An adaptive stepsize controlled solver for the dynamic WDM semiconductor optical amplifier response

Abstract

A time-domain solver for the response of a Semiconductor Optical Amplifier (SOA) relying on multigrid numerical techniques and a wideband steady state material gain coefficient is presented for the first time. Multigrid techniques enable the efficient solution of implicit time discretization schemes for the associated system of coupled differential equations, namely the carrier rate equation in the time domain and the signal amplification in the spatial domain, which in turn enable accuracy-instead of stability-restricted time-discretization of the signals. This allows lifting off the limitations of an equidistant spatio-temporal grid for the representation of the incoming signals adopted by traditional explicit SOA models, releasing an adaptive stepsize controlled solver for the dynamic SOA response with dense timesampling under a rapidly varying SOA signal output and scarce time-sampling when negligible changes are observed.

Efficient and Validated Time Domain Numerical Modeling of Semiconductor Optical Amplifiers (SOAs) and SOA-based Circuits

“…Vagionas and Bos [44] presented a novel multigrid solver for the dynamic response of the SOA, relying on the wideband steady-state gain coefficient of Eq. (2).…”

“…Section 5 presents a newly introduced efficient solver in the time domain, relying on implicit schemes and multigrid concepts. Implicit schemes allow developing an adaptive step sizecontrolled solver for the WDM SOA response [42][43][44], which extends the validated TMM model by lifting the limitations of spatiotemporal grids and releasing adaptive sampling at the SOA output. Toward application in realistic system-level scenarios, the last section presents experimentally validated numerical results for two predominant SOA-based all-optical signal processing circuits, such as a coupled SOA XGM flip-flop arrangement and an XOR gate based on SOA-MZI XPM configuration.…”