A Simple Method for the Design of Millimeter-structured Inclined Beams: Inclined Superpositions of Zeroth-order Bessel Beams

This work deals with a nondiffracting beam capable of providing arbitrary intensity patterns along a line inclined with respect to the normal plane of the aperture or generator (optical axis). These beams are built up from discrete superpositions of zeroth-order Bessel beams, all with the same frequency. The host medium is assumed lossless and isotropic. By assigning specific amplitude and phase values to each Bessel beam, it is possible to choose beforehand a particular intensity profile such as a millimeter long step function located a few centimeters away from the aperture and inclined by a few degrees (typically below 5°) from the optical axis. Moreover, it is observed that the resulting beam possesses a high transverse localization. In view of that, these localized beams could be applied in optical alignment, optical trapping, free space optics and manipulation of dielectric micro-sized particles in optical tweezers and bistouries systems, with the advantage of controlling the angle between the beam localization axis and the optical axis. Due to the flexibility of the method adopted, the analysis can be extended to higher-order beams, allowing us to analyze the orbital angular momentum transferred by those beams. In addition to that, absorbent media and an intensity pattern along a predetermined curvilinear path can also be easily incorporated. This is a first step towards an extension of the well-known “Frozen Waves” in order to achieve surface intensity beams without including additional optical elements (e.g., mirrors) and without performing additional superpositions of Bessel beams along a plane parallel to that of the aperture.