Orbital Angular Momentum Miles Padgett

57 Pages·2013·4.57 MB·English

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