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Laser beams with precisely controlled intensity profiles are essential for many areas. We developed a beam shaping system based on the digital micromirror device (DMD) for ultra-cold atom experiments and other potential applications. The binary DMD pattern was first designed by the error diffusion algorithm based on an accurate measurement of the quasi-Gaussian incident beam from a real-world laser. The DMD pattern was projected to the image plane by a bandwidth-limited 4f telescope that converted this pattern to the grayscale image. The system bandwidth determined the theoretical limit of image precision by the digitization error. In addition, it controlled the spatial shape of the point spread function (PSF) that reflected the tradeoff between image precision and spatial resolution. PSF was used as a non-orthogonal basis set for iterative pattern refinement to seek the best possible system performance. This feedback process, along with stable performance of DMD, the blue-noise spectrum of the error diffusion algorithm, and low-pass filtering, guaranteed high-precision beam shaping performance. This system was used to produce various beam profiles for different spatial frequency spectra. First, we demonstrated high-precision slowly-varying intensity beam profiles with an unprecedented high intensity accuracy. For flattop and linearly-tilted flattop beams, we achieved 0.20-0.34% root-mean-square (RMS) error over the entire measurement region. Second, two-dimensional sinusoidal-flattop beams were used to evaluate image precision versus system bandwidth. System evaluation confirmed that this system was capable of producing any spatial pattern with <3% RMS error for the most system bandwidth. This experiment extended the beam shaping to any system bandwidth and provided a reference to estimate the output image quality based on its spatial spectrum. Later experiment using a Lena-flattop beam profile demonstrated the arbitrary beam profile generation. We implemented this system for applications on the homogenous optical lattice and dynamic optical trap generation. The DMD pattern was optimized by the iterative refinement process at the image feedback arm, and projected through a two-stage imaging system to form the desired beam profile at the working plane. Experiments demonstrated a high-precision beam shaping as well as a fast and dynamic control of the generated beam profile. / text

>Magister Scientiae - MSc / This dissertation consists of two main sections. The first section focuses on generating zero order Bessel beams using axicons. An axicon with an opening angle y = 5⁰ was illuminated with a Gaussian beam of width ω₀ = 1.67 mm from a cw fiber laser with central wavelength λ = 1064 nm to generate zero order Bessel beams with a central spot radius r₀ = 8.3 ± 0.3 μm and propagation distance ½zmax = 20.1 ± 0.5 mm. The central spot size of a Bessel beam changes slightly along the propagation distance. The central spot radius r₀ can be varied by changing the opening angle of the axicon, y, and the wavelength of the beam. The second section focuses on applications of the generated Bessel beams in laser microdrilling. A Ti:Sapphire pulsed femtosecond laser (λ = 775 nm, ω₀ = 2.5 mm, repetition rate kHz, pulse energy mJ, and pulse duration fs) was used to generate the Bessel beams for drilling stainless steel thin sheets of thickness 50 μm and 100 μm and microscopic glass slides 1 mm thick. The central spot radius was r₀ = 15.9 ± 0.3 μm and ½zmax = 65.0 ± 0.5 mm. The effect of the Bessel beam shape on the quality of the holes was analysed and the results were discussed. It was observed that Bessel beams drill holes of better quality on transparent microscopic glass slides than on stainless steel sheet. The holes drilled on stainless steel sheets deviated from being circular on both the top and bottom surface for both thicknesses. However the holes maintained the same shape on both sides of each sample, indicating that the walls are close to being parallel. The holes drilled on the glass slides were circular and their diameters could be measured. The measured diameter (15.4±0.3 μm) of the hole is smaller than the diameter of the central spot (28.2 ± 0.1 μm) of the Bessel beam. Increasing the pulse energy increased the diameter of the drilled hole to a value close to the measured diameter of the central spot.

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Diploma thesis deal with design of laser beam shaping system. The theoretical part presents basic information about the light spread lika the optical beams. There are also properties of optical and optoelectronic components that are used for shaping the laser beam. The next section provides basic molding methods, their principles and qualities. In the last, experimental, part is first introduced designed computer algorithm, which is then used to calculate the quality parameters shaped laser beams. Following, there are presented the results of measurements and calculations for some of these methods.

In this thesis, an investigation into the modal characteristics of novel beam shapes is presented. Sculpting the phase profile of a Gaussian beam can result in the generation of a beam with unique properties. Described in this thesis are Laguerre-Gaussian (LG), Hermite-Gaussian (HG) and Bessel beams (BBs). The diffraction of LG beam modes from a triangular aperture is explored and this effect can be used for the efficient measurement of the azimuthal mode index l that indicates the number of multiples of 2π of phase changes that the field displays around one circumference of the optical axis. In this study, only LG beams with zero radial mode index p, with p + 1 denoting the number of bright high intensity concentric rings around the optical axis, were considered. Then, a powerful approach to simultaneously determine both mode indices of a pure LG beam using the principal component analysis (PCA) algorithm on the observed far-field diffraction patterns was demonstrated. Owing to PCA algorithm, the shape of the diffracting element used to measure the mode indices is in fact of little importance and the crucial step is ‘training' any diffracting optical system and transforming the observed far-field diffraction patterns into the uncorrelated variables (principal components). Our PCA method is generic and it was extended to other families of light fields such as HG, Bessel and superposed beams. This reinforces the widespread applicability of this method for various applications. Finally, both theoretically and experimentally investigations using interferometry show the definitive linkage between both the radial and azimuthal mode indices of a partially coherent LG beam and the dislocation rings in the far-field cross-correlation function (CCF).