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We will demonstrate a Runge Kutta based algorithm for solving the Mone-Ampere-Problem. The method is utilizing its parabolic type. We will show the exact numerical solving method down to each step. The derived solution is used in the context of laser beam shaping to reshape any given input distribution to arbitrary output distributions free of any constraints other than diffraction, which includes a true black in said distribution. The presented algorithm will give the required phase which will be used to verify the solution theoretically via diffraction integral and practically via Spatial Light Modulator (SLM).

The laser is an extremely suitable non-contact tool for fast and automated in-line processes for example used to improve the efficiency of solar cells. With ultra-short pulsed laser radiation it is possible to decrease the reflectivity by modifying the surface topology of silicon. For the proposed modification, the optimum process window for altering the silicon surface topology on a micrometer scale is found at small laser fluencies at finite repetition rates. A promising up scaling method is process parallelization using in parallel a multiple set of interaction zones with the optimized process characteristics for single process interaction. Based on the single process, required laser process parameters and optical parameters for parallel processing are derived theoretically in order to enable a wafer processing in standard cycle times. Exemplarily 5-inch mc-silicon solar wafers are machined using a linear 7-times diffractive optical element (DOE), and in a second step solar cells are built up to determine the efficiency gain by the laser surface modification. A preliminary absolute efficiency gain of Δη > 0.2 % is achieved.

Nanoscale laser processing of wide-bandgap materials with temporally shaped femtosecond laser pulses is investigated experimentally. Femtosecond pulse shaping in frequency domain is introduced and applied to two classes of shaped pulses relevant to laser nano structuring. The first class, characterized by a symmetric temporal pulse envelope but asymmetric instantaneous frequency allows us to examine the influence of the sweep of the photon energy. In contrast, asymmetric temporal pulse envelopes with a constant instantaneous frequency serve as a prototype for pulses with time-dependent energy flow but constant photon energy. In our experiment, we use a modified microscope set up to irradiate the surface of a fused silica sample with a single shaped pulse resulting in ablation structures. The topology of the laser generated structures is measured by Atomic Force Microscopy (AFM). Structure parameters are investigated as a function of the pulse energy and the modulation parameters. We find different thresholds for surface material modification with respect to an asymmetric pulse and its time reversed counterpart. However, we do not observe pronounced differences between up- and down-chirped radiation in the measured structure diameters and thresholds.

Modifications of bulk aluminum irradiated well above ablation threshold (F . cm -2 ) have been investigated in situ by means of shadowgraphy and transient quantitative phase microscopy (TQPm) using ultrafast laser radiation ( t p =80 fs, λ=800 nm). This novel pump-probe technique enables quantitative time-resolved measurements of object's properties, e.g. dimensions of melt droplets and layer thickness or transient refractive index changes. A series of time-resolved phase images of vaporized material and/or melt, which are induced by n =1..8 pulses on an aluminum target, are obtained using TQPm. Dynamics and characteristics of melting, dependence of the ablated material volume on process parameters and thereby induced structural modifications have been studied. An increase of material ejection rate is observed at delay time of approximately τ=300 ns and τ>800 ns after the incident pulse. Transient refractive index modifications have been investigated in technical glass (Schott D263) by means of TQPm. By using high-repetition rate ultra-short pulsed laser radiation (t p =400 fs, λ=1045 nm, f rep =1 MHz) focused by a microscope objective (w 0 ≈ 4 μm) heat accumulation and thereby glass melting as well as welding is enabled. Transient optical phase variation has been measured up to τ=2.1 μs after the incident pulse and can be attributed to the generation of free charge carriers and compression forces inside glass.

Lighting applications like OLED or on silicon for electro-opti cal applications need a reproducible sealing process. The joining has to be strong, the permeability for gasses and humidity very low and the process itself has to be very localized not affecting any organic or electronic parts inside the sealed region. The actual sealing process using glue does not fulfill these industrial needs. A new joining process using ultra-fast laser radiation offers a very precise joining with geometry dimensions smaller than 50 µm. Ultra-fast laser radiation is absorbed by multi-photon absorption in the glass. Due to the very definite threshold for melting and ablation the process of localized heating can be controlled without cracking. Repeating the irradiation at times smaller than the heat diffusion time the temperature in the focus is in creased by heat accumulation reaching melting of the glass. Mowing the substrate relatively to the laser beam ge nerates a seal of re-solidified glass. Joining of glass is achieved by positioning the laser focus at the interface. A similar approach is used for glass-silicon joining. The investigations presented will demonstrate the joining geometry by microscopy of cross-sections achieved by welding two glass plates (Schott D263 and AF45) with focused IR femtosecond laser radiation (wavelength O = 1045nm, repetition rate f = 1 MHz, pulse duration t

Irradiation of metals with ultrashort laser pulses reveals a variety of versatile microscopic processes compared to longer pulses. In particular, the impact of some material-specific characteristics, such as the electron-phonon coupling, seems to get more significance in order to meet the machining requirements. Finding the optimal process parameter area has been therefore a dominating problem in materials processing with sub-picosecond laser radiation. Ablation of bulk metals (Al, Cu) has been investigated in-situ by means of high-resolution pump-probe photography using pump laser radiation of pulse duration t p =80 fs, at wavelength of 820 nm. This technique enables direct visualization of laser-induced processes up to 1 μs after the interaction of a single laser pulse with material. Variation of the fluence of the laser radiation, behavior and time characteristics of melting and post-melting processes have been matter of research. Depending on metal-specific parameters, qualitatively different ablation phenomena have been observed. Structural analysis by electron and optical microscopies reveals rosette-like surface structures showing the morphology of the ablated regions. The temporal development of the ablation dynamics can be conditionally categorized into different characteristic time regions. Particularly, laser induced melt injection has been observed in the time range of 700 ns to 1.0 μs after the initial laser-metal interaction.

Laser labelling inside glass induces micro-cracks by high energy densities in the focus. The micro-cracks reduce the mechanical stability of glass. Light scattering allows the observer to perceive the cracks as white pixels. Coloured marking of glass in this manner is not possible. Coloured marking inside glass by changing the oxidation state of the metal ions locally in the focus does not weaken the mechanical properties of the glass. Two kind of glass systems, lime-natron-silicate and borosilicate with 0.5 % mass-content of doping are investigated. The simultaneous presence of donators and acceptors allows a transition of electrons between polyvalent ions, and can lead to permanent colour-centres inside the glass, due to the fact that the absorption of the polyvalent ions is changed by the laser-induced conversion process. For this purpose a 3 ω Nd:YAG (wavelength λL = 355 nm, pulse duration t = 10 to 80 ns) and a Ti:Sapphire solid-state laser (wavelength λL = 810 nm, pulse duration t = 200 fs) are used. The radiation parameters and the chemical composition of the glass (mainly doping) are the dominant factors to generate coloured marking. The transmittance as a function of the fluence and the change of the absorption coefficient is measured and gives a statement of the colourshade. Further the difference between lime-natron-silicate and borosilicate glass (same doping variety) is examined. Actually mauve, yellow, red-brown an grey colouring can be produced. Cracks in the microstructure of glass can also be the cause for brown colour-centres generating.

Temporal and spatial changes in the matrix of glasses (BK7 glass, fused silica, quartz) and sapphire are investigated during and after irradiation by pulsed laser radiation (100 fs < t p < 3 ps) at the wavelength = 800 nm using high-speed photography, transient absorption spectroscopy, and Nomarski-microscopy in order to visualize the changes of optical properties, the plasma formation and expansion, the stress formation, the modification, and the cracking as well. Depending on the excitation conditions the glasses and sapphire exhibit different excitation and relaxation channels including various types of defect centers. Compared to laser radiation with pulse durations in the nanosecond regime the glasses and sapphire are heated within the irradiation zone for many nanoseconds resulting in modification by an increase of the refractive index without cracking, enabling the generation of photonic structures within the bulk. Irradiation at pulse durations in the picosecond regime originates in cracking enabling the marking and microstructuring in the bulk and at the surface. Keywords: glasses, sapphire, fs- and ps-laser radiation, interaction phenomena, modification, microstructuring

Sub-wavelength (1/4*λ-3/4*λ) laser induced periodic surface structures are generated by irradiation of either bulk fused silica and silicon or Er:BaTiO3 thin films by scanning a tightly focused beam (Θ = 1 μm) of femtosecond laser radiation (λ = 800 nm, tp = 100 fs) on the surface. The ripple pattern extends coherently over many overlapping laser pulses parallel and perpendicular to the polarization of the laser radiation. The dependence of the ripple spacing on the spacing of successive pulses, the direction of polarization and the properties of the material is investigated. The evolution of the ripples is investigated by applying pulse bursts with 1 - 20 pulses. The development conditions of the stuctures are specified and possible mechanisms of ripple growth are discussed.© (2004) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

In the harmonic generation using nonlinear optical crystals, phase-matching technique is indispensable for obtaining high conversion efficiency. As the first step of our study, we have investigated crystal temperature variation induced by laser absorption and its influence on conversion efficiency and beam profile in second harmonic generation (SHG) by solving the coupling problem composed of heat conduction equation and complex amplitude equations. In this study, we focused on the declination of irradiation angle of laser from the phase matching angle, which is equivalent to the declination of cut angle of crystal. The influences of angle declination and temperature rise of the crystal on SHG characteristics were examined by supposing KTiOPO 4 (KTP) crystal. Main results obtained are as follows: When the angle declination is only 0.1 deg, conversion efficiency easily decreases to half that under perfect phase-matching condition. Significant distortion of output beam profile of second harmonic is also caused by the angle declination. This essential problem on output beam profile should be considered in precision microfabrication. Influences of angle declination and temperature change on phase mismatching are superposed. Our analysis is useful to elucidate such compounded and complicated phenomena in frequency conversion. A possibility of cancellation of phase mismatching due to angle declination by keeping crystal temperature higher than phase matching temperature was suggested through numerical examples.

The change of the matrix structure of glass is investigated during and after irradiation with ultrashort pulsed laser radiation (100 fs t p ; < 3 ps) at the wavelength λ = 810 nm. The dynamics of the plasma expansion and the stress formations are visualized by time-resolved Normarski-photography. Optical microscopy visualizes the structural changes in glass. The spatial stress distribution and the refractive index change are shown in the time range 100 fs < t < 120 ns. The ionization state of atoms and/or the formation of color centers has been investigated by transient absorption spectroscopy (TAS) in the time regime 100 fs < t < 120 ns. The temporal change of the spectra shows different regimes, which can be explained by the electron and phonon relaxation.

Modifications and microstructures are generated on the surface and in the volume of silicate glasses using pulsed UV laser radiation of small pulse length. During the interaction of pulsed excimer laser radiation and frequency-trippled Nd:YAG laser radiation with intensities below the removal-threshold of the cerium- and silver-doped multi-component silicate glass absorption centers in the UV are induced. Subsequent thermal treatment and wet chemical etching results in crystallization of the laser-illuminated absorbing region and in the fabrication of microstructures on the surface. Processing of sodalime- and boro-silicate glass with pulsed ArF excimer laser radiation and frequency-doubled Nd:YAG laser radiation with intensities above the removal-threshold leads to microstructures including the generation of microcracks on the surface and in the bulk. The dynamics and the transmission of the expanding plasma and changes in the refractive index of the glass are investigated with speckle photography using the pump and probe method. The determination of plasma emission and crack generation is carried out using high speed and Nomarski photography. Morphological and chemical properties of the debris generated under defined processing gas atmospheres are investigated with REM, white light interferometry, XPS and EPMA. Induced absorption and changes of the crystalline- phase are probed using optical-spectroscopy and XRD as well REM. On the basis of these investigations the processes of the generation of induced absorption centers and crystallization on the one hand and the generation of cracks and debris on the other hand as well as the quality of the produced microstructures is discussed.

Micromachining of SiC with 1(omega) , 2(omega) , 3(omega) -Nd:YAG laser radiation with pulse durations in the ps to ns regime is performed in various processing gas atmospheres as a function of processing variables showing the influence of the heat and pressure load onto the precision of geometric structures generated. The physical and chemical processes involved in micromachining with laser radiation are characterized by a machine vision system and the produced structures are analyzed by profilometry, optical and electron microscopy as well as X- photoelectron spectroscopy. 3D microstructures are produced by scanning and turning the laser beam onto the material surface, width of structures < 100 micrometers and surface roughness < 2 micrometers , for example, require an overlap < 0.8 independent of the type of processing gas under investigation.© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

The interaction of picosecond pulsed laser radiation with BK7 glass has been investigated. Focusing laser pulses with 40 picosecond pulse duration in BK7 glass leads to plasma and crack formation by evaporation and induced stress. The plasma dynamics is measured by pump and probe techniques using the speckle method with a time resolution of 50 Ps and a spatial resolution of 1 ?m. Plasma transmission and refractive index changes are measured during and after irradiation on a picosecond time-scale. The plasma emission is investigated on the time scale of 10 ps -500 ns by high-speed photography and by time-resolved spectroscopy. The morphology of the cracks is evaluated using Nomarski microscopy.

Drillings in zirconia coated Ni-superalloys is done by melt extraction with pulsed laser radiation provided by a Nd:YAG slab laser with microsecond pulse duration. This laser system distinguishes itself by a high beam quality and offers the possibility to investigate drilling of holes with a diameter of 200 micrometer by percussion drilling and trepanning. The quality of drilled holes, e.g. the heat affected zone (HAZ), the recast layer and the conicality, are presented. During drilling different process gases are used. The results in drilling velocities, melt thickness and chemical composition of the melting zone are shown for oxygen, argon and nitrogen by SEM and EDX. A numerical simulation of the trepanning process will be presented. The different time scales of the contributing physical processes related, for example, to the small melt film layer during trepanning are described. A coating is distributed on the multilayer system to protect the blade from recast. Aim of the investigation is the production of holes in a multilayer system, consisting of CMSX-4, VPS-MCrAlY and EB-PVD-zirconia. With this used laser system inclined holes up to 60 degrees in this layer system can be drilled. No recast layer and no spalling of the zirconia-layer are observed.

Microprocessing and film deposition with laser radiation of short wavelength and pulse length are investigated to present their process capabilities for the manufacturing of surface structures and layers within precision ceramic (BaTiO3, Si3N4, SiC) components. The microprocessing with fundamental (1(omega) ) and higher harmonic (2(omega) , 3(omega) ) Nd:YAG laser radiation (ns- and ps-pulses) is performed yielding structural dimensions below 20 micrometers during drilling and caving with the results related to the removal threshold fluence and the removal rate per pulse. The film deposition with excimer laser radiation ((lambda) L equals 248 nm, (tau) L equals 20 ns) achieves monolayer thin films of different properties according to the laser parameters and processing variables with the results related to deposit multilayer film systems. The properties of the structures and of the films are analyzed by profilometry, optical and electrical microscopy, as well as X-ray photoelectron spectroscopy. Examples are highlighted for various ceramics and discussed in view of applications of the structures and films generated.

The removal processes of Si3N4- and SiC-ceramics and tungstencarbide were investigated using 40 ps and 10 ns laser pulses. The threshold fluence for removal and the removal rate per pulse were determined. Changes in the chemical composition of the processed surfaces are described and the influence of the removal strategy on the processing results are discussed. Micro-structures were produced in combination with high- resolution optics and precision motion control systems. In SiC-ceramics grooves were produced with geometries smaller than 30 micrometer. In Si3N4-ceramics holes were drilled with diameters smaller than 6 micrometer. The influence of scanning velocity, overlap of the laser pulses and pulse energy on material removal and surface finish were discussed.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.