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.
The range of possibilities ofthe laser manipulation with microscopic objects could be sufficiently expanded by using of the beams with predetermined spatial intensity and orbital momentum density distributions in the focusing plane. Such beams permit to realize rotation and fixed trace movement of absorbing particles. The spiral beams having intensity in the shape of triangular boundary, the line with self-intersection and Archimedes spiral were formed by composition of amplitude and phase masks produced on the base of bichromated gelatin. The spiral beams keep their intensity structure unchanged under propagation except scale and rotation. The Ar-laser and microscope MIN-8 with immersion micro objective (60x, NA=O.85) were used in experimental set-up. Particles of the cetylpiridiniumbromide and colored latex spheres were chosen as an objects for manipulation. Experimental results are presented on microobjects movement effectuated with spiral beams along different fixed trajectories. The motion direction is determined by the direction of the beams orbital momentums.