Bessel Beams: Unified and Extended Perspective

Abstract: We present a unified and extended perspective of Bessel beams, irrespective to their orbital angular momentum (OAM) -- zero, integer or noninteger -- and mode -- scalar or vectorial, and LSE/LSM or TE/TM in the latter case. The unification is based on the integral superposition of constituent waves along the angular-spectrum cone of the beam, and allows to describe, compute, relate, and implement all the Bessel beams, and even other types of beams, in a universal fashion. The paper first establishes the integral superposition theory. Then, it demonstrates the previously unreported existence of noninteger-OAM TE/TM Bessel beams, compares the LSE/LSM and TE/TM modes, and establishes useful mathematical relations between them. It also provides an original description of the position of the noninteger-OAM singularity in terms of the initial phase of the constituent waves. Finally, it introduces a general technique to generate Bessel beams by an adequate superposition of properly tuned sources. This global perspective and theoretical extension may open up new avenues in applications such as spectroscopy, microscopy, and optical/quantum force manipulations.