Features of faraday rotation in cs atomic vapor in a cell thinner than the wavelength of light

Features of the effect of Faraday rotation (the rotation of the radiation polarization plane) in a magnetic field of the D ₁ line in Cs atomic vapor in a nanocell with the thickness L varying in the range of 80–900 nm have been analyzed. The key parameter is the ratio L/λ, where λ = 895 nm is the wavelength of laser radiation resonant with the D ₁ line. The comparison of the parameters for two selected thicknesses L = λ and λ/2 has revealed an unusual behavior of the Faraday rotation signal: the spectrum of the Faraday rotation signal at L = λ/2 = 448 nm is several times narrower than the spectrum of the signal at L = λ, whereas its amplitude is larger by a factor of about 3. These differences become more dramatic with an increase in the power of the laser: the amplitude of the Faraday rotation signal at L = λ/2 increases, whereas the amplitude of the signal at L = λ almost vanishes. Such dependences on L are absent in centimeter-length cells. They are inherent only in nanocells. In spite of a small thickness, L = 448 nm, the Faraday rotation signal is certainly detected at magnetic fields ≥0.4 G, which ensures its application. At thicknesses L < 150 nm, the Faraday rotation signal exhibits “redshift,” which is manifestation of the van der Waals effect. The developed theoretical model describes the experiment well.     

Waves in a superlattice with anisotropic inhomogeneities

Dependences of the dispersion laws and damping of waves in an initially sinusoidal superlattice on inhomogeneities with anisotropic correlation properties are studied for the first time. The period of the superlattice is modulated by the random function described by the anisotropic correlation function K_?(r) that has different correlation radii, k _∥ ^?1 and k _⊥ ^?1 , along the axis of the superlattice z and in the plane xy, respectively. The anisotropy of the correlation is characterized by the parameter λ=1?k_⊥/k_∥ that can change from λ=0 to λ=1 when the correlation wave number k⊥ changes from k_⊥=k_∥ (isotropic 3D inhomogeneities) to k_⊥=0 (1D inhomogeneities). The correlation function of the superlattice K(r) is developed. Its decreasing part goes to the asymptote L that divides the correlation volume into two parts, characterized by finite and infinite correlation radii. The dependences of the width of the gap in the spectrum at the boundary of the Brillouin zone δν and the damping of waves ξ on the value of λ are studied. It is shown that decreasing L leads to the decrease of δν, and increase of ξ, with the increase of λ.     

Spin-Wave Resonance in Ge : Mn Thin Films with Percolation Magnetic Ordering

The mechanism of excitation and propagation of spin waves in Ge: Mn thin films with different nominal manganese concentrations (2, 4, and 8 at % Mn) with percolation magnetic ordering is explored. Concentration dependencies of Curie temperature T_C(n) and spin wave rigidity D(n) are determined, which enables to find the index of correlation distance. An exotic percolation magnetic state of samples of Ge: Mn thin films is confirmed by rectifying experimental dependences D(n) and D/T_C(n) in coordinates accepted in the percolation theory.     

Nanocell with a pressure-controlled Rb atomic vapor column thickness: Critical influence of the thickness on optical processes

A new device is designed: it consists of a nanocell (NC) filled with Rb atom vapors and placed in a vacuum chamber. When the pressure in the chamber changes in the range 0–1 atm, the NC thickness is smoothly varied in the range L = 140–1700 nm, which is caused by the pressure-induced deformation of thin garnet windows in the chamber. The pressure dependence has excellent reproducibility even after many hundreds of cycles of letting in of air and its complete pumping out from the chamber. The accuracy of setting required thickness L is much better than in the wedge-gap NCs to be moved mechanically that were used earlier. The processes of Faraday rotation (FR) of a polarization plane, resonance absorption, and fluorescence are studied using the D ₁-line narrow-band continuous laser radiation when the thickness changes from L = λ/2 (398 nm) to L = 2λ (1590 nm) at a step λ/2. The FR signal is shown to be maximal at L = λ/2 and 3λ/2 and to have the minimum spectral width (≈60 MHz). At L = λ and 2λ, the FR signal is minimal and has the maximum spectral width (≈200 MHz). The resonance absorption demonstrates the same oscillating behavior; however, the effect in the case of FR is much more pronounced. The oscillating effect is absent for resonance fluorescence: its spectral width and amplitude increase monotonically with L. The detected effects are explained and possible applications are noted.     

Faraday effect on the Rb <Emphasis Type="Italic">D</Emphasis> <Subscript>1</Subscript> line in a cell with a thickness of half the wavelength of light

The rotation of the radiation polarization plane in a longitudinal magnetic field (Faraday effect) on the D₁ line in atomic Rb vapor has been studied with the use of a nanocell with the thickness L varying in the range of 100–900 nm. It has been shown that an important parameter is the ratio L/λ, where λ = 795 nm is the wavelength of laser radiation resonant with the D₁ line. The best parameters of the signal of rotation of the radiation polarization plane have been obtained at the thickness L = λ/2 = 397.5 nm. The fabricated nanocell had a large region with such a thickness. The spectral width of the signal reached at the thickness L = 397.5 nm is approximately 30 MHz, which is much smaller than the spectral width (≈ 500 MHz) reached with ordinary cells with a thickness in the range of 1–100 mm. The parameters of the Faraday rotation signal have been studied as functions of the temperature of the nanocell, the laser power, and the magnetic field strength. The signal has been reliably detected at the laser power P_L ≥ 1 μW, magnetic field strength B ≥ 0.5 G, and the temperature of the nanocell T ≥ 100°C. It has been shown that the maximum rotation angle of the polarization plane in the longitudinal magnetic field is reached on the F_g = 3 → F_e = 2 transition of the ⁸⁵Rb atom. The spectral profile of the Faraday rotation signal has a specific shape with a sharp peak, which promotes its applications. In particular, Rb atomic transitions in high magnetic fields about 1000 G are split into a large number of components, which are completely spectrally resolved and allow the study of the behavior of an individual transition.     

Selective reflection from Rb vapor in half- and quarter-wave cells: Features and possible applications

The features of the effect of selective reflection from rubidium vapor in a nanocell with the thickness L ≈ λ/2 and L ≈ λ/4, where λ = 795 nm is the wavelength of laser radiation resonant with the Rb D₁ line, are studied. It is shown that, because of the behavior of the nanocell as a low-Q-factor Fabry–Pérot etalon, the sign of the derivative of the selective reflection spectra changes near L ≈ λ/2 from negative at L > λ/2 to positive at L < λ/2. The simplicity of the experimental implementation, large amplitude, and sub-Doppler width (40MHz) of a detected signal at an atomic transition frequency are appropriate for applications in metrology and magnetometry. In particular, selective reflection from the nanocell is a convenient frequency marker of atomic transitions; in this case, the amplitudes of peaks are proportional to the transition probabilities. The remote optical monitoring of a magnetic field with a spatial resolution L = λ/4 ≈ 199 of nm is possible on the basis of the splitting of selective reflection peaks in a strong magnetic field (up to 3 kG). A theoretical model describes well the experimental results.     

Optimization of sub-Doppler absorption contour in gas-dynamic beams

The formation of the Doppler contour P _D(?) of absorption lines upon the excitation of particles in the volume of a gas-dynamic beam by light propagating in a direction orthogonal (reduced) to the beam axis is analyzed. Integral representations of P _D(?) are obtained for arbitrary relations between the nozzle outlet diameter D and the collimating aperture diameter B in the excitation region are obtained. An optimal configuration at which the reduced Doppler contour is the narrowest at a high density of beam particles is revealed to be B/D = 2.     

Reflectance spectra and photonic band gaps of a one-dimensional photonic crystal based on a silicon-air periodic structure

The reflectance spectra of a one-dimensional photonic crystal based on a silicon-air periodic structure are calculated. A map of photonic band gaps is plotted, which makes it possible to deliberately choose the geometric parameters of the structure (the thickness of silicon partitions D _Si and the period A) for different ranges of the wavelength λ. To obtain structures with a photonic band gap in the range A/λ=0.15–0.5, the main region (as rule, corresponding to the lowest frequencies) can be used, and, taking into account the secondary photonic band gaps, the range A/λ can be extended to 1 and even more. In addition, it is found that, in the range D _Si/A=0.4–0.9, the secondary band gaps may be wider than the main ones (on the frequency scale). The influence of the filling factor D _Si/A on the formation of the edges of spectral bands is revealed.     

Spin fluctuations in the stacked-triangular antiferromagnet YMnO<Subscript>3</Subscript>

The spectrum of spin fluctuations in the stacked-triangular antiferromagnet YMnO₃ was studied above the Néel temperature using both unpolarized and polarized inelastic neutron scattering. We find an in-plane and an out-of-plane excitation. The in-plane mode has two components just above T _N : a resolution-limited central peak and a Debye-like contribution. The quasi-elastic fluctuations have a line width that increases with q as Dq ^z and the dynamical exponent z = 2.3. The out-of-plane fluctuations have a gap at the magnetic zone center and do not show any appreciable q dependence at small wave vectors.     

Time-Harmonic Gaussian Beams: Exact Solutions of the Helmhotz Equation in Free Space

An exact solution of the Helmholtz equation u _xx + u _yy + u _zz + k²u = 0 is presented, which describes propagation of monochromatic waves in the free space. The solution has the form of a superposition of plane waves with a specific weight function dependent on a certain free parameter a. If ka→∞, the solution is localized in the Gaussian manner in a vicinity of a certain straight line and asymptotically coincides with the famous approximate solution known as the fundamental mode of a paraxial Gaussian beam. The asymptotics of the aforementioned exact solution does not include a backward wave.     

Effect of nonuniform mechanical stresses on the domain structure of iron borate

A magnetooptic method is used to study the effect of nonuniform radial mechanical stresses on the domain structure, magnetic susceptibility, and magnetic hysteresis loops of a FeBO₃ single crystal. When a magnetic field is applied in the basal plane of FeBO₃ along the stress vector, a system of tapered domains appears in the crystal during magnetization. These domains exist in a certain temperature-dependent field range H₀ ≤ H ≤ H _c . The appearance of a system of tapered domains is found to substantially affect the technical magnetization of a stressed crystal. The results obtained are discussed within the thermodynamic theory of a domain structure. A theoretical model used is shown to adequately describe the experimental temperature and field dependences of the ratio \({D \mathord{\left/ {\vphantom {D {\sqrt L }}} \right. \kern-\nulldelimiterspace} {\sqrt L }}\) (where D and L are the average width and length of a tapered domain, respectively). The calculated value of D is approximately 1.3 times smaller than the experimentally observed domain width.     

Spin observables in <Emphasis Type="Italic">np</Emphasis> elastic scattering in the energy range 200–600 MeV. Complete experiment

A survey of available experimental data on the measurement of spin observables in neutron-proton (np) elastic scattering in the neutron energy range 200–600 MeV is presented. Sixteen spin observables (the polarization of recoil particles P _0n00, the analyzing power A _00n0, the spin correlation parameters A _00nn , A _00ss , A _00sk , and A _00kk , the spin transfer parameters K _0nn0, K _0ss0, and K _0sk0, the depolarization parameters D _0n0n , D _0s0s , and D _0s0k , and the three-spin parameters N _0nkk , N _0skn , N _0ssn , and N _0sns for energies of 200–590 MeV and scattering angles in the center of mass system of 60°–164°) were studied in experiments using polarized neutron beams and polarized proton targets at the Paul Scherrer Institute. The results of these investigations present a complete set of precision data on np elastic scattering which, along with the complete set of data for proton-proton (pp) elastic scattering obtained earlier, provides a basis for unambiguous determination of the amplitudes of the scattering matrix for nucleon-nucleon (NN) elastic scattering for the channel with the isotopic spin I = 0 and makes it possible to describe NN interaction in a model-independent way.     

Electron spin precession in the field of an electromagnetic wave

The solution of the Dirac equation for an electron in the field of a plane circularly polarized electromagnetic wave having an arbitrary intensity and a phase velocity v _ph different from the speed of light c is obtained. This solution is shown to describe the previously unknown effect of electron spin precession that exceeds the known precession effects caused by radiative corrections by six and more orders of magnitude and opens new possibilities for control of the polarization of electrons and for realization of various resonance methods associated with the spin precession. The predicted effect is in agreement with symmetry principles; however, it disappears at v _ph=c and is not described by the known Volkov solution.     

Spin correlation in pp elastic scattering and in pion production near threshold

An internal polarized gas target in conjunction with a beam of polarized protons stored in the IUCF Cooler storage ring has been used to measure analyzing power and spin correlation parameters between 200 MeV and 450 MeV over a wide range of angles. A consistent absolute beam and target polarization calibration was established by ramping the stored protons up and down in energy. The analyzing power A _y and the spin correlations A _xx , A _yy and A _xz were measured with transverse beam polarization, while determination of A _zz required the development of a longitudinally polarized beam. First experiments on the spin dependence on π₀-production have recently been carried out.     

An approximate analysis of the diffraction losses in corner reflectors

The fundamental mechanism of energy loss from a Gaussian beam scattered by the edge of a corner reflector is considered. An independent calculation is performed to estimate the relative losses for different polarizations with allowance for the Goos-Hanchen shift effect. For the angle of incidence α = π/4, the relative energy losses by waves polarized along the reflector’s edge and normally to this direction are estimated at (W _dif/W _inc)_E ? 7.03(λ₀/a) and (W _dif/W _inc)_H ? 3.82(λ₀/a), respectively, where λ₀ is the wavelength in free space and a is the effective radius of the beam.     

Influence of the dimension of a polycrystalline film and the optical anisotropy of crystallites on the effective dielectric constant of the film

The dimension D of a polycrystalline film and the optical anisotropy m = ε_z/ε_x of uniaxial crystallites with the principal components ε_x = ε_y and ε_z of the tensor of the dielectric constant have been shown to produce a strong influence on the effective dielectric constant ε_D^* and the effective refractive index n_D^* = (ε_D^*)^1/2 of the film in the optical transparency region, as well as on the boundaries of the intervals B_Dl ≤ ε_D^* ≤ B_Du. The intervals Δ₂(m) = B_2l–B_2u and Δ₃(m) = B_3l–B_3u are separated by a gap for m in the range 1 < m < 2, whereas the theoretical dependence ε₂^*(m) is separated by a gap from the interval Δ₃(m) for m in the range 1 < m < 4. This is confirmed by a comparison of the experimental (n_oP) and theoretical (n_D^*) ordinary refractive indices for uniaxial polycrystalline films of the conjugated polymer poly(p-phenylene vinylene) (PPV) with uniaxial crystallites and appropriate values of m. In the visible transparency region of the PPV films with a change in m(λ) in the range 2 < m(λ) < 3 due to the dependence of the components ε_x,z(λ) on the light wavelength λ, the refractive indices n_oP²(λ) = ε_oP(λ) are consistent with the theoretical values of ε₂^*(λ) and lie outside the interval Δ₃(m). For m(λ) > 3 near the electronic absorption band of the crystallites, the values of ε_oP(λ) lie in the region of the overlap of the intervals Δ₂(m) and Δ₃(m). The boundaries mc of the range 1 < m < m_c are determined, for which the interval Δ₂(m) is separated by a gap from the dependences ε₃^*(m) corresponding to the effective medium theory with spherical crystallites and hierarchical models of a polycrystal, as well as from the proposed new dependence ε₃^*(m).     

Magnetic structure of Er<Subscript>5</Subscript>Ge<Subscript>3</Subscript> at 4.2 K

A symmetry analysis of the possible magnetic structures of Er₅Ge₃ in the ground state is performed using the results of measurements of elastic magnetic neutron scattering at 4.2 K. It is shown that the minimum discrepancy factor R _m ≈9.5% corresponds to a modulated collinear magnetic structure in which the magnetic moments of erbium atoms are oriented along the a ₃ axis of the unit cell of the crystal structure and induce an antiferromagnetic longitudinal spin wave (AFLSW). The magnetic structure is characterized by the wave vector k=2π(0, 0, μ /a ₃) (where μ≈0.293) and the modulation period λ≈3.413a ₃. The magnetic ordering temperature T _N ≈38 K is determined from the temperature dependence of the intensity of magnetic reflections. __________ Translated from Fizika Tverdogo Tela, Vol. 45, No. 9, 2003, pp. 1653–1659. Original Russian Text Copyright ? 2003 by Vokhmyanin, Dorofeev.     

A tilted rotatory frame method for the measurement of nuclear spin diffusion coefficients in solids doped with paramagnetic centers: Mn-Doped CaF<Subscript>2</Subscript>

Nuclear magnetic resonance (NMR) experiments recording the recovery of the magnetization of the nuclei in one phase, following the excitation of the nuclei in the other phase, is a classical way of studying blends inhomogeneous at the nanometer scale. Interpretation of the time recovery in terms of the spatial dimension requires knowledge of the two-phase spin diffusion coefficientsD ₀. A new method of measurement of_{D 0} is proposed on the basis of variable angle-tilted rotatory frame relaxation in homogeneous samples doped with paramagnetic centers. The choice of the tilt angle allows one to finely balance the direct relaxation by the paramagnetic center and the spin diffusion. The shape of the relaxation is analyzed with the solution for the diffusion-limited regimeM(t)/M(0)=exp[?(r ₂ t)^1/2?r ₁ t] andD ₀ then calculated fromr ₁,r ₂ and the concentration of paramagnetic centers. Conditions where reliable results can be obtained both theoretically and numerically are explored. The method has been implemented and applied to polycrystalline Mn-doped CaF₂ leading toD ₀=540±60 nm²/s, in agreement with existing values on this model compound.     

Propagation of Airy-Gaussian beams in a quadratic-index medium

The propagation properties of the Airy-Gaussian beams are introduced in a quadratic-indexmedium analytically and numerically. The linear momentum, the beam width, the beam centerof the Airy-Gaussian beam are analyzed. The Airy-Gaussian beam shape and curvature repeatsitself at intervals proportional to \hbox{$1/\sqrt{az_{R}}$}1/azRdue to the potential barrier. The bend (the transversely acceleration) and the periodicityof the Airy-Gaussian beam depend on the parameters χ ₀ anda z _R .