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.
© 2014 Optical Society of America
Original Manuscript: June 3, 2014
Revised Manuscript: July 26, 2014
Manuscript Accepted: July 27, 2014
Published: August 18, 2014
Ivan Fernandez-Corbaton, Xavier Zambrana-Puyalto, and Gabriel Molina-Terriza, "On the transformations generated by the electromagnetic spin and orbital angular momentum operators," J. Opt. Soc. Am. B 31, 2136-2141 (2014)