Adapting Mach-Zehnder Mesh Equalizers in Direct-Detection Mode-Division-Multiplexed Links

A Mach-Zehnder mesh (MZM), which is comprised of a network of tunable $2\times 2$ Mach-Zehnder interferometers and embedded photodetectors (PDs), can be used to perform arbitrary unitary matrix multiplications in the optical domain and compensate modal crosstalk in short-reach mode-division-multiplexed (MDM) links that use direct detection (DD). MZMs can be adapted using a self-configuration method, proposed by Miller, where multiple low-speed and low-power code sequences are superimposed on parallel high-speed information streams. We show that self-configuration in its original form is a sub-optimal equalization method for high-speed data transmission because adaptation based on detected code strengths is adversely impacted by low measurement signal-to-noise ratios and interference from the high-speed information streams. These impairments prevent the method from accurately tracking the millisecond-timescale modal dynamics of short-reach DD-MDM channels. We propose small modifications to the self-configuration method that can enable the MZM to track up to $10<^>8$-fold faster channel dynamics. In particular, we show that replacing continuous equalization of low-power code sequences by periodic equalization of full-power training signals and using special optimization methods can yield faster MZM tuning. We also discuss the tradeoffs between MZM architectures that embed PDs inside the mesh and those that have PDs at the output ports only. Our results indicate that optimally designed MZMs and their associated control methods can increase the information capacity of short-reach multimode optical fiber links.