Production of radially or azimuthally polarized beams in solid-state lasers and the elimination of thermally induced birefringence effects

Production and amplification of radially and azimuthally (tangentially) polarized laser beams are demonstrated. Based on the different focusing between radially and tangentially polarized light in thermally stressed isotropic laser rods, Nd:YAG laser oscillators were developed to produce low-loss stable oscillation in a single polarization. Pure radially polarized light at 70 W with M2 = 2 and on-axis impure radially polarized light at 150 W with M2 = 2.5 were achieved. The radially polarized beams were then amplified while good beam quality and polarization purity were retained. Complete elimination of thermal-birefringence-induced aberrations was demonstrated. This should allow much better beam quality from rod-based high-power lasers.     

Existence and uniqueness results for large solutions of general nonlinear elliptic equations

We study under what condition there exists a solution of -u+f(u)=0 in a domain which blows-up on the boundary, independently of the regularity of the boundary, and we provide criteria for uniqueness. We apply our results to the case f(u)= e^au.     

The density of 0's in recurrence double sequences

Let be a double sequence over a finite field satisfying a linear recurrence with constant coefficients, with at most finitely many nonzero elements on each row. Given a nonzero element g of , we show how to obtain an explicit formula for the number of g's in the first qⁿ rows of A. We also characterize the cases when the density of 0's is 1.     

Preference Order Stochastic Knapsack Problems: Methodological Issues

A preference order dynamic programming model proposed in the literature for solving stochastic knapsack problems is shown to be somewhat limited from both the methodological and computational points of view. A counterexample is presented contradicting the optimality of a procedure designed for normal variates.     

Bousfield localization as an algebraic closure of groups

We show that the notion ofHZ-local groups due to A. Bousfield which is based on considerations from algebraic topology can be defined and understood in terms of solubility of certain systems of equations overG.     

‘Large’ solutions of semilinear elliptic equations: Existence,uniqueness and asymptotic behaviour

Dedicated to Professor Shmuel Agmon     

The product of a convergent sequence of matrices

We will prove that the normalized product of a convergent sequence of matrices transforms most vectors into the subspace of generalized eigenvectors with eigenvalues of maximal absolute value.     

Patterns of diffractive production

We discuss diffractive production in the context of two-component models. After defining the class of models that we consider and discussing their general properties, we develop integral equations for the generating functions of diffractive processes. We consider single and double diffraction and two fireball production. We investigate the behavior of the partial cross sections for n-particle production in all three cases and obtain a successful fit to recent data.