How can we generalize the definition a non-linear media?

Question

According to the definition: Nonlinear media are dielectric materials whose polarization density changes nonlinearly if a strong field is applied to them. If the field is small the nonlinear terms become negligible and the system becomes linear.

I am confused, about whether we can write the polarization density of all dielectric materials (or any materials) as a power series of nonlinear terms.

If yes can we say that all the dielectric media are nonlinear in nature if the incident field is strong enough?

If not why do some media have nonlinear polarization density or what is the condition for a medium to show nonlinear terms in their polarization density? And how can we generalize the fundamental definition of nonlinear optical media?

Answer 1

Generally all dielectric media become nonlinear if you pump them hard enough, but in some cases the polarization density cannot be written perturbatively as a power series of the nonlinear terms:

When the field frequency is close to resonance with a transition frequency of the dielectric medium, the dynamics of the two coupled atomic states need to be taken into account, which can lead to effects such as saturable absorption. This is discussed in Chapter 6 of Nonlinear Optics by Boyd.

When the field is comparable to or larger than the atomic field strength, then the dynamics can be understood in terms of free electrons interacting with the field being weakly perturbed by the nuclear Coulomb potential, leading to effects such as high harmonic generation. This is discussed in Chapter 13 of Nonlinear Optics.