Waveguide-waveguide coupling or directional coupler

kaps_nit

Hi,
There are probably hundreds of books explaining (mathematically!!) how a directional coupler works. Mathematically its straight forward how energy completely transfers from one waveguide to another waveguide periodically.
But what I fail to understand is what is the physical phenomena driving all the energy from one waveguide to another and vice versa.
Any opinion will be very much appreciated.

Thank you