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We show that it is possible to generate non-paraxial optical beams withpre-engineered trajectories and designed maximum amplitude along thesetrajectories. The independent control of these two degrees of freedom is madepossible by engineering both the amplitude and the phase of the optical wave oninput plane. Furthermore, we come to the elegant conclusion that the beam widthdepends solely on the local curvature of the trajectory. Thus, we can generatebeams with pre-defined amplitude and beam-width by appropriately selecting thelocal curvature. Our theoretical results are in excellent agreement withnumerical simulations. We discuss about methods that can be utilized toexperimentally generate such beam. Our work might be useful in applicationswhere precise beam control is important such as particle manipulation,filamentation, and micromachining.

Independent amplitude and trajectory/beam-width control of nonparaxial beams