Residue orbital angular momentum in interferenced double vortex beams with unequal topological charges S. H. Tao1, X.-C. Yuan1, 2, J. Lin1, and R. E. Burge3 1
Photonics Research Center, School of Electrical & Electronic Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798 2 Institute of Optoelectronics, Key Laboratory of Optoelectronic Devices and Systems of Chinese Education Ministry, Shenzhen University, 518060 Shenzhen, P R China 3 Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 0HE, UK
[email protected]
Abstract: When two vortex beams with unequal topological charges superpose coherently, orbital angular momentum (OAM) in the two beams would not be cancelled out completely in the interference. The residual OAMs contained by the superposed beam are located at different concentric rings and may have opposite orientations owing to the difference of the charges. The residual OAM can be confirmed by the rotation of microparticles when difference between the charges of two interfering beams is large. ©2006 Optical Society of America OCIS codes: (050.1970) Diffractive optics; (090.0090) Holography; (140.7010) Trapping
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
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1. Introduction In recent years, studies on the orbital angular momentum (OAM) of a vortex beam have extensively been reported.1-4 A vortex beam with helical phase structure of exp(ilθ ), where l #9855 - $15.00 USD
(C) 2006 OSA
Received 2 December 2005; revised 17 January 2006; accepted 18 January 2006
23 January 2006 / Vol. 14, No. 2 / OPTICS EXPRESS 535
is the topological charge and θ is the azimuthal angle, possesses OAM.1 Helical phase can exist in a Gaussian beam, namely the Laguerre-Gaussian (LG) beam, modulated vortices,5-7 or a high-order Bessel beam.8-10 A vortex beam with an integer charge always forms a zerointensity core encompassed by a bright ring in free-space propagation. As the tightly focused doughnut is associated with optical gradient force and OAM, so the beam can be used for trapping and rotating particles intrinsically or extrinsically.3 Moreover, the OAM carried by a vortex beam can also be applied for information encryption/decryption in free-space optical communications.11 Recently, generation and characterization of beams interfered by double vortex beams have intensively been implemented, and interferences by two vortex beams with charges of l1=-l2 have also been employed for stably trapping microparticles without rotation as the OAMs in each interfering beam have been cancelled out after the coherent superposition.12 However, when two vortex beams with charges of |l1|≠|l2| interfere, the OAMs of both the interfering beams are not equal and cannot totally be neutralized; as a result, the interferenced beam still possesses residual OAM, which is not identical to that of either of the vortex beams any more. To our best knowledge, optical rotation induced by a beam interfered by two vortex beams with unequal charges of |l1|≠|l2| has not been experimentally demonstrated. In this paper, we investigate intensity and phase evolutions of the beams interfered by two vortex beams with unequal charges, and generate the interferenced beams experimentally. Optical rotation induced by the interferenced beam is also demonstrated. 2. Simulation of beam propagation As we know, a vortex beam can be generated by a phase-only hologram with expression of exp(ilθ ) , and for a beam interfered by two vortex beams its complex amplitude can be expressed by, E ( x, y ) = A1 ( x, y ) ⋅ exp[il1θ ( x, y )] + A2 ( x, y ) ⋅ exp[il2θ ( x, y )] ,
(1)
where A1(x, y) and A2(x, y), l1 and l2 are the corresponding interfering vortex beams’ amplitudes and topological charges, respectively. The interference can be classified into two groups based on the charges: (1) l1·l2>0 and (2) l1·l2
