From geometrical optics, the laws of reflection and refraction, ray tracing techniques, conservation of energy within a bundle of rays, and the condition of constant optical path length provide a foundation for design of laser beam shaping systems. Geometrical optics design methods are presented for shaping the irradiance profile of both rotationally and rectangular symmetric laser beams. Applications of these techniques to design reflective and refractive laser beam shaping systems are presented.

We discuss what we believe are three most important factors effecting the difficulty of a beam shaping problem: scaling, smoothness, and coherence.

Geometrical optics - the laws of reflection and refraction, ray tracing, conservation of energy within a bundle of rays, and the condition of constant optical path length - provides a foundation for design of laser beam shaping systems. This paper explores the use of machine learning techniques, concentrating on genetic algorithms, to design laser beam shaping systems using geometrical optics. Specifically, a three-element GRIN laser beam shaping system has been designed to expand and transform a Gaussian input beam profile into one with a uniform irradiance profile. Solution to this problem involves the constrained optimization of a merit function involving a mix of discrete and continuous parameters. The merit function involves terms that measure the deviation of the output beam diameter, divergence, and irradiance from target values. The continuous parameters include the distances between the lens elements, the thickness, and radii of the lens elements. The discrete parameters include the GRIN glass types from a manufacturer's database, the gradient direction of the GRIN elements (positive or negative), and the actual number of lens elements in the system (one to four).

Analyzing of amplitude-phase characteristics of laser beam is topical in experimental physics and in a great number of laser applications, such as, for example, laser material treatment. The task of analyzing the amplitude-phase beam structure may be treated as that of analyzing the modal composition, if this is thought of as both analyzing individual modal powers and intermode phase shifts. In this paper the problem is tackled using a special diffractive optical element (DOE), called MODAN, matched to a group of laser radiation modes and their special combinations. The experimental results reported indicate that such an approach shows promise.

For the first time it can be shown, experimentally and theoretically, that the field of plane wave, which diffracted on the perfectly conducted half plane (Sommerfield's solution), is presented as a superposition of the half amplitude source wave and wave, which contains edge dislocation that is formed on the screen border and described by the complex Fresnel integral. These two waves are real waves, unlike traditional representation as sum geometric and boundary waves, and as we have shown, can be split and investigated experimentally. On basis of this new representation the problem of diffraction arbitrary beam on the perfectly conducted half plane was solved. It was shown (theoretically and experimentally) that a diffracted beam is presented as a sum of the source beam half amplitude and a beam contains edge dislocation that is caused by the border of the screen.

This contribution concentrates on modeling of diffraction processes in surface-relief gratings, occurring particularly within resonant regions. First, the characterization of mechanisms and diffraction processes is briefly presented, together with the regions with typical diffraction regimes, types of volume phase synchronism and their periodicity. The resonant regions are characterized by strong energy interchange processes (since new diffraction orders stat to become propagating), the diffraction efficiency behavior within such a region is described and interpreted. Two main subregions of resonant regions are found: (1) the region with effective behavior - mound and (2) the region with resonant coupling. The conditions for the existence of the first subregion are presented and explained, and the specific situation for the first/second diffraction order, TE vs. TM polarization, and for different relief profiles is also discussed.

A general resonator concept is discussed offering the flexibility of decoupling the mode shape inside and the laser beam outside of the laser resonator. Two examples for the use of the resulting design freedoms for optimization of the laser system are presented. The influence of the non-static behaviour of the active laser medium on the stability of the laser operation is discussed and design methods for improvement of this stability are presented.

An increasing number of applications are requiring fiber transmission of high-intensity laser pulses. Our particular interest have led us to examine carefully the fiber transmission of Q-switched pulses from multimode Nd:YAG lasers at their fundamental wavelength. The maximum pulse energy that can be transmitted through a particular fiber is limited by the onset of laser-induced breakdown and damage mechanisms. Laser breakdown at the fiber entrance face is often the first limiting process to be encountered, but other mechanisms can results in catastrophic damage at either fiber face, within the initial entry segment of the fiber, and at other internal sites along the fiber path. In the course of our studies we have examined a number of factors that govern the relative importance of different mechanisms, including laser characteristics, the design and alignment of injection optics, fiber end-face preparation, and fiber routing. The present study emphasizes the important criteria for injection optics in high-intensity fiber transmission, and illustrates the opportunities that now exist for innovative designs of optics to meet these criteria. Our consideration of diffractive optics to achieve desired began in 1993, and we have evaluated a progression of designs since that time. In the present study, two recent designs for injection optics are compared by testing a sufficient number of fibers with each design to establish statistics for the onset of laser-induced breakdown and damage. In this testing we attempted to hold constant other factors that can influence damage statistics. Both designs performed well, although one was less successful in meeting all injection criteria and consequently shows a susceptibility to a particular damage process.

A novel technique to multiplex high energy laser pulses from a Nd:YLF laser into an array of fibers at energies near the bulk damage limit of fused silica is presented with the object of delivering N equal high energy laser pulses with a minimal time dispersion. Characteristics of the multiple fiber system, diffractive grating splitter, and spatial mode structure of the laser to minimize fiber damage are presented along with preliminary results in scaling the system to larger fiber numbers (N approximately equals 200) with a high energy 10-Joule Nd:Glass laser system. Fiber array alignment techniques and morphologies of fiber damage will also be presented and discussed.

A 1-J laser was designed to launch light down 16, multi-mode fibers (400-μm-core dia.). A diffractive-optic splitter was designed in collaboration with Digital Optics Corporation¹ (DOC), and was delivered by DOC. Using this splitter, the energy injected into each fiber varied <1%. The spatial profile out of each fiber was such that there were no "hot spots," a flyer could successfully be launched and a PETN pellet could be initiated. Preliminary designs of the system were driven by system efficiency where a pristine TEM₀₀ laser beam would be required. The laser is a master oscillator, power amplifier (MOPA) consisting of a 4-mm-dia. Nd:YLF rod in the stable, q-switched oscillator and a 9.5-mm-dia. Nd:YLF rod in the double-passed amplifier. Using a TEM₀₀ oscillator beam resulted in excellent transmission efficiencies through the fibers at lower energies but proved to be quite unreliable at higher energies, causing premature fiber damage, flyer plate rupture, stimulated Raman scattering (SRS), and stimulated Brillouin scattering (SBS). Upon further investigation, it was found that both temporal and spatial beam formatting of the laser were required to successfully initiate the PETN. Results from the single-mode experiments, including fiber damage, SRS and SBS losses, will be presented. In addition, results showing the improvement that can be obtained by proper laser beam formatting will also be presented.

High power Nd:YAG laser beam with wavelength 1.064micrometers , pulse-width 20 and 100 pico-second was focused onto Zn coated target; and separated by beam splitter and delivered via optical fibers. Some key problems of ultra short pulsed high power laser beam transporting in optical fiber were involved and solved; laser ablation effect by laser irradiation and after optical fiber transportation were comparatively studied. Ablation rate was defined as ablated volume to laser fluence and used as a description of ablation ability. The relationship of ablation rate with laser fluence was plotted and optimum condition was found. Corresponding to the optimal condition, ablation effect in cases of 20 and 100 pico- second pulse-width, 90 degree(s) and 20 degree(s) laser incident angles, using spherical lens and cylindrical lens for laser beam focusing was compared respectively. It was shown that if other conditions unchanged, used spherical lens and cylindrical lens, ablation rate was almost same, but it was high as pulse-width equal to 100ps or laser incident angle equal to 90 degree(s) than as 20ps or 20 degree(s) respectively. In addition, laser beam over 5.6 watt, transporting rate near 90 per was output at the end of the optical fiber. Using the laser was this output power, the same thickness Zn coating was completely removed. Basing on this experiment, the possibility of laser surface ablation cleaning under complicated circumstance was confirmed.

The use of lasers in microelectronics is production for trimming, ablating, drilling and general micromachining continues to grow. As one example, traditional laser trimming techniques for passive and active microelectronic circuits have been used for nearly thirty years to improve yields and/or device performance. The majority of these processes have been accomplished using the fundamental wavelengths of the Nd:YAG laser source. However, recent technological advances in microelectronics laser processing, mainly for hybrid integrated circuits (HIC), dynamic random access memories (DRAM) and printed wiring boards (PWB) have resulted in new process techniques. Several new technologies, such as alternative wavelength processing and shaped, uniform laser spots have produced better processing quality, higher reliabiltiy, and greater yields. This paper will review the past, present and future of laser micromachining in microelectronics.

For many applications such as lithography and material processing, the hsaping and homogenization of a UV or Deep UV source needed. Often the divergence angle needed is fairly large ($GTR5 degree(s)half angle). This can be very difficult using diffractive homogenizers, especially when the divergence needed approaches 10 degree(s)half angle. Presented in this paper is a new technique that has the ability to homogenize and shape a deep UV source by more than 10 degree(s)half angle. This technique uses a deep ($GTR10 waves) microstructure that bends the light by the required amount. The fabrication of this microstructure is practical only with gray scale or analog lithography. With gray scale lithography, complicated smooth surface relief structures are possible in one lithography step. Older fabrication methods have good design freedom in the two dimensions associated with the plane of the wafer or optic but have limited design freedom in the dimension of the microstructure depth. Gray scale lithography opens up this dimension of the micro optic as a design freedom making higher performance micro optics possible and economical. Design, fabrication, modeling and test results will be discussed.

Multi-aperture beam integrators are used to homogenize high power multi- mode lasers and arc lamps for various industrial applications. Some applications, such as product marking and laser machining, require specific odd-shape irradiance patterns on the target. Current masking techniques waste laser power. We explore here the techniques of aperture flipping and highly aberrated lenslets in the beams segmenter element of multi-aperture beam integrators.

A novel technique for homogenizing the multitude of beams emanating from a laser diode array is described, as it related to use as an illumination system in a laser printer. This illumination system was required to efficiently transform the multiple beams from a laser array into a single line of uniform light, incident upon a spatial light modulator array, without a loss of brightness. The importance of the laser diode source properties, including both spatial coherence and source Lagrange, will be considered relative to their impact on the system design. The design of the beam shaping optics, including the beam combiner optics and the fly's eye integrator assembly, will also be discussed. The implementation of this illumination system in a laser printer employing a modulator array will be discussed, including issues of alignment, component properties, and the results obtained during system integration.

This contribution concentrates on a study and comparison of non- iterative design methods (error diffusion methods) based on a hardclip approach with iterative methods, namely iterative Fourier transform algorithm (IFTA), in designing binary phase-only diffractive optical elements (BPDOEs) for laser beam shaping. Two error diffusion methods as a non-iterative methods were considered, implemented and used for designing BPDOEs: the classical algorithm of error diffusion (ED) and the signal window minimum average error algorithm (SWMAE). Also, different schemes and approaches of IFTA algorithm were analyzed, implemented, and compared. The methods together with the simple hardclip method were analyzed for both diffusive and fan-out type objects: the signal-to-noise ratio and the diffraction efficiency dependencies on both the spatial-bandwidth product and on the signal-window position were obtained, enabling to determine the optimum design parameters and constraints within each method. As for the IFTA method, the role and a proper shape of the scale factor were analyzed, and a new way of characterization of the algorithm convergence was introduced, using the spectrum representation. The practical realization using e-beam lithography technology shows a good qualitative agreement with designed types of elements.

A lens system for shaping a laser beam profile has been designed, built, and tested. It consists of two plano-aspherical lenses which convert a Gaussian input beam into a uniform irradiance output beam. The optical design is based on solving differential equations expressing conservation of energy and constant optical path length condition as the beam passes through the system. Experimental results for the irradiance profile and wavefront shape of the output beam are presented and discussed. When this beam shaping system is used with light of different wavelengths than the design value, experimental results show that a small change in lens spacing enables the beam shaping optics to operate efficiently. An experimental tolerance analysis of this beam shaping system shows that it is stable with respect to assembly errors of tilt and misalignment of components.

A novel technique for controlling the beam width of a single-mode laser beam by Gaussian apodization is discussed. Although, beam truncation is often used to compensate for the typical variations in laser diode beam divergence, such truncation imparts side lobes to the outgoing beam. Gaussian apodization or attentuation of a laser beam provides controlled beam truncation, thereby producing a clean Gaussian beam without side lobes. Typically then, the magnitude of the allowable residual beam divergence variation will be determined by the system light efficiency requirements. However, use of a Gaussian apodizer provides beam divergence control without the use of a complicated zoom system. The implementation of this concept in a prototype flying spot laser print is also discussed, with respect to the impact on the system design and other beam shaping optics, the properties of the prototype Gaussian apodizer, and the results observed during system integration.

The design of the Shenguang system calls for a beam sampler to provide 3^rd harmonic laser energy for diagnostics in the highly constrained area of the target chamber, The beam sampler should diffract 0.01%-0.5% of the 3^rd harmonic light into a calorimeter at a small angle to estimate its corresponding energy. In order to achieve low efficiency beam sampling with the least energy lost, two kinds of surface-relief grating have been designed with different method. One is the rectangular phase grating with its step height and width optimized. Another one is the sinusoidal phase grating. For each kind of beam sampler, the permissible fabrication errors have been analyzed. The characteristics of them have been compared in detail.

A diffractive optical element (DOE) is designed with a new algorithm for transforming a rotationally symmetrical Gaussian beam into a nearly diffraction-limited flat-top by Fourier transformation system. The simulating results indicate that size of the shaped spot is only twice more than one of the diffraction limited spot, the diffraction efficiency is about 71.38$ and the edge of the uniform area is dramatically sharper than the one without DOE.

We use a simple formalism, based on the convolution between rectangular and gaussian functions, to represent the propagation of beams with high energy, and the CO₂ laser, used in material processing. We show the validity of such approximation comparing with samples makes on transparent material.