Direct measurement of free carrier nonlinearity in semiconductor-doped glass with picosecond pump-probe Z-scan experiment

We report the direct measurement of free carrier nonlinearity in a semiconductor-doped glass with picosecond pump-probe Z-scan experiment. A strong Z-scan signal from a weak and time delayed probe beam is observed. The probe beam Z-scan signal is comparable in magnitude to the Z-scan signal of the intense pump beam, clearly showing the dominance of the effective fifth order nonlinearity due to the pump beam generated free carriers in the overall nonlinear response of semiconductor-doped glass. The estimated magnitude of the fifth order nonlinearity is consistent with that obtained from earlier reported experiments.     

Localization in one-dimensional Soukoulis-Economou model with incommensurate potentials

The localization of one-dimensional Soukoulis- Economou model with incommensurate potentials ε_n=1.9 [cos(2πωn)+1/3cos(4πωn)], where ω=σ≡(√5?1)/2 is studied by the use of two methods: the scaling analysis of bandwidth in successively periodic approximation, and the mutlifractal analysis of wave functions. A mobility edge is found in a gap of the fifth subband. We found that all the states at higher energies are localized while all those at lower energies are extended. These results are different from those given in previous works.     

The Lorenz model for single-mode homogeneously broadened laser: analytical determination of the unpredictable zone

We have applied harmonic expansion to derive an analytical solution for the Lorenz-Haken equations. This method is used to describe the regular and periodic self-pulsing regime of the single mode homogeneously broadened laser. These periodic solutions emerge when the ratio of the population decay rate ? is smaller than 0:11. We have also demonstrated the tendency of the Lorenz-Haken dissipative system to behave periodic for a characteristic pumping rate “2C _P ”[7], close to the second laser threshold “2C _2th ”(threshold of instability). When the pumping parameter “2C” increases, the laser undergoes a period doubling sequence. This cascade of period doubling leads towards chaos. We study this type of solutions and indicate the zone of the control parameters for which the system undergoes irregular pulsing solutions. We had previously applied this analytical procedure to derive the amplitude of the first, third and fifth order harmonics for the laser-field expansion [7, 17]. In this work, we extend this method in the aim of obtaining the higher harmonics. We show that this iterative method is indeed limited to the fifth order, and that above, the obtained analytical solution diverges from the numerical direct resolution of the equations.     

Microwave generation analysis with higher order dispersion parameters in two cascaded Mach-Zehnder modulators

Dispersion is one of the major limiting factors for microwave/millimeter wave generation in microwave photonics. In this paper, we analyze the individual and combined effect of second order-, third order-, fourth order and fifth order dispersion parameter on microwave/millimeter wave generation. We have used the two cascaded Mach-Zehnder modulators in our proposed model, which have been not discussed earlier. Intensity at the output of photodetector versus modulation depth (β) with effects of dispersion parameters have been discussed and it has been found that output intensity of photodetector reduces when dispersion term up to fifth order are added.     

High order vibrational matrix elements for diatomic molecules; dipole moment function and transition moments of CO

The fifth and sixth-order contributions to the vibrational matrix elements are obtained for the transitions v→v'(v'?v+4) using an eight power internuclear Dunham potential and a quartic power series expansion of the dipole moment function. The results for the dipole moment coefficients M₀ to M₄ of CO and the transition moments R_v^v' (with v=5, 10, 20) deduced from a calculation including succesively third, fourth, fifth and sixth-order perturbation theory are compared. The validity of these results is discussed.Using a quintic dipole moment function, general expressions for the vibrational matrix elements corresponding to the transitions v→v'(v'? v+5) are also presented and the influence of these contributions on the calculation of the dipole moment coefficients as well as the hot band transition moments of CO is shown.     

Various types of five-dimensional warp factor and effective Planck scale

Based on the assumption that the warp factor of four-dimensional spacetime and the one of fifth dimension are tied through a parameter α, we consider five-dimensional gravity with a 3-brane coupled to a bulk scalar field. For arbitrary value of α, the form of the warp factor is implicitly determined by hypergeometric function. Concretely, we show that the warp factor becomes explicit form for appropriate value of α, and study the relation between four-dimensional effective Planck scale and the brane tension. This setup allows the possibility of extending the diversity of brane world.     

Algebraic and geometric properties of Bethe Ansatz eigenfunctions on a pentagonal magnetic ring

The exact solution of the eigenproblem of the Heisenberg Hamiltonian for the XXX model in the case of a magnetic ring with N=5 nodes is presented in a closed algebraic form. It is demonstrated that the eigenproblem itself is expressible within the extension of the prime field Q of rationals by the primitive fifth root of unity, whereas the associated Bethe parameters, i.e. pseudomomenta, phases of scattering, and spectral parameters, require some finite field extensions, such that the nonlinearity remains algebraic rather than transcendental. Classification of exact Bethe Ansatz eigenstates in terms of rigged string configurations is presented.     

Synthesis of broadband interference filters: II. Suppression of high reflection bands of the fourth,fifth, and sixth orders

The spectral properties of multilayer interference systems formed by multiple replication of the symmetric ternary period ABCBA are investigated. The problem of synthesis of structures with suppression of adjacent bands of high reflection of the fourth, fifth, and sixth orders among their spectral characteristics is solved. It is shown that there are only six variants of selection of the optical thicknesses of layers in a period. When the high reflection bands of the fourth, fifth, and sixth orders are suppressed, the high reflection band of the first order remains in only four cases. The values of refractive indices of layers for which the problem hasa solution are found. The refractive indices of layers in all six cases are described by different relations determining the dependence of the refractive index of one of the components on arbitrarily selected refractive indices of the other two components.     

Fundamental length hypothesis and new concept of gauge vector field

Through an analysis of quantum field theory with “fundamental length” l[1–10], a new concept of gauge vector field is determined. The electromagnetic field is considered in detail. The new electromagnetic potential turns out to be a 5-vector associated with the De Sitter group SO(4,1). The extra fifth component, called τ-photon, similar to the scalar and longitudinal photons, does not correspond to an independent dynamical degree of freedom. Gauge-invariant equations of motion for all components of the electromagnetic 5-potential are found. Though the new gauge group remains Abelian, it is nevertheless larger than the conventional gauge group. In particular, the new gauge transformations intrinsically depend on the fundamental length l. Therefore one can consider them as a base for modification of QED at small distances (?l) in a profound way. The underlying physics becomes much richer due to the appearance of new interactions mediated by the τ-photons [14].     

Complex Cabibbo angle and CP violation in a class of gauge theories

A class of gauge theories which incorporate CP violation is discussed. The CP violating effects arise as a consequence of performing a different rotation in the SU(3) space for the left- and right-handed strangeness conserving charged currents. It is suggested that it is possible to understand the smallness of these effects in the $\text{K}{}_0\text{?}\text{K}{}_0$ system even in the presence of a large relative phase between the left- and right-handed weak currents. The electric dipole moments of hadrons are of fifth order in the semi-weak coupling constant whereas for leptons they are of seventh order. These electric dipole moments are considerably smaller than the experimental upper limits.     

Nonlinear dynamos: A complex generalization of the Lorenz equations

Plane nonlinear dynamo waves can be described by a sixth order system of nonlinear ordinary differential equations which is a complex generalization of the Lorenz system. In the regime of interest for modelling magnetic activity in stars there is a sequence of bifurcations, ending in chaos, as a stability parameter D (the dynamo number) is increased. We show that solutions undergo three successive Hopf bifurcations, followed by a transition to chaos. The system possesses a symmetry and can therefore be reduced to a fifth order system, with trajectories that lie on a 2-torus after the third bifurcation. As D is then increased, frequency locking occurs, followed by a sequence of period-doubling bifurcations that leads to chaos. This behaviour is probably caused by the Shil'nikov mechanism, with a (conjectured) homoclinic orbit when D is infinite.     

Theory of higher-order stark effect of symmetric top molecules

The Stark effect formula for symmetric top molecules, which is correct to the fifth order of an external electric field, is given. The formula is applicable to linear molecules without or with electronic angular momenta coupled in Hund;s case a. Numerical tables are given for the special case of linear molecules without any electronic angular momentum. The effect of centrifugal stretching is considered to the first order. It is shown that our perturbation formula, which is correct to the sixth order of an external electric field, is good even when μE/B is about 1.     

The anisotropic heisenberg model: High temperature series expansions in the regime of planar ordering

The procedure of Betts and coworkers, to obtain the high temperature series expansions for the XY-model is extended to the anisotropic Heisenberg model. On the f.c.c. lattice the series for the free energy and the fluctuation of the order in the XY-plane are derived up to sixth and fifth order in the inverse temperature, respectively. These series are too short to be analysed with success.     

Squeezing and sub-Poissonian effects up-to fourth order in fifth harmonic generation

The concept of squeezing of the electromagnetic field is investigated in fundamental mode in fifth harmonic generation with the approximation |gt|²?1, where g is coupling constant and t, the interaction time between waves during the process. It has been found that squeezing occurs in amplitude, amplitude-squared, amplitude-cubed and fourth-order amplitude states of the field for selective phase values of field amplitude of fundamental mode. The dependence of squeezing on the photon number has also been investigated and found to be sub-Poissonian in nature. The signal to noise ratio has been studied in different order. It is found that the signal to noise ratio is higher in lower order.     

Electronic structure,field-induced magnetization density and neutron magnetic form factor of palladium

The magnetic field induced magnetization density and neutron magnetic form factor of Pd metal is obtained from an abinitio APW energy band study of its electronic structure and properties. The magnetization consists of the spin density calculated for states on the Fermi surface and a much smaller orbital contribution. The solid state wavefunctions are found to yield a spatial localization of the spin density which is greater than that of the very contracted Hartree-Fock density of the free Pd²⁺ ion. The theretical magnetic form factor, which is dominated by the contribution of the fifth band, is found to be in excellent agreement with the measurements of Cable, Wollan, Felcher, Brun and Hornfeldt.     

Generation of harmonics of femtosecond radiation from the surface of aluminum targets

The results of a study of the generation of harmonics from a laser plasma resulting from the interaction of radiation of femtosecond duration (λ=1.06 μm, t=475 fs, and I～2×10¹⁷ W cm^?2) with aluminum targets are presented. The observed frequency shift of harmonics to the short-wavelength region (1.6 and 5.1 nm for the second and fifth harmonics, respectively) is determined by a collisionless absorption resulting from an anomalous skin effect. The efficiencies of conversion into the second and fifth harmonics in an s-polarized pumping field were lower than the conversion efficiencies in a p-polarized pumping field by a factor of eight and a factor of two, respectively (for intensities I<10¹⁷ W cm^?2). With a further increase in the pumping intensity, these values decreased to 0.8 and 0.5, respectively. The mechanisms of such behavior of the conversion process are considered.     

Analytical approach to the Curie temperature Tc(S,d) of spin-S Ising model on d-dimensional hypercubic lattice

An effective mean-field theory based on cumulant expansion (EMFC) is applied to the spin-S Ising model on general d-dimensional hypercubic lattice. It gives straightforwardly the analytical expressions T_c^(ν)(S,d) that approach the Curie temperature order by order. For general d, the results up to fifth order are given. Numerical results up to seventh order for d=2,3,4 are presented.     

On multivortex solutions of the weierstrass representation

The connection between the complex sine-Gordon equation on the plane associated with a Weierstrass-type system and the possibility of constructing several classes of multivortex solutions is discussed in detail. It is shown that the amplitudes of these vortex solutions represented in polar coordinates satisfy the fifth Painlevé equation. We perform the analysis using the known relations for the Painlevé equations and construct explicit formulas in terms of the Umemura polynomials, which are τ functions for rational solutions to the third Painlevé equation. New classes of multivortex solutions to the Weierstrass system are obtained through the use of this proposed procedure.     

Transcendent self-dual solutions for SU(2) gauge fields on euclidean four-dimensional space

By applying the method of separation of variables, we find a particular class of solutions of Yang's equations in the R-gauge for self-dual SU(2) static, axisymmetric gauge fields on euclidean four-dimensional flat space. The solutions obtained are depending functionally on a particular form of the fifth Painlevé transcendent.