Abstract
We present a unified and extended perspective of Bessel beams, irrespective of 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 enables us to describe, compute, relate, and implement all Bessel beams, and even other types of beams, in a universal fashion. We first establish the integral superposition theory. Then, we demonstrate the existence of noninteger-OAM TE/TM Bessel beams, compare the LSE/LSM and TE/TM modes, and establish useful mathematical relations between them. We also provide an original description of the position of the noninteger-OAM singularity in terms of the initial phase of the constituent waves. Finally, we introduce a general technique for generating Bessel beams using an adequate superposition of properly tuned sources. This global perspective and theoretical extension may be useful in applications such as spectroscopy, microscopy, and optical/quantum force manipulations.
Highlights
Electromagnetic Bessel beams represent a fundamental form of structured light
This paper presents a general electromagnetic vectorial spectral formulation that applies to all Bessel beams, and even to other types of conical (e.g., Mathieu, Weber) and nonconical beams (e.g., Gauss-Laguerre and Hypergeometric Gaussian beams), providing novel perspectives and possibilities
Existence and Characterisation of TE/TM with noninteger orbital angular momentum (OAM) – Whereas vectorial TE/TM Bessel beams [4], [28], [19], [31] and scalar Bessel beams with arbitrary OAM [20], [32] have been separately described in the literature, we report here for the first time the existence of TE/TM Bessel beams with non-integer OAMs, and present a detailed description of these new modes, showing superior focusing capabilities [33] than their LSE/LSM counterparts in addition to richer optical force opportunities
Summary
Electromagnetic Bessel beams represent a fundamental form of structured light. They are localized waves [1], [2] with transverse Bessel function profiles that carry orbital angular momentum (OAM) along their propagation axis. They are monochromatic beams with a transverse amplitude pattern that follows Bessel functions of the first kind, Jn(αρ), multiplied by the phase function einφ (n ∈ Z), or combinations of such waves in the noninteger OAM case Their simplest forms are the scalar Bessel beams, existing in acoustics and restricted to the paraxial approximation in optics. This paper presents a general electromagnetic vectorial spectral formulation that applies to all Bessel beams (scalar and vectorial, with integer and noninteger OAM, LSE/LSM and TE/TM, and all related combinations), and even to other types of conical (e.g., Mathieu, Weber) and nonconical beams (e.g., Gauss-Laguerre and Hypergeometric Gaussian beams), providing novel perspectives and possibilities. We present here an efficient and generic approach for the practical implementation of any Bessel beam (and other conical or nonconical beams)
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