We demonstrate that the propagation of a light wave in an elliptic gradient-index medium can be regarded as a joint fractional Fourier transform. The distinctive features of the Wigner distributon function and the recurrence of the original function are analyzed qualitatively. q1998 Elsevier Science B.V. All rights reserved.

We present a local density functional calculation of the effect of an external electric field on the work function change of Pd and Ag adsorption on an Al(001) surface. The adsorption of K has also been considered for comparison. We found that the work functions for all the systems increased linearly when the strength of the external electric field was increased. Since the polarized dlectrons at the interstitial regions between the adsorbate and substrate for Pd/Al(001) and Ag/Al(001) react to the external electric field differently, the subtle differences between Pd/Al(001 and Ag/Al(001) bondings has been characterized through the comparison of the slopes of the work function change versus electric field.

A technique based on the path-integral effective-potential theory to calculate the thermodynamic properties of a linear chain of atoms is extended to include all-neighbor interactions. The configuration averages are performed using the classical Monte Carlo technique. The theory is applied to a system interacting with a Mie-Lennard-Jones potential to make contact with earlier work. Results for the internal energy and specific heat are presented and compared with those using only nearest-neighbor interactions and the quantum Monte Carlo method. This is a useful step toward the application of the effective-potential theory to realistic systems with long-range interactions.

In this paper the Laguerre-Gaussian (LG) series representation of the twodimensional fractional Fourier transform is derived from conventional ordinary Fourier transform in polar coordinates. The kernel of this series representation is constituted by Laguerre-Gaussian functions, from which the series representation of a fractional Hankel transform can be easily derived. The connection between the gradient-index medium and the LG series representation is illustrated as an example of its applications.

Using density functional calculations, we found that the ground state configuration of some bcc (001) surfaces are field dependent because different configurations experience different Stark shifts of surface states. When the W (001) surface is positively biased, an external electric field stabilizes a cs2 3 2d array of surface vacancies, so that the ground state is no longer the well-established "Debe-King" model. Similar behavior is found for Mo (001), but not for Nb (001). The field-induced change of ground state provides a natural explanation for the anomalous behavior of W (001) inside field ion microscopes.