Orbital angular momentum of light and Laguerre-Gaussian modes PDF
Preview Orbital angular momentum of light and Laguerre-Gaussian modes
Optical Angular Momentum Laguerre-Gaussian Modes of Laser Light Dimitri Dounas-Frazer [email protected] Department of Physics University of California, Berkeley phy250(cid:150)p.1/14 Beth’s 1936 experiment ‘ Laguerre-Gaussian (LG ) modes p ‘ Production of LG modes p ‘ Circularly polarized LG beams p Overview phy250(cid:150)p.2/14 ‘ Laguerre-Gaussian (LG ) modes p ‘ Production of LG modes p ‘ Circularly polarized LG beams p Overview Beth’s 1936 experiment phy250(cid:150)p.2/14 ‘ Production of LG modes p ‘ Circularly polarized LG beams p Overview Beth’s 1936 experiment ‘ Laguerre-Gaussian (LG ) modes p phy250(cid:150)p.2/14 ‘ Circularly polarized LG beams p Overview Beth’s 1936 experiment ‘ Laguerre-Gaussian (LG ) modes p ‘ Production of LG modes p phy250(cid:150)p.2/14 Overview Beth’s 1936 experiment ‘ Laguerre-Gaussian (LG ) modes p ‘ Production of LG modes p ‘ Circularly polarized LG beams p phy250(cid:150)p.2/14 Beth’s 1936 experiment Each photon in a (cid:27) beam (cid:6) ~ carries (cid:6) spin angular momentum Birefringent plate transforms (cid:27) beam to (cid:27) (cid:0) + Plate experiences torque Both classical and quantum the- ories predict same value R. A. Beth, Phys. Rev. 50, 115 (1936) phy250(cid:150)p.3/14 Laguerre polynomial with p + 1 radial nodes Gaussian with beam waist w Vortex with topological charge ‘ ~ Orbital angular momentum ‘ per photon Cylindrically symmetric solutions to the wave equation LG‘ Laguerre-Gaussian ( ) modes p 2 2 2 2 ‘ ‘ ‘ (cid:0)r =w (cid:0)i‘(cid:30) u (r; (cid:30)) / r L (2r =w ) e e p p phy250(cid:150)p.4/14 Laguerre polynomial with p + 1 radial nodes Gaussian with beam waist w Vortex with topological charge ‘ ~ Orbital angular momentum ‘ per photon Cylindrically symmetric solutions to the wave equation LG‘ Laguerre-Gaussian ( ) modes p 2 2 2 2 ‘ ‘ ‘ (cid:0)r =w (cid:0)i‘(cid:30) u (r; (cid:30)) / r L (2r =w ) e e p p Laguerre polynomial with p + 1 radial nodes phy250(cid:150)p.4/14 Gaussian with beam waist w Vortex with topological charge ‘ ~ Orbital angular momentum ‘ per photon Cylindrically symmetric solutions to the wave equation LG‘ Laguerre-Gaussian ( ) modes p 2 2 2 2 ‘ ‘ ‘ (cid:0)r =w (cid:0)i‘(cid:30) u (r; (cid:30)) / r L (2r =w ) e e p p Laguerre polynomial with p + 1 radial nodes Gaussian with beam waist w phy250(cid:150)p.4/14
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