Field-based treatment of transient gain in short-pulse optical amplifiers

Recent advances in burst-mode sources of ultrashort optical pulses are enabling a range of applications. However, the growing complexity of pulse propagation in these systems now exceeds the capabilities of existing models. Critical gain dynamics with coupled spectral and temporal dependencies cannot be captured, which precludes effective analysis and design of advanced short-pulse sources. In this work, we introduce a field-based gain model (as opposed to existing power-based models) that integrates transient rate equations for the populations with the unidirectional pulse propagation equation. This model offers a comprehensive framework for the treatment of spectral and temporal dynamics that arise from ultrafast transient gain, spontaneous emission, dispersion, and Kerr and Raman nonlinearities. A frequency-scaled Fourier transform is introduced to facilitate the computation of coherent and incoherent processes that occur on disparate time scales and enhances the computational speed by orders of magnitude. The field-based model is applied to studies of (i) gain-managed nonlinear amplifiers that generate 40–fs pulses at burst rates of hundreds of gigahertz and (ii) the initiation of mode-locking from noise in a laser.