Fig. 1: Simplified vision of a spectrally sliced OAWG system that comprises \({\boldsymbol{N}}={\mathbf{4}}\) channels with active phase stabilization and that allows to generate optical arbitrary waveforms varying on timescales of a few picoseconds.

A transmitter frequency comb (Tx comb) is used to generate \(N=4\) phase-locked optical tones at frequencies \(f_{1}, \, f_{2}, \, f_{3},\, f_{4}\), spaced by a free spectral range (FSR) \({f}_{{\rm{FSR}}}^{{\rm{(tx)}}}\), see Inset Ⓐ. These tones are separated by a demultiplexing filter (Demux) and subsequently serve as optical carriers for in-phase and quadrature (IQ) modulation. The IQ modulators (IQMs) are electrically driven by an array of 2\(N=8\) synchronized digital-to-analog converters (DACs) having each a bandwidth \(B > ({f}_{{\rm{FSR}}}^{{\rm{(tx)}}}/2)\). The drive signals are calculated based on the desired output waveform using a digital signal processing (DSP) unit. The various output signals of the IQMs are combined by a binary signal-combining tree (SCT) that consists of \(N - 1=3\) signal-combining elements (SCEs). Each SCE merges two spectrally adjacent tributaries, see Inset Ⓒ, where the slowly varying phase offset \(\Delta\varphi(t)\) is compensated by a closed-loop control. To this end, the various tributaries are designed to exhibit a slight spectral overlap with their respective neighbor. This leads to interference within well-defined overlap regions (ORs), Insets Ⓑ and Ⓒ, which provide the feedback signals for the closed-loop control. The output signal of the last SCE corresponds to the desired optical waveform \({\underline{a}}_{{\rm{S}}}(t)\) with spectrum \({\underline{\tilde{a}}}_{{\rm{S}}}(f)\), Inset Ⓓ