Symmetry of the Talbot effect and its applications

The Talbot effect is one of the most basic optical phenomena that has received extensive investigations both because its new results provide us more understanding of the fundamental Fresnel diffraction and also because of its wide applications. We summarize our recent results on this subject. Symmetry of the Talbot effect, which was reported in Optics Communications in 1995, is now realized as the key to reveal other rules for explanation of the Talbot effect for array illumination. The regularly rearranged-neighboring-phase-differences (RRNPD) rule, a completely new set of analytic phase equations (Applied Optics, 1999), and the prime-number decomposing rule (Applied Optics, 2001) are the newly obtained results that reflect the symmetry of the Talbot effect in essence. We also reported our results on the applications of the Talbot effect. Talbot phase codes are the orthogonal codes that can be used for phase coding of holographic storage. A new optical scanner based on the phase codes for Talbot array illumination has unique advantages. Furthermore, a novel two-layered multifunctional computer-generated hologram based on the fractional Talbot effect was proposed and implemented (Optics Letters, 2003). We believe that these new results should bring us more new understanding of the Talbot effect and help us to design novel optical devices that should benefit practical applications. (C) 2004 Society of Photo-Optical Instrumentation Engineers.

A novel method for measuring the coma of a lithographic projection system by use of mirror-symmetry marks

A novel method for measuring the coma of a lithographic projection system is proposed and the principle of the method is described. By utilizing mirror-symmetry marks, the adverse effects of axial aberrations on the coma measurement are avoided. Experimental results demonstrated that the method has high accuracy. Compared with TAMIS, the conventional technique used for coma measurement, the method is more reliable because the influences of the process factors on the lateral displacements have been considered. (c) 2006 Elsevier Ltd. All rights reserved.

Numerical simulation of wavefronts diffracted by apertures with circular symmetry

The numerical simulation of the wavefronts diffracted by apertures with circular symmetry is realized by a numerical method. It is based on the angular spectrum of plane waves, which ignored the vector nature of light. The on-axial irradiance distributions of plane wavefront and Gauss wavefront diffracted by the circular aperture have been calculated along the propagation direction. Comparisons of the simulation results with the analytical results and the experimental results tell us that it is a feasible method to calculate the diffraction of apertures. (c) 2006 Published by Elsevier GmbH.

I. Non-linear effects in a self-consistent calculation of SU_3 symmetry breaking in strong interaction coupling constants. II. Direct-channel reggeization of strong interaction scattering amplitudes

The thesis is divided into two parts. Part I generalizes a self-consistent calculation of residue shifts from SU₃ symmetry, originally performed by Dashen, Dothan, Frautschi, and Sharp, to include the effects of non-linear terms. Residue factorizability is used to transform an overdetermined set of equations into a variational problem, which is designed to take advantage of the redundancy of the mathematical system. The solution of this problem automatically satisfies the requirement of factorizability and comes close to satisfying all the original equations.

Part II investigates some consequences of direct channel Regge poles and treats the problem of relating Reggeized partial wave expansions made in different reaction channels. An analytic method is introduced which can be used to determine the crossed-channel discontinuity for a large class of direct-channel Regge representations, and this method is applied to some specific representations.

It is demonstrated that the multi-sheeted analytic structure of the Regge trajectory function can be used to resolve apparent difficulties arising from infinitely rising Regge trajectories. Also discussed are the implications of large collections of "daughter trajectories."

Two things are of particular interest: first, the threshold behavior in direct and crossed channels; second, the potentialities of Reggeized representations for us in self-consistent calculations. A new representation is introduced which surpasses previous formulations in these two areas, automatically satisfying direct-channel threshold constraints while being capable of reproducing a reasonable crossed channel discontinuity. A scalar model is investigated for low energies, and a relation is obtained between the mass of the lowest bound state and the slope of the Regge trajectory.