Scalar model; monochromatic wave কী?

In most of wave optics the vector nature of light plays no role (the superposed waves share one polarization, or the light is unpolarized and the polarizations average out): the field is replaced by a real scalar vibration

with an amplitude $a(M)$ and a phase $\varphi(M)$ at each point, both slowly varying on the scale of a wavelength. A monochromatic wave has a single $\omega$: an idealization, since a real source emits over a band of frequencies. Visible light: $\lambda_0$ from $400$ to $750\,\mathrm{nm}$ in vacuum, $\nu = c/\lambda_0$ from $7.5 \times 10^{14}$ to $4 \times 10^{14}$ Hz, periods of about $2\,\mathrm{fs}$.