On the transformations generated by the electromagnetic spin and orbital angular momentum operators

Ivan Fernandez-Corbaton*, Xavier Zambrana-Puyalto, Gabriel Molina-Terriza

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


We present a study of the properties of the transversal "spin angular momentum" and "orbital angular momentum" operators. We show that the "spin angular momentum" operators are generators of spatial translations that depend on helicity and frequency and that the "orbital angular momentum" operators generate transformations that are a sequence of this kind of translation and rotation. We give some examples of the use of these operators in light-matter interaction problems. Their relationship with the helicity operator allows us to involve electromagnetic duality symmetry in the analysis. We also find that simultaneous eigenstates of the three "spin" operators and parity define a type of standing mode that has recently been singled out for the interaction of light with chiral molecules. With respect to the relationship between "spin angular momentum," polarization, and total angular momentum, we show that, except for the case of a single plane wave, the total angular momentum of the field is decoupled from its vectorial degrees of freedom even in the regime in which the paraxial approximation holds. Finally, we point out a relationship between the three "spin" operators and the spatial part of the Pauli-Lubanski four vector.

Original languageEnglish
Pages (from-to)2136-2141
Number of pages6
JournalJournal of the Optical Society of America B: Optical Physics
Issue number9
Publication statusPublished - 1 Sept 2014


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