A note on traversal time for tunneling

A simple approach to study the traversal time for tunneling is given. By using the WKB wave function to evaluate the velocity field of particles in the barrier region, an expression for the traversal time τ=εdx[m/2(V(x)-E)]^1/2 is obtained in conformity with the recent results.     

Discrete wavelet structure and discrete energy of classical plane light waves

We find by the wavelet transform that the classical plane light wave of linear polarization can be decomposed into a series of discrete Morlet wavelets.In the theoretical frame,the energy of the classical light wave becomes discrete;interestingly,the discretization is consistent with the energy division of P portions in Planck radiation theory,where P is an integer.It is shown that the changeable energy of a basic plane light wave packet or wave train is H_(0 k)=nP_(0 k)ω(n=1,2,3,...;k=|k|),with discrete wavelet structure parameter n,wave vector k and idler frequency ω,and a constant p_(0 k).The wave-particle duality from the Mach-Zehnder interference of single photons is simulated by using random basic plane light wave packets.     

Spin waves on chains of YIG particles: dispersion relations,Faraday rotation,and power transmission

We calculate the dispersion relations for spin waves on a periodic chain of spherical or cylindrical Yttrium Iron Garnet (YIG) particles. We use the quasistatic approximation, appropriate when kd ? 1, where k is the wave number and d the interparticle spacing. In this regime, because of the magnetic dipole-dipole interaction between the localized magnetic excitations on neighboring particles, dispersive spin waves can propagate along the chain. The waves are analogous to plasmonic waves generated by electric dipole-dipole interactions between plasmons on neighboring metallic particles. The spin waves can be longitudinal (L), transverse (T), or elliptically polarized. We find that a linearly polarized spin wave undergoes a Faraday rotation as it propagates along the chain. The amount of Faraday rotation can be tuned by varying the off-diagonal component of the permeability tensor. We also discuss the possibility of wireless power transmission along the chain using these coupled spin waves.     

Giant Faraday and Kerr rotation with strained graphene

Polarized electromagnetic waves passing through (reflected from) a dielectric medium parallel to a magnetic field undergo Faraday (Kerr) rotation of their polarization. Recently, Faraday rotation angles as much as 0.1?rad were observed for terahertz waves propagating through graphene over a SiC substrate. We show that the same effect is observable with the magnetic field replaced by an in-plane strain field which induces a pseudomagnetic field in graphene. With two such sheets a rotation of π/4 can be achieved, which is the required rotation for an optical diode. Similarly a Kerr rotation of 1/4 rad is predicted from a single reflection from a strained graphene sheet.     

Duality rotation for 2-D classical ferromagnets

Using an ansatz that allows for propagation of spin excitations, the Landau-Lifshitz equation for 2-D Heisenberg ferromagnets is reduced to a non-linear system of the integrable type. An associated linear set is derived that can be interpreted as an L-A pair of equations, as well as a duality symmetry transformation.     

Faraday rotation under cw saturation and self-induced transparency conditions

Faraday rotation angles in excess of 180° were observed in Na vapor in a 1 kOe magnetic field with intensity transmissions greater than 80%. Identical angles were seen in both the cw saturation (SAT) and self-induced transparency (SIT) limits. This agrees with the theoretical expectation that when the absorption linewidth is large compared with the saturation hole or inverse pulse width, the linear, SAT, and SIT angles are equal.     

Preparation and Faraday rotation of Bi-YIG/PMMA nanocomposite

Bismuth-substituted yttrium iron garnet (Bi-YIG) nanoparticles (NPs) were prepared by coprecipitation and subsequent heating treatment. Thermal gravity-differential thermal analysis was performed to investigate the thermal behavior of the Bi-YIG precursors and to decide the best annealing temperature. Phase formation of garnet NPs was investigated by X-ray powder diffraction. The size of Bi-YIG NPs was investigated by transmission electron microscopy, and the magnetic properties of Bi-YIG NPs were measured using a vibrating sample magnetometer. The results show that the temperature needed for the transformation of Bi-YIG from the amorphous phase to the garnet phase decreases with increasing Bi content, and Bi-YIG NPs with sizes of 28–78 nm are obtained after heating treatment at 650–1000 °C. The saturation magnetization of Bi-YIG NPs increases as the Bi content increases. Moreover, the Faraday rotation of polymethyl methacrylate (PMMA) slices doped with Bi-YIG NPs was investigated. The results indicate that the angle of Faraday rotation increases with increasing Bi content in PMMA composites, and the maximum value of the figure of merit is 1.46°, which is comparable to the value of a sputtered film. The Bi-YIG NPs-doped PMMA slices are new promising materials for magneto-optical devices.     

Potential wells for classical acoustic waves

The acceleration theorem of Bloch waves is utilized to construct random potential wells for classical acoustic waves in systems composed of alternating‘cavities’and‘couplers’.One prominent advantage of this method is these‘cavities’and‘couplers’are all monolayer structures.It allows forming more compact classical potential wells,which leads to the miniaturization of acoustic devices.We systematically investigate properties of harmonic,tangent,hyperbolic function,and square classical potential wells in quasi-periodic superlattices.Results show these classical potential wells are analogues of quantum potential wells.Thus some technologies and concepts in quantum potential well fields may be generalized to classical acoustic wave fields.In addition,some abnormal cases regarding forming classical potential wells are also found.     

Amplitude equation and pattern selection in Faraday waves

A nonlinear theory of pattern selection in parametric surface waves (Faraday waves) is presented that is not restricted to small viscous dissipation. By using a multiple scale asymptotic expansion near threshold, a standing wave amplitude equation is derived from the governing equations. The amplitude equation is of gradient form, and the coefficients of the associated Lyapunov function are computed for regular patterns of various symmetries as a function of a viscous damping parameter gamma. For gamma approximately 1, the selected wave pattern comprises a single standing wave (stripe pattern). For gamma<1, patterns of square symmetry are obtained in the capillary regime (large frequencies). At lower frequencies (the mixed gravity-capillary regime), a sequence of sixfold (hexagonal), eightfold, ...patterns are predicted. For even lower frequencies (gravity waves) a stripe pattern is again selected. Our predictions of the stability regions of the various patterns are in quantitative agreement with recent experiments conducted in large aspect ratio systems.     

Berry phase and traversal time in asymmetric graphene structures

The Berry phase and the group-velocity-based traversal time have been calculated for an asymmetric non-contacted or contacted graphene structure, and significant differences have been observed compared to semiconductor heterostructures. These differences are related to the specific, Dirac-like evolution law of charge carriers in graphene, which introduces a new type of asymmetry. When contacted with electrodes, the symmetry of the Dirac equation is broken by the Schrödinger-type electrons in contacts, so that the Berry phase and traversal time behavior in contacted and non-contacted graphene differ significantly.     

Different amplitude and time distribution of the sound of light and classical music

Several pieces of different musical kinds were studied measuring A(t), the output amplitude of a peak detector driven by the electric signal arriving to the loudspeaker. Fixed a suitable threshold , we considered N(A), the number of times that , each of them we named event and N(t), the distribution of times t between two consecutive events. Some N(A) and N(t) distributions are displayed in the reported logarithmic plots, showing that jazz, pop, rock and other popular rhythms have noise-distribution, while classical pieces of music are characterized by more complex statistics. We pointed out the extraordinary case of the aria “La calunnia è un venticello”, where the words describe an avalanche or seismic process, calumny, and the rossinian music shows N(A) and N(t)distribution typical of earthquakes. Received 10 March 2000     

Multiphonon effects on dispersion and Faraday rotation associated with point-imperfections

Here we consider effects of phonons on the absorption, dispersion and Faraday rotation due to the model imperfection considered previously [1]. To make the problem tractable, we assumed that the phonons have a single frequency and Γ⁺₁ symmetry. The temperature assumed is 0 K. Detailed calculations are given which show an asymmetry in dispersion and in the rotation which does not appear unless explicit phonon effects are considered. Phonon fine structure appears in all three curves, which can only be eliminated by assuming a very large “damping” factor relative to the classical value. We attribute the large value to be caused by the phonon dispersion, i.e. a range in the frequency not explicity included in our calculations.     

Modulation and suppression of weak Cotton-Mouton effect by Faraday rotation

Polarization of electromagnetic waves in magnetized plasma is studied in conditions, when Cotton-Mouton effect is weak enough as compared with Faraday one. Evolution of polarization state is described by new mathematical approach, namely, by angular variables technique (AVT) which describes evolution of the angular parameters of polarization ellipse in magnetized plasma. The method of consequent approximations is applied, which uses the ratio (Ω _⊥/Ω ₃) of Cotton-Mouton and Faraday terms, as a small parameter of a problem and allows obtaining simple analytical expressions for azimuthal and ellipticity angles in frame of the first and second approximations. The phenomenon of ellipticity modulation and suppression by Faraday rotation is revealed, which consists in ellipticity decreasing for stronger Faraday rotation, what makes polarization closer to linear one. Numerical illustration of the phenomenon are presented. It is shown that account of the second-order terms of the method of consequent approximation provides an accuracy better than 1% even in conditions, when small parameter Ω _⊥/Ω ₃ achieves the value 1/4.     

法拉第效应实验装置中光路的设计

根据目前多数法拉第效应实验装置没有磁致旋光与自然旋光区别的实验功能，设计了特殊的光路．实现了磁致旋光和自然旋光的区分，且光路调节容易．现象直观清晰．