A key role of transversality condition in quantization of photon orbital angular momentum

Abstract

The effect of the transversality condition on the quantization of the photon orbital angular momentum is studied. The quantum gauge that is deduced from the transversality condition is shown to be a Berry gauge. It determines a helicity-dependent reference point relative to which the position is canonically conjugate to the momentum. As a result, the photon orbital angular momentum about the origin of the laboratory reference system split into two parts. One is the orbital angular momentum of the photon about the reference point, which is canonical. The other is the orbital angular momentum of the photon concentrated at the reference point, which is dependent on the helicity. Only when the Berry-gauge degree of freedom of a paraxial beam is perpendicular to the propagation direction, does the total orbital angular momentum reduce to its canonical part. One of the observable effects of the Berry-gauge degree of freedom is also clarified.