Closed formulas to know the Spin part and Orbital part of the Angular Momentum of a beam of light are well-known for free-space beams. See for example [1,2,3]:
But these formulations are valid in free space. What formulations can be applied to separate the Angular Momentum into its spin and orbital parts when non-homogeneous materials are involved?
For instance, I am interested in a disc dielectric resonator supporting whispering gallery modes. It is generally known that in such a resonator each photon carries an orbital angular momentum of L*h, where L is the order of the mode (number of wavelengths in a circle). [4]
The spin part of orbital momentum in this case is (I believe) zero.
However, my doubt is: when L = 1 (the lowest order mode, in which the dielectric resonator acts like a dipole if it is small enough) the mode is radiative, and in the center of the dielectric resonator there is a circularly polarized electric field, suggesting that the photons in this resonance have spin angular momentum. Will they only have spin part, and not orbital part, in that case? Or some of both?
I would appreciate any references or suggestions regarding this, or regarding in general the calculation of orbital momentum in non-homogenoeus structures like resonators.
1. L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185–8189 (1992).
2. S. M. Barnett and L. Allen, "Orbital angular momentum and nonparaxial light beams," Opt. Commun. 110, 670–678 (1994).
3. S. J. van Enk and G. Nienhuis, "Spin and Orbital Angular Momentum of Photons," Europhys. Lett. 25, 497–501 (1994).
4. A. Matsko, A. Savchenkov, D. Strekalov, and L. Maleki, "Whispering Gallery Resonators for Studying Orbital Angular Momentum of a Photon," Phys. Rev. Lett. 95, 143904 (2005).
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Electromagnetism