The Orbital and Spin Momenta of Light

by kderakhshani
Tags: angular momentum, light, momenta, optics, orbital, spin
kderakhshani is offline
Feb15-14, 07:29 AM
P: 10
Hi everybody,

In most classical or quantum optics texts an angular momentum is considered for the EM radiation as the following:

[itex] J = ε_0 ∫_V r [E(r, t) B(r, t)] d^3 r [/itex]

Then it is claimed that:

"Using the usual formula for a double vector product and integrating by parts, bearing in
mind the assumption that the fields are zero at the surface of volume V introduced for the
mode expansion, one finds that JR can be written as a sum of two terms:

[itex]J = L + S , [/itex]
given by
[itex]L = ε_0 ∑_{j=(x,y,z)} ∫d^3r Ej (r, t)(r ∇)Aj (r, t) ,[/itex]
[itex]S = ε_0 ∫d^3r E(r, t) A(r, t) [/itex]

Would you please help me derive them?

Thank you
Phys.Org News Partner Physics news on
Researchers develop scalable methods for manufacturing metamaterials
Researchers find tin selenide shows promise for efficiently converting waste heat into electrical energy
After 13 years, progress in pitch-drop experiment (w/ video)

Register to reply

Related Discussions
Orbital Angular Momenta - Conversion to a Different Origin Classical Physics 1
Addition of spin angular momenta Quantum Physics 3
Orbital Spin Distribution Quantum Physics 5
Sum of two orbital angular momenta Quantum Physics 0
operating on spin angular momenta Quantum Physics 1