Eigenfunction description of laser beams and orbital angular momentum of light

Enk, S. J. van; Nienhuis, G.

doi:10.1016/0030-4018(92)90424-p

Cited by 174 publications

(87 citation statements)

References 4 publications

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“…The AM of a propagating beam in the z-direction is commonly considered in the literature [3,16,17,18,19] to be equivalent to the line density, that is to say, to the AM per unit length in the z-direction. In order to avoid any possible ambiguity that may arise from the AM density [30,31], I do not use this notion here.…”

Section: Am Properties Of Non-paraxial Beamsmentioning

confidence: 99%

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Spin and orbital angular momentum of a class of nonparaxial light beams having a globally defined polarization

2009

Phys. Rev. A

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It is shown that the momentum density of free electromagnetic field splits into two parts. One has no contribution to the net momentum due to the transversality condition. The other yields all the momentum. The angular momentum that is associated with the former part is spin, and the angular momentum that is associated with the latter part is orbital angular momentum. Expressions for the spin and orbital angular momentum are given in terms of the electric vector in reciprocal space. The spin and orbital angular momentum defined this way are used to investigate the angular momentum of nonparaxial beams that are described in a recently published paper [Phys. Rev. A 78, 063831 (2008)]. It is found that the orbital angular momentum depends, apart from an l-dependent term, on two global quantities, the polarization represented by a generalized Jones vector and a new characteristic represented by a unit vector I, though the spin depends only on the polarization. The polarization dependence of orbital angular momentum through the impact of I is obtained and discussed. Some applications of the result obtained here are also made. The fact that the spin originates from the momentum density that has no contribution to the net momentum is used to show that there does not exist the paradox on the spin of circularly polarized plane wave. The polarization dependence of both spin and orbital angular momentum is shown to be the origin of conversion from the spin of a paraxial Laguerre-Gaussian beam into the orbital angular momentum of the focused beam through a high numerical aperture.

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Section: Am Properties Of Non-paraxial Beamsmentioning

confidence: 99%

“…But up till now, there is no satisfactory theory to elucidate the difference and relation. The distinction that the spin is carried by the polarization and the orbital AM is carried by the helical wave front was drawn basically from the knowledge of a type of paraxial beams [3,16,17]. It is not valid for non-paraxial beams [18,19,20].…”

Section: Introductionmentioning

confidence: 99%

Spin and orbital angular momentum of a class of nonparaxial light beams having a globally defined polarization

2009

Phys. Rev. A

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“…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.…”

Section: Introductionmentioning

confidence: 99%

Quantum-mechanical properties of Bessel beams

Jáuregui

Hacyan

2005

Phys. Rev. A

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Bessel beams are studied within the general framework of quantum optics. The two modes of the electromagnetic field are quantized and the basic dynamical operators are identified. The algebra of these operators is analyzed in detail; it is shown that the operators that are usually associated to linear momentum, orbital angular momentum and spin do not satisfy the algebra of the translation and rotation group, and that this algebra is not closed. Some physical consequences of these results are examined.

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“…Concluding the exposed analysis we shall try to connect the results obtained in series of experimental investigation of photon orbital angular momentum [11][12][13][14][15][16][17][18][19][20]. We did not describe all quoted experiments.…”

Section: Resultsmentioning

confidence: 99%

Photon's Structure of Motion

Delić

Tošić²,

Šetrajčić

et al. 2009

Acta Phys. Pol. A

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A free photon Hamiltonian is linearized using Pauli's matrices. Based on the correspondence of Pauli's matrices kinematics and the kinematics of spin operators, it has been proved that a free photon integral of motion is a sum of orbital momentum and spin momentum for a half-one spin. Linearized Hamiltonian represents a bilinear form of products of spin and momentum operators. Unitary transformation of this form results in an equivalent Hamiltonian, which has been analyzed by the method of Green's functions. The evaluated Green function has given possibility for interpretation of photon reflection as a transformation of photon to antiphoton with energy change equal to double energy of photon and for spin change equal to Dirac's constant. Since photon is relativistic quantum object the exact determining of its characteristics is impossible. It is the reason for series of experimental works in which photon orbital momentum, which is not integral of motion, was investigated. The exposed theory was compared to the mentioned experiments and in some elements the satisfactory agreement was found.

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Eigenfunction description of laser beams and orbital angular momentum of light

Cited by 174 publications

References 4 publications

Spin and orbital angular momentum of a class of nonparaxial light beams having a globally defined polarization

Spin and orbital angular momentum of a class of nonparaxial light beams having a globally defined polarization

Quantum-mechanical properties of Bessel beams

Photon's Structure of Motion

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