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In The Principles of Nonlinear Optics by Shen, he says that the generation of harmonics at low frequencies were long-known before Franken did SHG in the optical range.

Franken's idea was simple. Harmonic generation of electro­magnetic waves at low frequencies had been known for a long time. Harmonic generation of optical waves follows the same principle and should also be observable.

Which are those experiments ?

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It is done all the time in acoustics, ask any musician!

However Shen probably was referring to harmonic generation in radio frequencies; with radio is is called a frequency multiplier. The heterodyne technique was invented in 1901.

The Kerr effect was first found about 1876. The first footnote in this article provides some historical background: altering the polarization of light with strong magnetic fields. This is non-linear optics, but there is no change to the frequency.

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  • $\begingroup$ Rectification on crystals seems to have been discovered in 1874... $\endgroup$ – CuriousOne May 26 '16 at 2:47

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