If you think about how a diode mixer works then you're using a square wave LO, same for a Gilbert cell. Remember, a square wave is just a sum of odd harmonics.

If you think about how a diode mixer works then you're using a square wave LO, same for a Gilbert cell. Remember, a square wave is just a sum of odd harmonics. The only downside is that a strong signal at a multiple of the signal of interest might get aliased into your IF. Hence bandpass filtering on the input is important.