  The use of directly modulated lasers (DMLs) is attractive in low-power,
cost-constrained short-reach optical links. However, their limited modulation
bandwidth can induce waveform distortion, undermining their data throughput.
Traditional distortion mitigation techniques have relied mainly on the separate
training of transmitter-side pre-distortion and receiver-side equalization.
This approach overlooks the potential gains obtained by simultaneous
optimization of transmitter (constellation and pulse shaping) and receiver
(equalization and symbol demapping). Moreover, in the context of DML operation,
the choice of laser-driving configuration parameters such as the bias current
and peak-to-peak modulation current has a significant impact on system
performance. We propose a novel end-to-end optimization approach for DML
systems, incorporating the learning of bias and peak-to-peak modulation current
to the optimization of constellation points, pulse shaping and equalization.
The simulation of the DML dynamics is based on the use of the laser rate
equations at symbol rates between 15 and 25 Gbaud. The resulting output
sequences from the rate equations are used to build a differentiable
data-driven model, simplifying the calculation of gradients needed for
end-to-end optimization. The proposed end-to-end approach is compared to 3
additional benchmark approaches: the uncompensated system without equalization,
a receiver-side finite impulse response equalization approach and an end-to-end
approach with learnable pulse shape and nonlinear Volterra equalization but
fixed bias and peak-to-peak modulation current. The numerical simulations on
the four approaches show that the joint optimization of bias, peak-to-peak
current, constellation points, pulse shaping and equalization outperforms all
other approaches throughout the tested symbol rates.
