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Physics Today
A Fine Point on Light’s Angular Momentum Miles J. Padgett, L.J. Allen
Published Jan 1, 2005 • 0 citations
Abstract Padgett and Allen reply: In our experiment, the particle was Teflon and had an absorption of a few percent, which meant it could be trapped within optical tweezers. In the review, we called it transparent to contrast it with the earlier work of H. He and coworkers. 1 1. H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995). https://doi.org/10.1103/PhysRevLett.75.826 In hind-sight, as Anthony Siegman suggests, we should have described it as “slightly, or partially, absorbing.”Both the spin and orbital angular momentum of a beam can always be calculated from the transverse components of linear momentum. This transverse linear momentum arises both from the azimuthal phase gradient (orbital AM) and a combination of the beam’s intensity gradient and polarization (spin AM). For circularly polarized annular beams, as Siegman correctly describes, the azimuthal linear momentum from the spin contribution has equal and opposite senses on the inner and outer edges of the ring. As a consequence the particle spins, as shown in figure 4 of our article. A detailed consideration can be found in reference 2 2. L. Allen, M. J. Padgett, Opt. Commun. 184, 67 (2000). https://doi.org/10.1016/S0030-4018(00)00960-3 .REFERENCESSection:ChooseTop of pageREFERENCES <<1. H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995). https://doi.org/10.1103/PhysRevLett.75.826 , Google ScholarCrossref2. L. Allen, M. J. Padgett, Opt. Commun. 184, 67 (2000). https://doi.org/10.1016/S0030-4018(00)00960-3 , Google ScholarCrossref© 2005 American Institute of Physics.
DOI 10.1063/1.4796720 Related papers Manipulation of Photonic Orbital Angular Momentum for Quantum Information Processing
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Padgett and Allen reply: In our experiment, the particle was Teflon and had an absorption of a few percent, which meant it could be trapped within optical tweezers. In the review, we called it transparent to contrast it with the earlier work of H. He and coworkers. 1 1. H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
https://doi.org/10.1103/PhysRevLett.75.826 In hind-sight, as Anthony Siegman suggests, we should have described it as “slightly, or partially, absorbing.”Both the spin and orbital angular momentum of a beam can always be calculated from the transverse components of linear momentum. This transverse linear momentum arises both from the azimuthal phase gradient (orbital AM) and a combination of the beam’s intensity gradient and polarization (spin AM). For circularly polarized annular beams, as Siegman correctly describes, the azimuthal linear momentum from the spin contribution has equal and opposite senses on the inner and outer edges of the ring. As a consequence the particle spins, as shown in figure 4 of our article. A detailed consideration can be found in reference 2 2. L. Allen, M. J. Padgett, Opt. Commun. 184, 67 (2000).
https://doi.org/10.1016/S0030-4018(00)00960-3 .REFERENCESSection:ChooseTop of pageREFERENCES <<1. H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
https://doi.org/10.1103/PhysRevLett.75.826 , Google ScholarCrossref2. L. Allen, M. J. Padgett, Opt. Commun. 184, 67 (2000).
https://doi.org/10.1016/S0030-4018(00)00960-3 , Google ScholarCrossref© 2005 American Institute of Physics.
More than a century ago, pioneeringworks carried out by Poynting (1909) and other physicists have provided the evidence of the validity of Marxwell equations for an electromagnetic field, showing how a beam of light carries energy and momentum, both in the linear and angular components. In particular the angular momentum of light, related to the generator of rotations in quantum mechanics, has been typically associated with its polarization, and more specifically with its circular polarization components. An optical beam traveling in the positive direction of the z axis that is circularly polarized, carries a z-component angular momentum content σ = ±h per photon, which is positive if the circular polarization is left-handed and negative if it is right-handed. This angular momentum content is not just a formal property, but a very concrete one that can have significant mechanical effects as for example an observable induced rotation by absorption to amaterial particle Beth (1936); Friese et al. (1998)
The orbital angular momentum density of Bessel beams is calculated explicitly within a rigorous vectorial treatment. This allows us to investigate some aspects that have not been analysed previously, such as the angular momentum content of azimuthally and radially polarized beams. Furthermore, we demonstrate experimentally the mechanical transfer of orbital angular momentum to trapped particles in optical tweezers using a high-order Bessel beam. We set transparent particles of known dimensions into rotation, where the sense of rotation can be reversed by changing the sign of the singularity. Quantitative results are obtained for rotation rates. This paper's animations are available from the Multimedia Enhancements page.
The Search and Discovery report titled “An electrical insulator turns metallic within a femtosecond” (Physics Today, February 2013, page 13) is a compelling account of the recent breakthrough experiments on dynamic Stark effects performed by Ferenc Krausz and collaborators. It describes how a strong nonresonant 4-fs laser pulse can be used to generate electric currents along a nanojunction on a femtosecond time scale. Phenomenologically, the current arises from the nonlinear interaction of the active material in the silica glass nanojunction with an incident laser pulse of low temporal symmetry. By varying the degree of time asymmetry of the laser, one can change the sign and magnitude of the photoinduced current. Microscopically, the underlying rectification mechanism of that rather spectacular effect is Stark shifts so large that they can dramatically modify the electronic structure of the silica glass and even bridge its large energy gap.Significantly, and in a broader context, the groundbreaking experiment by Krausz and coworkers falls into a class of symmetry-breaking laser-control scenarios known to induce net currents in spatially symmetric systems through laser fields of low temporal symmetry.11. E. Dupont et al., Phys. Rev. Lett. 74, 3596 (1995); https://doi.org/10.1103/PhysRevLett.74.3596A. Haché et al., Phys. Rev. Lett. 78, 306 (1997); https://doi.org/10.1103/PhysRevLett.78.306S. Flach, O. Yevtushenko, Y. Zolotaryuk, Phys. Rev. Lett. 84, 2358 (2000); https://doi.org/10.1103/PhysRevLett.84.2358G. Kurizki, M. Shapiro, P. Brumer, Phys. Rev. B 39, 3435 (1989); https://doi.org/10.1103/PhysRevB.39.3435S. Kohler, P. Hänggi, Nat. Nanotechnol. 2, 675 (2007). https://doi.org/10.1038/nnano.2007.357 The idea of using Stark effects as the main microscopic mechanism for the production of currents arose in an earlier theoretical proposal to use Stark effects to bridge the energy gap of a semiconducting material.22. I. Franco, M. Shapiro, P. Brumer, Phys. Rev. Lett. 99, 126802 (2007). https://doi.org/10.1103/PhysRevLett.99.126802 The experiments demonstrate how such ideas can be applied to induce currents in a material with an energy gap as large as 9 eV.REFERENCESSection:ChooseTop of pageREFERENCES <<1. E. Dupont et al., Phys. Rev. Lett. 74, 3596 (1995); https://doi.org/10.1103/PhysRevLett.74.3596, Google ScholarCrossref, ISIA. Haché et al., Phys. Rev. Lett. 78, 306 (1997); https://doi.org/10.1103/PhysRevLett.78.306, , Google ScholarCrossref, ISIS. Flach, O. Yevtushenko, Y. Zolotaryuk, Phys. Rev. Lett. 84, 2358 (2000); https://doi.org/10.1103/PhysRevLett.84.2358, , Google ScholarCrossref, ISIG. Kurizki, M. Shapiro, P. Brumer, Phys. Rev. B 39, 3435 (1989); https://doi.org/10.1103/PhysRevB.39.3435, , Google ScholarCrossref, ISIS. Kohler, P. Hänggi, Nat. Nanotechnol. 2, 675 (2007). https://doi.org/10.1038/nnano.2007.357, , Google ScholarCrossref2. I. Franco, M. Shapiro, P. Brumer, Phys. Rev. Lett. 99, 126802 (2007). https://doi.org/10.1103/PhysRevLett.99.126802, Google ScholarCrossref© 2013 American Institute of Physics.
Again an article in Physics Today, (by Carlos Sá de melo October 2008, page 45), has incorrectly implied that Anthony Leggett was the first person to study the crossover from Bardeen-Cooper-Schrieffer to Bose–Einstein condensation. On page 47 of the article, it states that “a clear picture of the BCS-to-BEC evolution at zero temperature didn’t emerge until 1980, when Anthony Leggett realized that the physics could be captured by a simple description in real space of paired fermions with opposite spins.” Although the model I considered in my 1969 paper 1 1. D. M. Eagles, Phys. Rev. 186, 456 (1969). https://doi.org/10.1103/PhysRev.186.456 is slightly different from Leggett’s, figure 4 in my paper clearly shows regions where pairing without superconductivity occurs and where superconductivity is limited by the Bose- condensation temperature of pairs, and on page 458 I discuss a limit at which the diameter of pairs is small compared with the distance between them.I also disagree with a statement in the box on page 47 of Sá de Melo’s article that “the evolution from a Bardeen-Cooper-Schrieffer superfluid to a Bose–Einstein condensation superfluid cannot be studied in … superconductors.” At least in ceramic samples of SrTiO3 with 3% of the titanium replaced by zirconium, the transition has been studied by varying the carrier concentration via differing heat treatments to produce different concentrations of oxygen vacancies. 2 2. R. J. Tainsh, C. Andrikidis, Solid State Commun. 60, 517 (1986) https://doi.org/10.1016/0038-1098(86)90729-5 D. M. Eagles, Solid State Commun. 60, 521 (1986) https://doi.org/10.1016/0038-1098(86)90730-1 D. M. Eagles, R. J. Tainsh, C. Andrikidis, Physica C 157, 48 (1989). https://doi.org/10.1016/0921-4534(89)90466-8 It is possible that such a transition may be found in other superconducting semiconductors when people start to search for suitable materials. However, in three dimensions the pairing strength has to be above some threshold value to obtain the possibility of reaching the Bose-gas regime. Also, many authors think that the BEC regime occurs in underdoped cuprates, 3,4 3. Q. Chen, J. Stajic, S. Tan, K. Levin, Phys. Rep. 412, 1 (2005). https://doi.org/10.1016/j.physrep.2005.02.005 4. A. S. Alexandrov, J. Supercond. Nov. Magn. 20, 481 (2007). https://doi.org/10.1007/s10948-007-0258-z while the consensus is that overdoped samples are BCS-like.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. D. M. Eagles, Phys. Rev. 186, 456 (1969). https://doi.org/10.1103/PhysRev.186.456 , Google ScholarCrossref, ISI2. R. J. Tainsh, C. Andrikidis, Solid State Commun. 60, 517 (1986) https://doi.org/10.1016/0038-1098(86)90729-5 , Google ScholarCrossref, ISI D. M. Eagles, Solid State Commun. 60, 521 (1986) https://doi.org/10.1016/0038-1098(86)90730-1 , , Google ScholarCrossref, ISI D. M. Eagles, R. J. Tainsh, C. Andrikidis, Physica C 157, 48 (1989). https://doi.org/10.1016/0921-4534(89)90466-8 , , Google ScholarCrossref, ISI3. Q. Chen, J. Stajic, S. Tan, K. Levin, Phys. Rep. 412, 1 (2005). https://doi.org/10.1016/j.physrep.2005.02.005 , Google ScholarCrossref, ISI4. A. S. Alexandrov, J. Supercond. Nov. Magn. 20, 481 (2007). https://doi.org/10.1007/s10948-007-0258-z , Google ScholarCrossref, ISI© 2009 American Institute of Physics.