Exercise: Verify that the electric field in a laser beam with intensity Ilaser =1GW/cm2is much smaller than that seen by an electron in the first Bohr orbit. Hint Recall, that
(1.7)
For the perturbation series to converge we require that
(1.8)
However, even for small fields, higher order terms may become important when resonant enhancement of susceptibilities occurs. A different, non-perturbative theory is then required. The other case in which greater sophistication of the theoretical treatment is necessary is when the laser field exceeds the atomic field. This is covered under extreme nonlinear optics.
Other approximation made in the above description is the electric - dipole approximation which amounts to retaining only the electric dipole term in the multipole expansion of the field. In general, the field can also excite higher multipoles which are neglected. The smallness parameter in the multipole expansion is atomic size/ wavelength of light. This too may need modification near a surface where the fields vary rapidly.
It is important in nonlinear optics specially to keep track of all approximations that are made because we are dealing with qualitative new effects of small terms in polarization. Often, we may find that it becomes necessary to go beyond the simplest description. And yet, we will also see that the perturbative nonlinear optics itself describes a great variety of phenomena which in turn yield a large number of devices and methods.
can also excite higher multipoles which are neglected. The smallness parameter in the multipole expansion is atomic size/ wavelength of light. This too may need modification near a surface where the fields vary rapidly.