# Selection Rules and Light with Orbital Angular Momentum

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1. Jan 7, 2015

### zen loki

When we first learn of selection rules for atomic transitions, we learn that electrons have to change between states that differ in angular momentum by at most 1ħ, because photons have 1 unit of spin angular momentum.

However, photons can have arbitrarily high integer quantities of orbital angular momentum, meaning the total angular momentum available can be more than 1. So, would we expect that different transitions and selection rules are possible? In specific circumstances, would light with orbital angular momentum absorb differently than the same frequency without orbital angular momentum?

2. Jan 8, 2015

### DrDu

The point is that due to the long wavelength of light as compared with atomic dimensions, by far the strongest transitions are dipole transitions. Transitions corresponding to the absorption of light with higher angular momentum have a much lower intensity. Specifically, the eigenstates of light angular momentum are the vector spherical harmonics and e.g. a plane wave can be decomposed into them.