Photon orbital angular momentum: problems and perspectives

Electromagnetic fields can carry, besides energy, linear and angular momentum. The exchange of linear momentum with matter produces forces due to radiation pressure. That comet tails point away from the Sun because light carries linear momentum was first suggested by Kepler. A complete account of radiation pressure was developed by Poynting in 1905 in terms of electromagnetic linear momentum density and in 1909 Einstein showed that the black-body radiation is made compatible with molecular motion assuming a linear angular momentum k per photon (k = 2π/λ, where λ is the wavelength) [1]. Since then, the large body of work on the mechanical effects of radiation on matter concerned almost exclusively with linear momentum [2]. In recent times, the radiation linear momentum was exploited in atom trapping and cooling. That circularly polarized light could transfer an angular momentum of per photon to a quarter waveplate was first realized by Poynting in 1909 [3]. An elegant experiment was made by Beth, using a quarter waveplate hanging from a torque balance [4, 5]. Similar torque experiments were repeated on metallic screens in the microwave region by Carrara in 1949 [6]. The mechanical torque measured in all these experiments relays on the polarization of the incident light and it is due to what it usually referred to as the intrinsic (or spin) angular momentum of photons. The component of the intrinsic angular momentum of photons along their propagation direction is the photon helicity (z-component of the photon spin) and takes the values of± per photon. A full electromagnetic approach to radiation, however, yields to the following expression for the total angular momentum of the electromagnetic field in a volume V [7]