Commutation Rules and Eigenvalues of Spin and Orbital Angular Momentum of Radiation Fields

Quantum-mechanical properties of Bessel beams

“…(34) is well defined only if the electromagnetic field vanishes faster than r −2 . Van Enk and Nienhuis [7] studied the consequences of quantizing the electromagnetic field in terms of creation and annihilation operators related to such localized electromagnetic modes: they have shown that even under this boundary condition the corresponding operatorsL andŜ cannot be identified with angular momentum operators because they satisfy a closed but different algebra. However, if the electric and magnetic fields are written using a basis formed by non localized modes, there is no natural separation of spin and orbital momentum since the integrals are not well defined.…”

“…Recent interest in defining angular momentum in optics can be traced back to the works of Lenstra and Mandel [4], Allen et al [5], and van Enk and Nienhuis [6,7]. Lenstra and Mandel considered periodic boundary conditions that limit the isotropy of the EM field and thus affect the angular momentum.…”

“…Allen et al showed that angular momentum can indeed be decomposed into orbital and spin parts for Laguerre-Gaussian modes, i. e., paraxial elementary waves with cylindrical symmetry. Finally, van Enk and Nienhuis [7] studied this decomposition and showed that neither the spin nor the orbital quantum operators of the electromagnetic field satisfy the commutation relations of angular momentum; they made the assumption that the total angular momentum obtained from Noether theorem is given directly as a sum of these operators; however, this is not the case in many situations where boundary conditions give rise to important surface effects.…”

Helicity and angular momentum: A symmetry-based framework for the study of light-matter interactions

“…Consequently, for our purposes, we may only use properties of the electromagnetic field which are associated with a hermitian operator in M. Only then can we consider their associated symmetry. This rules out the separate use of the components of L and S, since their associated operators transform a transverse Maxwell field into a non-transverse field [21], [16, B I .2]: they do not act within the required vector space. From this point of view, L and S are qualitatively different from J, the linear momentum P, the energy H or, as we will discuss, helicity Λ.…”

Subwavelength chiral surface plasmons that carry tuneable orbital angular momentum

“…7 However, interest in the angular momentum of light was reawakened in 1992 when it was demonstrated 8 that Laguerre-Gaussian beams can transport orbital angular momentum (OAM). [9][10][11][12] The OAM of EM fields has been also studied using plasmonic vortex structures, 13,14 and it has been extensively used in research areas as diverse as biophysics, micromechanics, and microfluidics. 15 At a quantum level, single photons with OAM have the potential for realizing highdimensional quantum spaces with applications in information technologies.…”