Angular momentum in optics

In classical Maxwell electrodynamics the Poynting vector is a linear momentum density of electromagnetic field.

${\displaystyle \mathbf{S}(\mathbf{r},t)={\mathrm{ϵ<!--\; ϵ\; -->}}_0{c}^2\mathbf{E}(\mathbf{r},t)\times <!--\; \times \; -->\mathbf{B}(\mathbf{r},t).}$

The angular momentum density vector ${\displaystyle \mathbf{L}(\mathbf{r},t)}$ is given by a vector product as in classical mechanics:

${\displaystyle \mathbf{L}(\mathbf{r},t)=\mathbf{r}\times <!--\; \times \; -->\mathbf{S}(\mathbf{r},t).}$

The above identities are valid locally, i.e. in each space point ${\displaystyle \mathbf{r}}$ in a given moment ${\displaystyle t}$.