I had previously read that link before you made the OP and I am afraid I was just us puzzled as you were and also wondered exactly what “infinite wavelength” physically means in this context.
A photon is an oscillation of electric and magnetic fields where each generates the other through space. If a photon has infinite wavelength, then those electric and magnetic fields no longer oscillate and the implications of that are ....?
Originally posted by AThousandYoung Infinite wavelength implies zero energy doesn't it?
This is certainly true for a photon moving through a vacuum. In fact, a photon moving through a vacuum with infinite wavelength technically doesn't exist. However, in the link in the OP, the context was an existing photon moving through a metamaterial so not sure what that implies in that context.