were deduced. Here α ‖, η ‖, α ⊥, η ⊥ are the optical and magneto-optical polarizability components along the parallel and the perpendicular axes of the axially symmetric molecule, respectively.

Interatomic interactions and the Cotton—Mouton effect for helium

We report calculations of the interaction-induced polarizability (δαanis), magnetizability (δξanis;) and hypermagnetizability (δηanis) anisotropies for the helium gas as a function of the interatomic separation. From these data we determine the virial coefficients for the Cotton—Mouton effect and the hypermagnetizability anisotropy of helium. We also find the mean polarizability and magnetizability as a function of the interatomic separation and the virial coefficients for these properties. The results for the Cotton—Mouton effect indicate that pressure affects the Cotton—Mouton constant to the same extent as it does the second hyperpolarizability (γ) and the virial coefficient bCME(ω, T) lies in the range of −1.6 to −1.8 cm3 mol−1. This means that pressure effects for the Cotton-Mouton constant could be detected with modern experimental techniques. All calculations were carried out using the full configuration interaction technique and large basis sets of London atomic orbitals. The polarizability calculations were performed both for relevant optical frequencies as well as the static case.

Magnetic birefringence of light in hematite

Peculiarities in the propagation of IR radiation in the easy-plane antiferromagnet α-Fe2O3 are investigated. In the geometry of the Cotton-Mouton effect, magnetic birefringence is measured and magnetooptical constants are estimated.

Molecular polarizability of organic compounds and their complexes: XLVII. Conformations of some 2,4,6-triarylpyridines, 2-aryl-4-phenyl-6-tert-butylpyridines, and the corresponding pyridinium cations in solutions, as determined from the cotton-mouton effect

The conformations of some 2,4,6-triarylpyridines, 2-aryl-4-phenyl-6-tert-butylpyridines, and the corresponding pyridinium cations in dioxane and acetonitrile solutions were determined from the Cotton-Mouton effect. These systems are nonplanar; the angles by which the aryl substituents at positions 2 and 6 of the heteroring are turned relative to the heteroring plane are close to those observed in biphenyl and its p-substituted derivatives; these angles depend on substituents in the rings and, in the case of cations, at the pyridinium nitrogen atom.

The Cotton–Mouton effect of gaseous N 2, CO, CO 2, N 2O, OCS and CS 2: a density functional approach to high-order mixed electric and magnetic properties

The static hypermagnetizability anisotropies of N 2, CO, CO 2, N 2O, OCS and CS 2 are computed using density functional theory (DFT). Also, the anisotropy of the electric dipole polarizability at a wavelength of 632.8 nm and that of the magnetizability are obtained. We can thus compare the temperature dependence of the Cotton–Mouton constant for all six molecules to the results of previous ab initio studies and to those of the experimental study by Kling and Hüttner [Chem. Phys. Lett. 90 (1984) 207]. The agreement is satisfactory.

The Cotton–Mouton effect of gaseous CO2, N2O, OCS, and CS2. A cubic response multiconfigurational self-consistent field study

The hypermagnetizability and the hypermagnetizability anisotropy of CO2, N2O, OCS, and CS2 are computed at a wavelength of 632.8 nm using cubic response theory with multiconfigurational self-consistent field wave functions. The anisotropies of the electric dipole polarizability and of the magnetizability are also obtained. This allows us to study the temperature dependence of the Cotton–Mouton constant for all four molecules and thus to compare to the results of the experimental study by Kling and Hüttner [Chem. Phys. Lett. 90, 207 (1984)]. We also assess the importance of pure and zero-point vibrational effects on the relevant molecular properties. In particular, we show that for CO2, OCS, and CS2, the pure vibrational effects to the hypermagnetizability anisotropy can be even more important than the electronic contribution.

Anisotropy of the linear and quadratic magnetic birefringence in rare-earth semiconductors (γ-Ln2S3 (Ln=Dy3+, Pr3+, Gd3+, La3+)

The field and angular dependence of the magnetic linear birefringence (MLB) in noncentrosymmetric cubic (symmetry class Td) rare-earth (RE) semiconductors γ-Ln2S3 (Ln=Dy3+, Pr3+, Gd3+, La3+) was studied. The field dependence of the MLB in Dy2S3 and Pr2S3 is a combination of two contributions, quadratic and linear with respect to the magnetic induction B, both possessing a strong anisotropy. The quadratic birefringence related to the Cotton-Mouton effect manifestations at a wavelength of λ=633 nm is characterized in Dy2S3 by the value of β=1.5 deg/(cm T2) and the anisotropy parameter a=−0.7 and in Pr2S3, by β=0.2 deg/(cm T2) and a=2. The non-reciprocal MLB caused by the magnetic-field-induced spatial dispersion reaches γ 0.55 and 0.71 deg/(cm T) in Dy2S3 and Pr2S3, respectively. The relationship between parameters A and g of the γijkl tensor describing contributions of the Bikj type to the dielectric tensor eij(ω, k, B) is A=2g in Dy2S3 (as well as in boracite crystals containing 3d ions), which is characteristic of the second-order magnetoelectric permittivity manifestations in the optical frequency range. In Pr2S3, the relationship A=3.3g is evidence of manifestations of the additional quadrupole mechanism. A comparison of the Cotton-Mouton and Faraday effects in Ln2S3 and in magnetic semiconductors Cd1−xMnxTe shows a principal difference between these systems and indicates that both phenomena in Ln2S3 are determined by the optical transitions in RE ions rather than by the interband or exciton transitions. This is also confirmed by the comparison of the Cotton-Mouton effect manifestations in Ln2S3, in dielectric Dy3Ga5O12 and Dy3Al5O12 single crystal cubic garnets, and in Dy2O3. An analysis of the non-reciprocal MLB mechanisms related to manifestations of the local interconfiguration optical transitions 4fN→ 4fN−15d in RE ions showed that this phenomenon, in contrast to the Cotton-Mouton and Faraday effects, is caused by the presence of odd components of the crystal field acting upon the RE ion in Ln2S3. In Gd2S3, as well as in diamagnetic Ln2S3, neither the Cotton-Mouton effect nor the non-reciprocal MLB are manifested at T=294 K, which is explained by different microscopic mechanisms of the magnetooptical phenomena for ions in the S-state and diamagnetic ions, on the one hand, and RE ions with nonzero orbital moment, on the other hand.

Manifestation of the cotton-mouton effect in the ionosphere plasma

Polarization methods used to sound ionospheric plasma are based on the Faraday and Cotton-Mouton effects. While the Faraday effect (rotation of the polarization plane) covers almost the entire ray path, the Cotton-Mouton effect gives rise to local transformation of circularly polarized waves near a point of orthogonality of the ray and the Earth's magnetic field. Comparison of the input and output polarization of probing electromagnetic waves, emitted by a satellite and received by ground stations, can provide valuable information about local plasma parameters near the orthogonality point. This paper presents a theory of interaction of circular waves near this point based on the quasi-isotropic approximation (QIA) of geometrical optics and describes algorithms that can be used to retrieve local plasma parameters from polarization measurements. Experimental configurations to observe the Cotton-Mouton effect with linearly and arbitrarily polarized receivers are discussed.

A dipole high-field pulsed magnet to explore the magnetic birefringence of vacuum

The existence of a magnetic birefringence of vacuum denotes one of the most important predictions of quantum electrodynamics which have not yet been verified. We introduce an experimental setup which compared to previous attempts to measure the Cotton–Mouton effect of vacuum improves the signal level by two orders of magnitude. Keystone of the proposed assembly is a specially designed 1.5 m long 25 T pulsed magnet which will be discussed in detail.

Magnetoelectric birefringences of the quantum vacuum

We calculate the optical properties of a vacuum when a static magnetic field ${B}_{0}$ and electric field ${E}_{0}$ are applied perpendicular to the direction of light propagation. Apart from the known Cotton-Mouton and Kerr effects, with crossed fields we find magnetoelectric linear birefringence with optical axes parallel to the external fields. With parallel fields we find magnetoelectric Jones birefringence with optical axes under 45\ifmmode^\circ\else\textdegree\fi{} with the external fields. Both birefringences are linear in ${E}_{0}{B}_{0},$ and have the same magnitude.

Chiral electromagnetic waves at the boundary of optical isomers: Quantum Cotton-Mouton effect

We demonstrate that the boundary of two optical isomers with opposite directions of the gyration vectors (both parallel to boundary) can support propagation of electromagnetic waves in the direction perpendicular to the gyration axes (Cotton-Mouton geometry). The components of electromagnetic field in this wave decay exponentially into both media. The characteristic decay length is of the order of the Faraday rotation length for the propagation along the gyration axis. The remarkable property of the boundary wave is its chirality. Namely, the wave can propagate only in one direction determined by the relative sign of nondiagonal components of the dielectric tensor in contacting media. We find the dispersion law of the boundary wave for the cases of abrupt and smooth boundaries. We also study the effect of asymmetry between the contacting media on the boundary wave and generalize the results to the case of two parallel boundaries. Finally we consider the arrangement when the boundaries form a random network. We argue that at a point, when this network percolates, the corresponding boundary waves undergo quantum delocalization transition, similar to the quantum Hall transition.

Erratum to “Cotton–Mouton effect, magnetizability anisotropy and molecular charge distribution of boron trichloride”: [Chem. Phys. Lett. 310 (1999) 150–154

Erratum to “Cotton–Mouton effect, magnetizability anisotropy and molecular charge distribution of boron trichloride”: [Chem. Phys. Lett. 310 (1999) 150–154

Cotton–Mouton effect, magnetizability anisotropy and molecular charge distribution of boron trichloride

Abstract Measurements of the magneto-optical Cotton–Mouton effect of gaseous BCl3 over a range of temperature (295.6–361.9 K) are analyzed in conjunction with the known electric polarizability anisotropy, mean magnetizability, molecular quadrupole moment and molecular geometry to obtain the magnetizability anisotropy (Δχ=χzz−χxx) and related magnetic properties (χzz, χxx, Δχd, Δχp, gzz− 1 2 gxx) of this species. The observation that Δχ is negative in sign is consistent with Pauling's view of the molecular structure in terms of pπ–pπ interactions, ionic–covalent resonance, partial double bond character and electron delocalization.

The magnetochiral effect and related optical phenomena

The magnetochiral effect has only recently been experimentally detected and measured. The interest for the effect lies less in any foreseeable practical application, than rather in the symmetry principles that govern it. In this article we first show how the magnetochiral effect is related to other optical and magneto-optical phenomena, such as natural optical activity, the Faraday, Cotton–Mouton effects and quadratic magnetic field-enhanced optical activity. The general principles of the measurements of magnetochiral birefringence and magnetochiral dichroism are then briefly described. The basic theory of the non-linear-optical, inverse magnetochiral birefringence is presented and possibilities of its detection are explored. The emphasis of this paper lies in the discussion of selection rules and in symmetry considerations.

The differential magnetizability and the Cotton—Mouton effect of gases

The effect of the interaction of the magnetic field associated with a propagating wave with an atomic or molecular system in a static magnetic field is investigated. This leads, in the case of molecules, to small contributions to the magnetic field induced birefringence (Cotton—Mouton effect). These are not entirely negligible also in view of the increasing sophistication of experimental equipment. Test calculations on a few linear molecules (H2, N2, C2H2 and HF) show that the extra terms, which were neglected in previous analyses, contribute in the range of a few ppm to the induced birefringence. For the systems under study, this is in principle within the sensitivity of current experimental techniques.

The differential magnetizability and the Cotton-Mouton effect of gases

The differential magnetizability and the Cotton-Mouton effect of gases