SQUARE LAW MODULATOR
The characteristics of a nonlinear device in general can be written :
working point: 
modulating information : 
carrier: 
The signal that drives the nonlinear device is the sum of working point, information and carrier.
Spectrum
The spectrum can be obtained by using the trigonometric identities:
, 
Frequency Components
Modulation Index
The moduation index m of the AM signal created with a square law modulator is not the quotient of the modulating signal
and the carrier. It can be calculatd by having a look at the components at the particular frequencies of the upper (or lower) sideband and the carrier.