  We present a theoretical model and its efficient numerical implementation for
the simulation of wavelength-swept waveform propagation in fiber systems such
as Fourier domain mode-locked (FDML) lasers, fully accounting for the
polarization dynamics in fiber spools and further polarization dependent
optical components in the setup. This approach enables us to perform long-time
simulations of the FDML laser dynamics over more than 100000 cavity roundtrips,
as required for some FDML configurations to ensure convergence to the steady
state operating regime. The model is validated against experimental results for
single propagation through a fiber spool and for stationary FDML operation. The
polarization dynamics due to the fiber spool, inducing polarization-mode
dispersion, bending birefringence as well as cross-phase modulation, and other
optical components such as the Faraday-rotating mirror used for polarization
compensation is thoroughly investigated.
