DISTRIBUTION FUNCTION OF A DRIFTING ELECTRON-GAS FOR GENERAL ENERGY-BAND STRUCTURES

The usual application of the Lei-Ting balance equation method for treating electron transport problems makes use of a Fermi distribution function for the electron motion relative to the center of mass. It is pointed out that this presumes the existence of a moving frame of reference that is dynamically equivalent to the rest frame of reference, and this is only true for electrons with a constant effective mass. The method is thus inapplicable to problems where electrons governed by a general energy-band dispersion E(k) are important (such as in miniband conduction). It is demonstrated that this difficulty can be overcome by introducing a distribution function for a drifting electron gas by maximizing the entropy subject to a prescribed average drift velocity. The distribution function reduces directly to the usual Fermi distribution for electron motion relative to the center of mass in the special case of E(k)=($) over bar h(2)\k\(2)/2m*. This maximum entropy treatment of a drifting electron gas provides a physically more direct as well as a more general basis for the application of the balance equation method.

BAND DISPERSION IN THE RECURSION METHOD

The advantages of the supercell model in employing the recursion method are discussed in comparison with the cluster model. A transformation for changing complex Bloch-sum seed states to real seed states in recursion calculations is presented and band dispersion in the recursion method is extracted with use of the Lanczos algorithm. The method is illustrated by the band structure of GaAs in the empirical tight-binding parametrized model. In the supercell model, the treatment of boundary conditions is discussed for various seed-state choices. The method is useful in applying tight-binding techniques to systems with substantial deviations from periodicity.

Chirped fiber Bragg gratings for optical fiber dispersion compensation

The use of alpha-power chirped fiber Bragg gratings for dispersion cancellation in an optical fiber link is discussed. Numerical and theoretical investigation of recompressing the dispersion-broadened pulse by using alpha-power chirped gratings is made, which shows that, the dispersion-broadened Gaussian pulse after 100 km standard fiber (with zero dispersion at lambda = 1.3 mu m) trnasmission at lambda = 1.55 mu m with initial width of T-FWHM = 33ps (full width at half maximum) can be perfectly recompressed with the peak reflectivity of 82% by using a 30 mm long alpha-power chirped fiber grating with proper a value and optimal grating parameters.

Design and optimization of highly nonlinear low-dispersion crystal fiber with high birefringence for four-wave mixing

We have proposed a novel type of photonic crystal fiber (PCF) with low dispersion and high nonlinearity for four-wave mixing. This type of fiber is composed of a solid silica core and a cladding with a squeezed hexagonal lattice elliptical airhole along the fiber length. Its dispersion and nonlinearity coefficient are investigated simultaneously by using the full vectorial finite element method. Numerical results show that the proposed highly nonlinear low-dispersion fiber has a total dispersion as low as +/- 2.5 ps nm(-1) km(-1) over an ultrabroad wavelength range from 1.43 to 1.8 mu m, and the corresponding nonlinearity coefficient and birefringence are about 150 W-1 km(-1) and 2.5 x 10(-3) at 1.55 mu m, respectively. The proposed PCF with low ultraflattened dispersion, high nonlinearity, and high birefringence can have important application in four-wave mixing. (C) 2010 Optical Society of America

Numerical investigation of particle velocity distributions in aeolian sand transport

Particle velocity distribution in a blowing sand cloud is a reflection of saltation movement of many particles. Numerical analysis is performed for particle velocity distribution with a discrete particle model. The probability distributions of resultant particle velocity in the impact-entrainment process, particle horizontal and vertical velocities at different heights and the vertical velocity of ascending particles are analyzed. The probability distributions of resultant impact and lift-off velocities of saltating particles can be expressed by a log-normal function, and that of impact angle comply with an exponential function. The probability distribution of particle horizontal and vertical velocities at different heights shows a typical single-peak pattern. In the lower part of saltation layer, the particle horizontal velocity distribution is positively skewed. Further analysis shows that the probability density function of the vertical velocity of ascending particles is similar to the right-hand part of a normal distribution function, and a general equation is acquired for the probability density function of non-dimensional vertical velocity of ascending particles which is independent of diameter of saltating particles, wind strength and height. These distributions in the present numerical analysis are consistent with reported experimental results. The present investigation is important for understanding the saltation state in wind-blown sand movement. (C) 2009 Elsevier B.V. All rights reserved.