Light in a Twist: Orbital Angular Momentum Miles Padgett Kelvin Chair of Natural Philosophy The talk today •  Orbital Angular Momentum, what is it? •  What has been done with OAM •  A couple of example of what we have done and doing! A question •  A photon carries a spin angular momentum of  •  So how does a multi-pole transition (ΔJ > ) conserve angular momentum? Linear momentum at a radius exerts a torque k r k x r -> multipole transition Providing the lever is long enough, a fixed linear momentum can exert an arbitrary high torque Getting started on Orbital Angular Momentum of Light •  1992, Allen, Beijersbergen, Spreeuw and Woerdman Miles Padgett •  1994, Les meets Miles at dinner…... Orbital Angular Momentum from helical phase fronts r" E" z" p! B" p E" z" B" p = 0 p ≠ 0 θ θ Angular momentum in terms of photons •  Spin angular momentum σ = +1! –  Circular polarisation (cid:2)  σ per photon •  Orbital angular momentum σ = -1! –  Helical phasefronts (cid:2)   per photon  = 0!  = 1!  = 2!  = 3! etc! Optical vortices, Helical phasefronts , Angular momentum •  Intensity, I ≥0 = 0! •  Phase, 2π ≥ φ ≥0  = 0, plane wave  = 1, helical wave = 1!  = 2, double helix I n t  = 3, pasta fusilli e r f e etc. r = 2! e n c e + / -  #  = 3!  = vortex charge! I! φ& I! Orbital angular momentum from Skew rays Poynting vector Making helical phasefronts with holograms