[edit 3/2/18] There are problems with the title and wording of this question. I would edit, but to do so would alter the relationship between the question and the answer that I accepted. So, I have re-asked the question in a way that better describes what I was trying to learn. You can find the new version of this question here.
This is a newbie question. The manufacturer's data sheet for a material shows its attenuation curve over a range of frequencies. Does that curve represent the material's linearity of its attenuation? Or, does linearity mean that if the input waveform is sinusoidal, the attenuated signal will also be sinusoidal? Or, does it mean something else?
My understanding from the answer to a previous question is that high field strength can cause an attenuator to become non-linear, so that it attenuates more or less at a particular frequency, depending on the detail of the non-linearity. What does this mean? Is it that 1) the manufacturer's attenuation curve is altered, so that attenuation is enhanced or diminished at certain frequencies relative to when it's operating linearly, or 2) e.g., an input sine wave is output as a square wave, or 3) an input signal at one frequency is output at a different frequency, or 4) something else?