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.

中文翻译：

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贝塞尔光束：统一且扩展的视角

无论贝塞尔光束的轨道角动量（OAM）（零，整数或非整数）和模式（标量或矢量），以及LSE / LSM或TE / TM，我们都会对其进行统一和扩展的介绍。统一是基于组成光束沿光束的角谱锥的整体叠加，并使我们能够以通用的方式描述，计算，关联和实现所有贝塞尔光束，甚至其他类型的光束。我们首先建立积分叠加理论。然后，我们证明了非整数OAM TE / TM贝塞尔光束的存在，比较了LSE / LSM和TE / TM模式，并在它们之间建立了有用的数学关系。我们还根据组成波的初始相位提供了非整数OAM奇异性位置的原始描述。最后，我们介绍了一种使用适当调谐的信号源的适当叠加来生成贝塞尔光束的通用技术。这种整体观点和理论扩展在诸如光谱学，显微镜学和光学/量子力操纵的应用中可能是有用的。