The intensity of spiral beams remains unchanged under propagation and focusing neglecting scaling and rotation. The spiral beam with predetermined intensity in the shape of any planar curve can be generated by use of amplitude and phase elements concurrently. We introduce the new method of singular laser fields formation, close to spiral type, by means of pure phase modulation. Our algorithm is based on the well-known Gerchberg-Saxton phase retrieval algorithm and spiral beams optics. It demonstrates fast convergence and some other advantages: phase distributions obtained are stable to spatial resolution changing (it is enough 128 x 128 pixels for some patterns), theoretical energy efficiency is about 85 % with acceptable intensity homogeneity. We demonstrate theoretical results on fields formation in the shape of closed-curves (triangular, square, "snowflake") and open-ended curve (Archimedes spiral) by means of elements on dichromate gelatin. Besides, the example of experiment on micromanipulation with the use of the square-shaped field is presented.
Formation of light fields with preset intensity is of the interest for different laser applications. Spiral beams optics is the
universal method of such fields generation. One of the experimental ways of spiral beams formation is the astigmatic
transform of specially realized one-dimensional light field to the intended spiral beam. The presence of phase
singularities is the feature of spiral beams. Traditional interference detection of singularities of spiral beams can be
inconvenient if the number of isolated zeros located within the low intensity area. It is typically for beams in the shape of
closed curves. The same astigmatic transform can also be used for the beams analysis.
Spiral beams while propagating and focusing, keep their intensity structure unchanged neglecting scale and rotation. One of the experimental ways to obtain spiral beams is the astigmatic transformation method. It allows producing spiral beams by means of structurally one-dimensional amplitude-phase elements and simple cylindrical optics. The paper is dedicated to modeling of spiral light fields formed with one-dimensional spatial light modulators. The effect of the ultimate resolution of the modulator and ultimate accuracy of the intensity and phase choice on the quality of the synthesized field in a far-zone of diffraction has been estimated in this work. The results can be of interest for various laser applications including the laser manipulation with micro-objects.