The I/Q modulators , when used as continuous phase shifters, generally exhibit a non-linear tranfer function.  Fig.1 gives a first-order representation of it . This pattern repeats itself indefinitely modulo 2pi. The (small) deviations from the linear response can be decomposed in Fourier series within the 2pi window.
 

When the I/Q modulator is used as a frequency translator, the different components of the series act as as many modulating frequencies,generating  individual lines, as sketched in Fig.2.  The fundamental line remains unaffected.