Methods will be described for achromatizing a previously described highly efficient refractive laser beam reshaper which allow a propagating, collimated, diffraction limited flat-top laser beam to be generated over a 200 nm spectral interval. Although the beam reshaper utilizes two aspheric lenses, the achromatizers detailed in this paper use only conventional spherical refracting elements. This allows a practical and cost effective path to upgrade such a beam reshaper to broad wavelength operation.

Circular gaussian-to-supergaussian beam shapers can easily be designed with ray tracing lens design software that provides access to the merit function. Noncircular top hats or supergaussian have traditionally used iterative back-propagation methods, such as Gershberg-Saxon routines for generating the phase function of the shaper. This paper presents a simple method to design rectangular top-hat beam shapers with ray tracing software by proper generation of the ray targets and selection of the diffractive element coefficients to vary under optimization. The design method is much quicker than previously used back-propagation algorithms.

A state-of-the-art laser beam shaper zoom optical system has been developed. This optical device, efficiently converts a 532 nm single-mode Gaussian intensity profile into top hat lines of variable size with peak-to-valley non-uniformities of ≤±8%. This hybrid zoom system is capable of generating line lengths ranging between 0.16 mm to 1 mm, and line widths of up to 15 μm. The lines are of square-like shape in the long axis while they remain Gaussian in the short axis. The system was designed, fabricated, and tested using a laser with a nominal input Gaussian beam waist of 2.25 mm at the 1/e² intensity points, and a nominal M² of less than 1.1. Techniques associated with the system alignment during the optical assembly and system integration are discussed. The optical design and test results of the diffractive-optical system are also presented.

This paper is focused on a design of flexible laser systems capable to provide spatial transformation of the pump radiation into the spectral domain of the output laser oscillation using specially designed “spatially dispersive” laser cavity. These systems also provide ultrabroadband or controlled spectral linewidth of the output laser oscillation. The theoretical analysis based on gaussian approximation for the designed laser cavities with “spatial dispersion” was used to provide maximum spatial resolution of the spatial-spectral transformation. The transformations of the spatial distribution of the pump radiation into the spectral domain of the output laser oscillation were experimentally demonstrated in the gain-switched LiF:F₂^+** and LiF:F₂^- lasers with total efficiencies of up to 20% and output pulse spectrum width wider than 140 nm, centered at 0.96 μm and 1.14 μm, correspondingly. As a result of the optimization of the angular dispersion of the output radiation, the simultaneous phase-matching for second harmonic generation in the single nonlinear crystal was realized for the whole oscillation spectral range. This technique allows to use a nonlinear frequency conversion for nonlinear transformation of the beam spatial distribution. Due to this, the ultra broadband (>100 nm) or multiline (20 lines) second harmonic and sum frequency oscillations were demonstrated in a LiIO₃ nonlinear crystal with an overall efficiencies of up to 12%.

At LBOC6 meeting we presented an alternative approach for laser beam characterization, based on the decomposition of the electrical field distribution at certain cross section of the laser beam into a system of orthogonal functions. As such orthogonal function systems we selected "natural" laser eigenmodes of either GL or GH type. The looked for strength of the individual modal components then can be achieved by measuring the output signal of multi-channel correlation filters placed in a Fourier set-up, whereas the correlation filters themselves have been realized as DOEs by laser lithography. In between different systems of such GL and GH correlation filters have been designed, manufactured and experimentally tested with miscellaneous laser beams. Achieved results demonstrate a very good conformity between optical experiment and computer simulation. First attempts to compare results of our method with results of "standard" beam characterization methods (ISO11146) indicated principal conformity, but illustrated the continuing demand for a sophisticated adjustment procedure for the filter during application.

For the design of DOE with rotational symmetric phase distribution, the Fourier Transform (FT) and Inverse Fourier Transform (IFT) take the form of the first order of Hankel transform. The speed of numerical calculation for Hankel transform becomes the bottleneck of phase retrieval algorithms. A new fast Hankel transform method is applied to DOE designing process, in which Hankel transform is achieved by one time's of projection integration and one time's of Fast Fourier Transform (FFT). Utilizing the merits of FFT, speed of Hankel transform is greatly improved. Therefore, rotational symmetric DOE can be designed with fast speed and good designed result can be obtained more easily. Some examples of DOE designing with the help of FHT are given.

Off-line conditioning of full-size optics for the National Ignition Facility required a beam delivery system to allow conditioning lasers to rapidly raster scan samples while achieving several technical goals. The main purpose of the optical system designed was to reconstruct at the sample plane the flat beam profile found at the laser aperture with significant reductions in beam wander to improve scan times. Another design goal was the ability to vary the beam size at the sample to scan at different fluences while utilizing all of the laser power and minimizing processing time. An optical solution was developed using commercial off-the-shelf lenses. The system incorporates a six meter relay telescope and two sets of focusing optics. The spacing of the focusing optics is changed to allow the fluence on the sample to vary from 2 to 14 Joules per square centimeter in discrete steps. More importantly, these optics use the special properties of image relaying to image the aperture plane onto the sample to form a pupil relay with a beam profile corresponding almost exactly to the flat profile found at the aperture. A flat beam profile speeds scanning by providing a uniform intensity across a larger area on the sample. The relayed pupil plane is more stable with regards to jitter and beam wander. Image relaying also reduces other perturbations from diffraction, scatter, and focus conditions. Image relaying, laser conditioning, and the optical system designed to accomplish the stated goals are discussed.

We present a vector angular spectrum approach by using self-iterative algorithms for beam shaping. It is rigorous and still valid to sub-wavelength feature size. The approach bases on scalar angular spectrum theory and modifies by keeping the variation of the beam's polarization. The comparison of this approach with Fraunhofer diffraction integrals by using different self-iterative algorithms to design the diffractive optical elements for beam shaping shows the former one is more efficient. Design example in the near field for beam shaping with sub-wavelength minimum feature is also presented.

This paper is presented a kind of simple and convenient method to measure energy distribution of hollow fiber. The application of energy distribution in mode purity analysis and detection of different coupling status is also considered. Furthermore, the problem about focus of output beam is discussed.

We propose the use of structured microlens arrays to achieve beam shaping, diffusion, and homogenization. Practical results are presented that elucidate the capabilities of structured microlens arrays to perform complex beam shaping tasks, both intensity control and spatial energy distribution, with high efficiency (mostly limited by surface losses) and without the presence of image artifacts. In addition, the refractive nature of the array naturally yields broadband operation with no zero order. The concept of a structured microlens array incorporates both deterministic and random components so that each microlens is individually designed to perform at least some portion of the beam-shaping task. At the same time, the design process ensures that any statistically significant ensemble of microlenses represents a random process described by select probability density functions. As a result, the structured microlens array incorporates the ability of deterministic diffusers to attain optimal scatter properties and the desirable robustness and homogenizing capabilities of random diffusers. These attributes make structured microlens arrays suitable for a wide variety of applications, from excimer laser beam shaping to display screens. We have designed and fabricated structured microlens arrays using a laser writing system that exposes low-contrast photoresist to a modulated beam on a point-by-point basis to produce a continuous surface-relief profile. The method allows the fabrication of arbitrary surface-relief profiles and depths greater than 100 microns. Experimental results include small-angle (less than 1 degree) and large-angle (up to 180-degree span) diffusion, beam shaping into singly- and multiply-connected domains, flat and controlled intensity profiles.

An innovative method of optically combining the multiple emitters of high power stripe laser diodes is presented. A multi-beam integrator approach is used along with a means of optically rotating the emitters by 90 degrees. The 90-degree rotation allows better balancing of the optical invariants in the slow and fast axis directions, making it easier to "circularize" the image for coupling into fibers or to increase the irradiance for laser machining applications.

An innovative multi-aperture beam integrator system producing a polygon pattern or other complex pattern on an image plane, which can be continuously varied in size, aspect ratio, or shape, is described in this paper. The multi-aperture function of the integrator system consists of three array elements, one stationary and the other two movable laterally. The first array element forms an array of Galilean telescopes which collect the light with 100% fill factor, segments the incoming beam into multiple beamlets, and reduces the diameter of each beamlet in order to prevent vignetting at the following movable arrays. The second and third array elements each contain a plurality of the anamorphic lenslets, not all the same, each lenslet pair of which forms one of the sides of the polygon or complex image. These array elements have a surface profile or phase function, which can be described as a general polynomial of the pupil coordinates. An aberration-free integrator lens overlaps the beamlets in the image plane to accomplish beam homogenization and produce a uniform intensity for all the sides of the polygon or segments of the complex image. Small lateral translations of the second and third array elements cause the image characteristics to change continuously.

There are numerous laser applications that require the laser irradiance to possess a controlled shape and uniformity across a specific area at some distance from the source. Such applications include material processing (cutting, welding, drilling, heat-treating), scribing, marking, and microfabrication. One method of achieving this goal is to employ a double-sided micro lens array (MLA) in an imaging multi-aperture beam integrator configuration as discussed by Brown, Dickey, and Weichman. Such a configuration consists of two elements-the-double-sided MLA and a focusing lens. The micro lens array serves to segment the incoming beam at each subaperture into multiple beams, which are then overlapped at the image plane by the focusing lens. The resultant image will have the same shape as the subapertures of the micro lens array, which means that almost any shape can be generated. Lenslet subapertures having square, rectangular, or hexagonal shapes that can be stacked with 100% fill factor are typically used in order to reduce the amount of energy lost at the image plane. The operation of microlens arrays as diffusers are examined in the following paper from a ray optics and a physical optics point of view. Modeling examples/techniques are discussed for both approaches as well.

The design of beam shaping optics for laser micromachining applications must be optimized for maximum beam efficiency and quality across a given image plane. The need for faster UV and IR laser processes for drilling microvias, dicing and trimming wafers led to our utilization of hybrid optics and shaping methods, where standard refractive and computer generated holographic and diffractive optics could be meshed together to construct a system that would out perform optical beam delivery technology occupying the marketplace today. This paper covers the beam shaping technology developed, the computer modeled beam shaping and propagation plots over the length of an industry standard system as well as a comparison of the computer model images to the actual results from testing, using profilometer techniques. The later portions of the paper cover the final image formed at the target plane, including uniformity, various shapes, optical efficiency and an example of image stability while using a step and scan technique through a standard galvanometer system over a 25 mm x 25 mm field size. Specific performance details will be shared with regards to total system performance as well. A further section covers a brief overview of materials processing attributes including several specific material cross sections and scanning electron images as well as various errors created by misalignment of specific elements of the shaper with respect to the beam delivery system.

The use of radially polarized light is known to produce, when focused by a high numerical aperture objective lens, a spot of light whose polarization is predominantly axial. We have generated radially polarized beams accurately and have confirmed this behavior experimentally and have also shown that the axial polarization leads to a ring type image of sub-resolution gold beads.

New waveguide effects are considered on the basis on various variants for self-focusing of the living cells of aquatic plant by laser beam irradiation. It is studying the process of forming of the 'living multi-mode fiber-optic' into the road of laser's beam in water with motion of green living cells. Analysis gives that the wide set of different profiles of the refractive index in this 'living optical fiber' could be easy produced depending the frequency of applied lasers. Optical waveguide approach gives high sensitivity in living layer readout and control, this waveguides could be apply to environmental processing or for a cell's studying, also different medical application could be realized according described mechanism.

By using a diffractive optical element (DOE), a new method to generate dark hollow laser beam (DHLB) is presented in this paper. The optimization theories to design the DOE can obtain a globally optimal solution in an exact analytic form. The generated DHLB shows good performances for actual applications, which testifies the validity of this new method.

Axially symmetrical diffractive phase planes (DPPs) are easily fabricated and have been used in a variety of applications, especially for realizing uniform loop focal spot with steep side, flat top, flat side lobe and high efficiency. A kind of hybrid design algorithm combined ST algorithm and input-output algorithm is introduced for axially symmetrical DPPs design to realize uniform loop focal spot. The computer simulation has shown that the algorithm is robust and convergent. The DPPs has been designed to product uniform loop focal spot with high diffractive efficiency of the energy inside the loop spot, high uniformity for both main lobe and side lobe (both more than 96%), and steep side simultaneously.

Beam shaping theory is naturally one of the inverse problems and it is unable to get a unique minimum resolution. In the case of high demands to target beam quality such as uniform illumination, or the complex style of incident beams, one still needs to improve the classical design algorithm to satisfy fabrications and applications. In this paper, new iteration algorithm based on phase mixture algorithm (PMA) and input-output (IO) algorithm is presented. By using random phase mixture factor instead of fixed phase mixture factor in PMA and random feedback factor in IO algorithm, and introducing a selection rule in each loop of the iteration, the degree of freedom of the iteration is increased and better target beam quality is obtained. A continuous diffractive optical element (DOE) for uniform illumination of annular Gaussian incident beam with diameter 240 mm is shown as a design example. Comparison of iteration results between the new algorithm and classical PMA or IO shows that the new algorithm provided better target beam quality and thinner DOE phase thickness. The design result of new algorithm only has 2.25% top profiled error (TPE) with a phase thickness of about 8 π while the best simulated result of PMA and IO algorithm has 3.42% TPE with a phase thickness of 12.4 π.

An aperiodic two-dimensional diffractive optical element (DOE) with subwavelength features as an uniform beam shaper which shapes an input laser beam into an uniform intensity distribution in an observation plane has been designed. A rigorous design method combined an iterative optimization algorithm with a rigorous electromagnetic computation -- the finite-difference time-domain (FDTD) method has been proposed. The design method and the FDTD method have been discussed in detail. The simulated results have shown that the DOE designed by this rigorous method can produce an uniform field distribution with flat-top, steep edge and low profile error in an observation plane.

The thermally induced birefringence was successfully compensated by placing a quarter-wave plate into a plane parallel Nd:YAG laser resonator of 130 W output power in multi-mode. The optimal conversion efficiency was 38.3% and the slope efficiency was 58.2% with output coupler of 80% reflectance, and the beam quality factor of M² was 26.7. For higher modes elimination, an aperture of 1.5 mm in diameter was inserted into resonator, and M² was decreased to 1.8. However, the insertion of quarter-wave plate made an additional improvement to 1.15 of M² value by alternating their radial and tangential polarization directions every bouncing feedback. We report the experimental results with theoretical analysis for high power solid-state laser fabrication with better beam quality.

Diffractive optical element (DOE) is used to convert inputting optical field to the outputting one on image plane with desired intensity distribution. Since DOE design is a numerical process, the definition of performance parameter of approach distance (PPAD) under continuous condition is given and methods of calculation from discrete samples are argued. Correspondingly, discrete performance parameter of approach distance (DPPAD) is defined to evaluate designed results during designing process under discrete condition. According to the PPAD calculation equation under continuous condition and DPPAD under discrete condition, a general DOE designed result shows that sometimes there are tremendous differences between PPAD value and DPPAD. By analyzing the errors of DPPAD, it is pointed out that to design a faithful DOE result, the sampling interval between 2 neighbor points on outputting plane must has extra limitation despite of sampling theory. Otherwise, the designed result just looks good but it is a bad one in fact, and the DPPAD will not be consistent with PPAD. In the end, an example of faithful designed DOE is given.

Authors have worked out a nonstationary signal analysis method on the example of research of laser lines. This method disclosed relationship between signal approximation coefficients and geometry signal characterizations(for instance, energy center, moment of inertia). The example, which is demonstrating an application of this method for exact coordinate determination problem in laser line at displacement compensation in laser imaging are present. Various extrapolation approaches of laser beam location in real time are considered.

This paper presents a lossless method and apparatus to transform a collimated straight line beam into a collimated spherical arc beam. This apparatus consists of two coaxial axicons, and the propagation direction of the incoming beams is parallel to the optical axis of the two axicons. At least one of the axicons has to be a converging one. The same method can also be used to transform a collimated rectangular beam into a collimated meniscus shape beam. By reversing the beam direction, a collimated spherical arc beam input can be transformed into a collimated straight line beam output, and a collimated meniscus shape beam can be converted into a collimated rectangular beam. A collimated spherical arc beam of certain radius can also be transformed into a collimated spherical arc beam of any desired radius. Numerical simulations and ray trace examples are provided.