SO the real question here whose answer would clear up a lot of confusion is
>what is a wave?
A wave is something that satisfies the wave equation, and that's it.
[math]\left(\frac{\partial^2}{\partial t^2}-v^2\nabla^2\right)f(\vec{x},t)=0[/math]
If the function f(x,t) is something which corresponds to something physical, call that something a wave.
A perfect example is the plane wave:
[math]f(x,t) = \exp(ik\cdot x - i\omega t)[/math]
It is known that in a quantum mechanical system, free states which begin their life with some uncertainty in their momentum (say they were produced at some location in space, then their momentum might be distributed in a Gaussian fashion) will evolve so that the momentum becomes more precise, and the position becomes less precise. In time scales much larger than the scales associated with the production of these states, the momentum will become infinitely well defined and the position the opposite. These "asymptotic states" that exist far away from their location of origin, must naturally be expressed as plane waves then. The plane wave is what I just described.
Thus in (asymptotic) quantum field theory, we may be justified in quantizing the field by expanding local field operators using a basis with the functional form of a plane wave and the algebraic form of a quantum state - namely using the harmonic oscillator algebra, where states do not define energies, but number of quanta. This looks like
[math]\hat{\phi}(x,t) = \int \frac{d^4k}{(2\pi)^4}\frac{1}{\sqrt{2\omega_k}}\left(f_{k}(x,t)\hat{a}_k + f^*_{-k}(x,t)\hat{a}^\dagger_{-k}\right)[/math]
The quantity
[math]\hat{\phi}(x,t)|0>[/math]
physically refers to the creation of a particle at position x and time t. |0> is the physical vacuum.
This not the quantization of the photon field, but something similar. Particle and wave do not refer to the same thing, but merely reference descriptive properties of something more fundamental, the quantum field.