I always thought brain waves are only artifacts of the flow of electrons within the brain - a moving charge creates an EM field. In the same way one could talk about "CPU waves" - EM emissions generated by electricity flowing through the processor.
One of the most important ways the brain communicates is actually not just ionically through chemo-ionic channels but through summed wave activity. This is especially important in sleep and also during long term potentiation of circuits.
If you're curious about brain waves, I highly recommend this book. It is fascinating.