Multiple coaxial foci generation by phase-only pupil filters

A new procedure for creating simultaneous multiple foci along the same optical axis with phase-only pupil-plane filters is proposed. Pupil-plane filters consist in phase-only masks described by simple circularly symmetric analytical functions. The axial separation between foci and their energy distribution are independently controlled by two different parameters of the filter. The main advantage of this new design is that, unlike other methods that required slow iterative algorithms, the proposed phase masks are straightforwardly calculated from analytical expressions. Moreover, real-time dynamic foci control could be achieved by using a computer addressed spatial light modulator that allowed the generation of variable phase patterns. The phase profiles we propose can be combined with multiple transversal foci phase patterns to actually form axial replicas of the transversal foci. Thus, it should be expected that three-dimensional structures were dynamically driven fast enough to perform real-time interactive multiple foci manipulation. Experimental verification of the multiple coaxial foci creation by static phase filters is shown.