Flatness-based pre-compensation of laser diodes

TL;DR

This paper introduces a flatness-based feed-forward control method for laser diodes that compensates distortions in optical signals, enabling high-fidelity light modulation suitable for fiber-optic communication.

Contribution

It demonstrates that laser diode models are flat systems and develops a practical control scheme using analytic approximations for real-time implementation.

Findings

The proposed method effectively compensates diode distortions in simulations.

The control scheme is robust against modeling and implementation errors.

Analytic approximations enable simple electronic circuit design.

Abstract

A physical nonlinear dynamical model of a laser diode is considered. We propose a feed-forward control scheme based on differential flatness for the design of input-current modulations to compensate diode distortions. The goal is to transform without distortion a radio-frequency current modulation into a light modulation leaving the laser-diode and entering an optic fiber. We prove that standard physical dynamical models based on dynamical electron and photons balance are flat systems when the current is considered as control input, the flat output being the photon number (proportional to the light power). We prove that input-current is an affine map of the flat output, its logarithm and their time-derivatives up to order two. When the flat output is an almost harmonic signal with slowly varying amplitude and phase, these derivatives admit precise analytic approximations. It is then possible to design simple analogue electronic circuits to code approximations of the nonlinear computations required by our flatness-based approach. Simulations with the parameters of a commercial diode illustrate the practical interest of this pre-compensation scheme and its robustness versus modelling and analogue implementation errors.