Light’s Twist Miles Padgett FRS Kelvin Chair of Natural Philosophy
! Light beams carry a Linear Momentum
• Light carries a linear momentum – Force exerted = Power/c
• Laser pointer exerts 10-11 N
• Strong enough to move cells and bacterial
• Or (with a very large sail!) a spacecraft…. Light’s Angular Momentum in History
We now refer to this as the SPIN angular momentum of the photon
But light has an extra angular momentum in addition to photon spin (this extra momentum is needed for some rare atomic transitions) 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
E
E B S B S
Sθ = 0 Sθ ≠ 0 Angular momentum in terms of photons
• Spin angular momentum σ = +1! – Circular polarisation σ! per photon • Orbital angular momentum σ = -1! – Helical phasefronts ℓ! per photon A double-start helix (ℓ=2)
Chambord castle (chateaux de la Loire) Orbital angular momentum from Skew rays
Poynting vector
E
B S Orbital angular momentum from skew rays Angular Momentum Transfer
Spin Angular Momentum Orbital Angular Momentum (circular angular momentum) (helical phasefronts) OAM and SLM control OAM in Phenomenology in micromanipulation
OAM in Quantum OAM in Imaging OAM in Communications Optics The OAM communicator
• Every OAM state forms an independent channel
Linear vs. Rotational Doppler shifts
Light source! Light source! - exerts force = P/c! - exerts torque = ℓP/ω !
Ω! v!
Doing work on a light beam changes its energy and hence shifts it’s frequency Doppler shift from a SPINNING surface
N photons per second
Torque= ℓN!ω/ω
Work Done= ΩNℓ!
Work per photon Ω≠0! !Δω = Ωℓ!
Frequency shift Δω = Ωℓ
v=0! Illuminate with OAM at +/- ℓ and measure Δω'
A B 0
L -5 dB
H -10 -15
Power -20 . -25 Rel -30 2200 2250 2300 2350 2400 2450 2500
fmod Hz C 500 H L 450 L
1 400 - s . 350 rad H 300 W 250 200 1200 1400 1600 1800 2000 2200 2400 2600
fmod Hz
H L Me Sonja Franke-Arnold Johannes Courtial Students/RAs, Students/RAs,
Richard Bowman especially Graham Gibson Martin Lavery Jonathan Leach Kevin O’Holleran Jackie Romero
Les Allen Steve Barnett Collaborators Bob Boyd External Jon Cooper Mark Dennis Mervyn Miles Monika Ritsch-Marte Wilson Sibbett