A Taylor series expansion of a nonlinearity will show multiplications that give rise to the desired higher order products.
Design goals for mixers seek to select the desired heterodyne products and suppress the undesired ones.
One classic design for a harmonic mixer uses a step recovery diode (SRD).
The resulting impulse train has the harmonics of the input sine wave present to a high frequency (such as 18 GHz).
This forms the basis of many simple 'bug detectors' where the intention is to detect transmission on any frequency, even if not known in advance.
When the required frequency multiple is lower, such as doubling, tripling or quadrupling, then Schottky diode circuits are more common.
Unlike a normal mixer, there is a fairly clear optimum drive level, above which the conversion loss increases.