p g n

and their net topological charge is found to depend on the beam plitudes,6 or by the cations.8 superposit fascinatin we reveal perposition of noncoaxial vortex beams creates light pat ind arit imp tion her W ent tra trates these points is the superposition of two identi-f charge ith topo-arge m. position t beams m2 1. contains only one single-charge vortex, regardless of the sepa-idual x ition ams. neg-form twoterns with a richer vortex content than that of the ividual beams. The results fully reveal the curious hmetic of screw wave-front dislocations and hold ortant practical implications for the implementa-and operation of optical multitweezers with co-ent light beams. e address the linear superposition of two coher-light beams with nested vortices, with the general ration between the vortices carried by the indiv beams. Such a single-charge vortex is located at x1 1 x22, y y1 1 y22. In what follows, we examine the superpos of vortices nested in noncoaxial Gaussian be For simplicity we assume that diffraction is ligible, so the individual fields have the FnXn, Yn An exp2Xn2 1 Yn2wn2. Thensverseshapes and their relative widths and am-by the superposition of laser cavity modes,7 explosions of perturbed higher-order dislo-Our goal in this Letter is to show that the ion of noncoaxial beams opens the door to a g new range of possibilities. In particular, and experimentally observe that the su-cal and coaxial beams with a nested vortex o m: The resulting field carries not a vortex w logical charge 2m but rather a vortex with ch A similar insight is also provided by the super of the vortices nested in the mathematical hos F1 F2 constant. To be specif ic, let m1 Then, one readily finds that Sx, y alwaysThe curious arithm