Optical phases, 0 electrodynamics, phase

Therefore, the distinction between the topological and dynamical phase has vanished, and the realization has been reached that the phase in optics and electrodynamics is a line integral, related to an area integral over Bt3> by a non-Abelian Stokes theorem, Eq. (553), applied with 0(3) symmetry-covariant derivatives. It is essential to understand that a non-Abelian Stokes theorem must be applied, as in Eq. (553), and not the ordinary Stokes theorem. We have also argued, earlier, how the non-Abelian Stokes explains the Aharonov-Bohm effect without difficulty. 

The received view, in which the phase factor of optics and electrodynamics is given by Eq. (554), can describe neither the Sagnac nor the Tomita-Chiao effects, which, as we have argued, are the same effects, differing only by geometry. Both are non-Abelian, and both depend on a round trip in Minkowski spacetime using 0(3) covariant derivatives. 

Phase functions can also be used to measure the size and refractive index of a microsphere, and they have been used by colloid scientists for many years to determine particle size. Ray et al. (1991a) showed that careful measurements of the phase function for an electrodynamically levitated microdroplet yield a fine structure that is nearly as sensitive to the optical parameters as are resonances. This is demonstrated in Fig. 21, which presents experimental and theoretical phase functions obtained by Ray and his coworkers for a droplet of dioctylphthalate. The experimental phase function is compared with two... 

Finally, in this section, we develop the concept of electromagnetic phase from U(l) to 0(3). This is a nontrivial development [4] that has foundational consequences for interferometry and physical optics for example. In U(l) electrodynamics, the electromagnetic phase is defined up to an arbitrary factor... 

These field equations are therefore the result of a non-Abelian Stokes theorem that can also be used to compute the electromagnetic phase in 0(3) electrodynamics. It turns out that all interferometric and physical optical effects are described self-consistently on the 0(3) level, but not on the U(l) level, a result of major importance. This result means that the 0(3) (or SO(3) = SU(2)/Z2) field equations must be accepted as the fundamental equations of electrodynamics. 

Physical optics, and interferometry in general, are described by the phase equation of 0(3) electrodynamics, Eq. (524). The round trip or closed loop in Minkowski spacetime is illustrated as follows ... 

Plasmon based optical spectroscopy of metal clusters is best described by electrodynamics. To describe the behavior of the plasmon oscillation it is appropriate to apply a quasi-static regime only for a cluster of around 10-20 nm. The static regime assumes that the phase shift in the colloidal particle is small enough to be neglected reducing the cluster oscillation to a simple dipole. 

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