I noted that in physics, to study electromagnetic wave phenomena when there is a sinusoidal behaviour, often is used the approximation of harmonic oscillation. I tried to understand the basics of why and I found, for example:
$$e^{ikx} \approx 1 + ikx +i^2\frac{k^2r^2}{2}+ \cdots $$
If we considered only the real part of the wave, we would have found the importance of the second term $kx$ which is the model of a recall force, used for the harmonic oscillator equation.
It can be used if we cut off the terms at the first order, using thus an approximation valid only for little oscillations. But this approximations are valid in a very extended physics area, so does this mean that almost every electromagnetic wave produce little oscillations in our daily life? Is this approximation still valid with very intense or high frequency fields, when the oscillations caused are not so small?