I understand that the modulation depth of a sinusoidally modulated signal can be defined as the modulation amplitude divided by the mean value, as explained here.
But why would one wish for a high modulation depth in an experiment? What advantages does it bring?
Some articles state that they have achieved a high modulation depth of 90%, but isn't what matter that amplitude of the signal or its "shape"/frequency?
The higher the modulation index is in a double sideband AM system (DSB) the higher is the SNR when detected; this is true for both coherent and non-coherent (envelope) detection methods.
Write the DSB-AM signal as $$x(t)=A_c(1+\kappa m(t)) \rm{sin} (\omega_c T) \tag{1}\label{1}$$ where $0 < \kappa \le 1$ is the modulation index, $-1 \le m(t) \le 1$ the modulation (information bearing signal) and $\omega_c$ is the carrier frequency whose amplitude is $A_c$. Assume that the signal is received in white normal noise of intensity $\mathcal N_0$ then for coherent detection the signal is detected with $$(SNR)_D=2(SNR)_T \frac{\kappa^2 \langle m^2 \rangle}{1+{\kappa^2 \langle m^2 \rangle}} \tag{2}\label{2}$$ Here $\langle m^2 \rangle$ is the variance of the modulation, and $(SNR)_T=\frac{P_T}{N_T}$ with $N_T=2\mathcal N_0 W$ and $P_T=\frac{1}{2}A_c^2(1+{\kappa^2 \langle m^2 \rangle})$ being the received RF noise and RF transmit powers, resp.
For non-coherent detection the received SNR is $$(SNR)_D=\frac{2(SNR)_T}{1+\frac{2}{(SNR)_T}} \frac{\kappa^2 \langle m^2 \rangle}{(1+{\kappa^2 \langle m^2 \rangle})^2} \tag{3}\label{3}$$
As you can see from $\eqref{2}$ and $\eqref{3}$ both coherent and non-coherent detection SNR are monotonically increasing function of the modulation index $\kappa$, higher the index $\kappa$ the higher the $SNR$ is.
An all-around excellent book to read on this (chapter 8) and also on many other subjects is
[1] Ziemer and Tranter: PRINCIPLES OF COMMUNICATIONS: Systems, Modulation, and Noise, Wiley 7th ed.
A general note of caution: in practice, the true performance of DSB-AM with high modulation index is quite sensitive to both transmitter and receiver nonlinearities that are always present and will inevitably degrade the theoretical SNR discussed here.
In the context of intensity-modulated optical communications systems, a high modulation depth is preferred because it implies high efficiency, where efficiency is defined in terms of bits of data transferred per joule of energy.
Only the modulation amplitude contributes a useful signal. The power that is present at the minimum of the signal doesn't carry any information. It increases the energy sent per bit without improving the signal-to-noise ratio of the system.
Practically, though, the goal is usually to achieve a modulation depth that is "high enough" rather than to maximize it, because beyond a certain point there are diminishing returns for additional improvements in modulation depth.
You would see a similar benefit (i.e. better signal discrimination with less optical power) if you were using a high-modulation-depth modulator, for example, to control the exposure of a sample in a fluorescence experiment (you wouldn't want to continue exposing the sample to pump light during the emission phase of the experiment).
And, as presented in your linked article, a high modulation-depth absorber is also essential to constructing a high-quality mode-locked laser.
