Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes

Allen, L. J.; Beijersbergen, Marco W.; Spreeuw, R. J. C.; Woerdman, J. P.

doi:10.1103/physreva.45.8185

Cited by 8,415 publications

(4,326 citation statements)

References 13 publications

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“…This is because extending the upper integration boundary is not an equally good approximation for the two integrals in (53) and (45). One can see from figure (9) that the agreement with the Lorentzian is better at the flanks and for higher values of λ. This is consistent with our considerations as for larger values of |λ| the justification for the approximation of the wavefunction in the Fourier integral becomes more valid.…”

Section: Lorentzian Approximationmentioning

confidence: 78%

“…From figure (9) and equation (53) it can be seen that the angular momentum mean is zero. The square of the uncertainty is thus given by:…”

Section: Lorentzian Approximationmentioning

confidence: 90%

“…In particular the expectation value of the commutator is zero for both eigenstates ofL z andφ θ , for which ∆L z = 0 and ∆φ θ = 0 respectively. Our simpler form of the uncertainty relation (2) arises on applying the limit L → ∞ to the expectation value of the commutator in (9). If the state has finite moments of L z then we can treat m − m ′ in the denominator of (8) as small compared with 2L + 1 and this leads to the uncertainty relation of the form…”

Section: The Uncertainty Relationmentioning

confidence: 99%

See 2 more Smart Citations

Large-uncertainty intelligent states for angular momentum and angle

Götte

Zambrini

Franke‐Arnold

et al. 2005

J. Opt. B: Quantum Semiclass. Opt.

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Abstract. The equality in the uncertainty principle for linear momentum and position is obtained for states which also minimize the uncertainty product. However, in the uncertainty relation for angular momentum and angular position both sides of the inequality are state dependent and therefore the intelligent states, which satisfy the equality, do not necessarily give a minimum for the uncertainty product. In this paper, we highlight the difference between intelligent states and minimum uncertainty states by investigating a class of intelligent states which obey the equality in the angular uncertainty relation while having an arbitrarily large uncertainty product. To develop an understanding for the uncertainties of angle and angular momentum for the large-uncertainty intelligent states we compare exact solutions with analytical approximations in two limiting cases.

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Section: Lorentzian Approximationmentioning

confidence: 78%

“…From figure (9) and equation (53) it can be seen that the angular momentum mean is zero. The square of the uncertainty is thus given by:…”

Section: Lorentzian Approximationmentioning

confidence: 90%

Section: The Uncertainty Relationmentioning

confidence: 99%

See 1 more Smart Citation

Large-uncertainty intelligent states for angular momentum and angle

Götte

Zambrini

Franke‐Arnold

et al. 2005

J. Opt. B: Quantum Semiclass. Opt.

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“…Finally, note that a wave beam that is not axially symmetric will also carry additional, "orbital" momentum [132,133]. The latter is included in Eq.…”

Section: Angular Momentummentioning

confidence: 99%

“…(48), and separating it from the SAM unambiguously may not be possible except in special cases, as usual; see, e.g., Ref. [132][133][134] or Ref. [128,Sec.…”

Section: Angular Momentummentioning

confidence: 99%

Axiomatic Geometrical Optics, Abraham-Minkowski Controversy, and Photon Properties Derived Classically

Fisch¹

2012

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By restating geometrical optics within the field-theoretical approach, the classical concept of a photon in arbitrary dispersive medium is introduced, and photon properties are calculated unambiguously. In particular, the canonical and kinetic momenta carried by a photon, as well as the two corresponding energy-momentum tensors of a wave, are derived straightforwardly from first principles of Lagrangian mechanics. The Abraham-Minkowski controversy pertaining to the definitions of these quantities is thereby resolved for linear waves of arbitrary nature, and corrections to the traditional formulas for the photon kinetic quantities are found. An application of axiomatic geometrical optics to electromagnetic waves is also presented as an example.

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Coded Orbital Angular Momentum Based Free‐Space Optical Transmission

Djordjević

2016

Wiley Encyclopedia of Electrical and Electronics Engineering

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In this article, we explore orbital‐angular‐momentum‐based (OAM) free‐space optical (FSO) transmission systems using low‐density parity‐check (LDPC) coded quadrature phase‐shift keying (QPSK) modulation format. The theory of OAM modes is discussed first, followed by the schemes to generate, multiplex/demultiplex, and detect OAM modes. Then, the FSO transmission systems with and without atmospheric turbulence are studied. The spatial‐ and time‐varying atmospheric turbulence is simulated via fast‐changing phase patterns, which are recorded by modified von Karman spectrum statistics. The atmospheric turbulence effects are discussed in terms of the intensity profile of OAM beam and power distribution among adjacent mode channels. In addition, we review the performance of LDPC coding based FSO transmission systems with a single OAM mode and with OAM multiplexing.

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Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes

Cited by 8,415 publications

References 13 publications

Large-uncertainty intelligent states for angular momentum and angle

Large-uncertainty intelligent states for angular momentum and angle

Axiomatic Geometrical Optics, Abraham-Minkowski Controversy, and Photon Properties Derived Classically

Coded Orbital Angular Momentum Based Free‐Space Optical Transmission

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