Possibility of measuring the Abraham force using whispering gallery modes

Critical experimental tests of the time-dependent Abraham force in phenomenological electrodynamics are scarce. In this paper, we analyze the possibility of making use of intensity-modulated whispering gallery modes in a microresonator for this purpose. Systems of this kind appear attractive, as the strong concentration of electromagnetic fields near the rim of the resonator serves to enhance the Abraham torque exerted by the field. We analyze mainly spherical resonators, although as an introductory step we consider also the cylinder geometry. The orders of magnitude of the Abraham torques are estimated by inserting reasonable and common values for the various input parameters. As expected, the predicted torques turn out to be very small, although probably not beyond reach experimentally. Our main idea is essentially a generalization of the method used by G. B. Walker et al. [Can. J. Phys. 53, 2577 (1975)] for low-frequency fields, to the optical case.