Light waves are not density waves. They reflect a change in the electric field emanating from something. The change is not observed everywhere immediately, but instead the information takes time to arrive.

A wave is simply a periodic function. Any pattern may be interpreted as overlapping sine waves by the Fourier transform and its cousins. Light waves are a convenient way to think of a phenomenon causing the electromagnetic field to carry energy from one place to another, but they are only an approximation of that. The field is the "real thing."

Photons and other particles are probability waves, where the value determines the likelihood of observing a particle at a given location. This probability field happens to coincide with the electromagnetic field because the quantum (Compton) wavelength of a photon is the same as the electromagnetic wavelength. But either way, such waves don t exist in any way except as an approximation of a field which has a value at every point in space.