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The Orbital and Spin Momenta of Light

by kderakhshani
Tags: angular momentum, light, momenta, optics, orbital, spin
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kderakhshani
#1
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
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