As seen in the previous slide the MZM has a nonlinear field transfer characteristic. To study the impact of this nonlinearity the spectrum of the driving signal and the spectrum of the modulator output are compared in the next slide. When modulating the optical carrier with a continuous sine wave (single tone) with frequency $\omega_0$ the spectrum of the modulated carrier shows harmonics, i.e. spectral components at integer multiples of $\omega_0$. When modulating with a single tone we operate the MZM in the quadrature point where the ouput field is in the normalized range -1...1.

The spectrum can also be studied for an On-Off keying (OOK) signal that uses binary symbols. In that case the modulator is operated in the minimum transmission point where the output power is in the normalized range 0...1

In order to mitigate the nonlinearity the modulation index can be decreased thus driving the modulator in the linear region of the sine shaped transfer characteristic. The modulation index $m$ is defined as $$ m = \frac{\max u_1}{U_\mathrm{full}}, $$ where $U_\mathrm{full}$ is the voltage yielding maximum output power. For $m < 1$ optical power is lost as the modulator is not driven in the full possible range. We therefore define the modulation excess loss $a=P_\mathrm{in}/P_\mathrm{out}$ with the mean optical input power $P_\mathrm{in}$ and the mean optical output power $P_\mathrm{out}$. In the following slide the relationship of nonlinear distortion, modulation index and modulation excess loss can be studied.