Micro-lens arrays generated by UV laser irradiation of doped PMMA

Micro-lenses with well-defined optical parameters are generated on polymethylmethacrylate (PMMA) substrates doped with diphenyltriazene (DPT) by controlled use of a swelling effect generated under conditions of subablative excimer laser illumination. The surface profiles depend on the laser spot size and energy density. A sensitively balanced combination of matrix softening, substrate volume expansion due to photochemical nitrogen release, and surface tension is responsible for the final shape of the lenses. Complete arrays of identical lenses with 15 μm diameters and a focal length of 30 μm are produced by irradiation of (0.25 wt. %) DPT-PMMA with a single laser pulse at a wavelength of 308 nm and a fluence of 3 J/cm². It is shown experimentally and theoretically that appropriate volume expansion is possible without introducing internal light scattering due to the formation of small bubbles. Received: 7 April 1999 / Accepted: 8 April 1999 / Published online: 5 May 1999     

Bestimmung des Harnstoffs

Ohne Zusammenfassung     

Enclosure of the Zero Set of Multivariate Exponential Interval Polynomials

The zero set of one general multivariate exponential polynomial with interval coefficients is enclosed by unions and intersections of closed half-spaces. Tighter enclosures are derived in the bivariate case. Common zeros of polynomial systems can be located by an appropriate intersection of these enclosure sets in an appropriate space. The resulting domains are directly brought into polynomial equation solvers.     

Plasma effects in picosecond-femtosecond UV laser ablation of polymers

Laser ablation of polyimide (PI) and polymethyl-methacrylate (PMMA) at 248 nm with pulse lengths ranging from 200 fs to 200 ps was investigated. The measured ablation rates show minima for pulse lengths of about 5 ps (PMMA) or 50 ps (PI).The reflected fraction of the ablating laser pulse was measured as a function of the pulse length. In the case of PMMA maximum reflectance corresponds to a minimum ablation rate.This behavior can be explained by a dynamic plasma reflection model: A fast build up of a dense plasma is followed by high obscuration for a brief transition time and a self-regulating opacity for the rest of the pulse. This model of plasma mediated ablation leads to a ^1/4-dependence of the ablation rate at fixed fluence, which fits very well to the measured data, in particular if an extension to nanosecond ablation data of PI and PMMA is considered. PACS 52.50.Jm; 61.80.Ba; 42.65.Re     

Abelian and Tauberian theorems for a class of integral transforms

Extending the Wiener-Ganelius method we give Abelian and precise Tauberian remainder results for a class of Fourier kernels which includes the Hankel transform $\text{?(x) = ∫}{}_0{}^{\mathrm{\infty }}\text{√xu J}{}_{\mathrm{r}}\text{(xu) ?(u) du, v ? ?}\text{1}\text{2}$. Further, we discuss applications to Fourier series and integrals.