Title: Optical fluxes in coupled $\cal PT$-symmetric photonic structures,
Abstract: In this work we first examine transverse and longitudinal fluxes in a $\cal
PT$-symmetric photonic dimer using a coupled-mode theory. Several surprising
understandings are obtained from this perspective: The longitudinal flux shows
that the $\cal PT$ transition in a dimer can be regarded as a classical effect,
despite its analogy to $\cal PT$-symmetric quantum mechanics. The longitudinal
flux also indicates that the so-called giant amplification in the $\cal
PT$-symmetric phase is a sub-exponential behavior and does not outperform a
single gain waveguide. The transverse flux, on the other hand, reveals that the
apparent power oscillations between the gain and loss waveguides in the $\cal
PT$-symmetric phase can be deceiving in certain cases, where the transverse
power transfer is in fact unidirectional. We also show that this power transfer
cannot be arbitrarily fast even when the exceptional point is approached.
Finally, we go beyond the coupled-mode theory by using the paraxial wave
equation and also extend our discussions to a $\cal PT$ diamond and a
one-dimensional periodic lattice.