Broadband amplification in Nd3+ phosphate glass: single effective oscillator model and beyond

Beamlines at the National Ignition Facility (NIF) use large neodymium-doped glass slabs for amplification of pulsed beams with various temporal shapes and transverse dimensions _40 cm _ 40 cm. Currently, the Virtual Beam Line (VBL) simulator1 computes saturable amplification according to the approach of Frantz and Nodvik, modified to include drain of the lasing transition's lower level. Linearly chirped pulses are amplified by gain media parameterized by an emission cross section value referenced to the instantaneous beam wavelength. Expanding the capabilities of VBL to a family of waveforms that is more diverse in terms of spectral amplitude and phase calls for the adoption of an approach that is fundamentally dispersive. In this work, we describe an approach to computing broadband amplification in the time domain according to coupled equations that describe evolution of the population inversion and the associated resonant polarization. Considering the diversity of glass species with respect to various gain inhomogeneities, we explore various model extensions for capturing the non-Lorentzian emission cross section in the small-signal regime and how the underlying resonant susceptibility is deformed by gain saturation. The polarization envelope acts as transverse-spatial sources to (3+1)D spectral envelope propagation that fully accounts for linear-optical diffraction and dispersion in the host glass, and includes the usual instantaneous non-resonant third-order electronic response (optical Kerr effect).