  We propose and demonstrate a high performance four-wavelength erbium-doped
fiber laser (EDFL), enabled by a figure-8 compound-ring-cavity (F8-CRC) filter
for single-longitudinal-mode (SLM) selection and a polarization-managed
four-channel filter (PM-FCF) for defining four lasing wavelengths. We introduce
a novel methodology utilizing signal-flow graph combined with Mason's rule to
analyze a CRC filter in general and apply it to obtain the important design
parameters for the F8-CRC filter used in this paper. By combining the functions
of the F8-CRC filter and the PM-FCF filter assisted by the enhanced
polarization hole-burning and polarization dependent loss, we achieve the EDFL
with fifteen lasing states, including four single-, six dual-, four tri- and
one quad-wavelength lasing operations. In particular, all the four
single-wavelength operations are in stable SLM oscillation, typically with a
linewidth of <600 Hz, a RIN of <=-154.58 dB/Hz@>=3 MHz and an output power
fluctuation of <=+/-3.45%. In addition, all the six dual-wavelength operations
have very similar performances, with the performance parameters close to those
of the single-wavelength lasing operations. Finally, we achieve the wavelength
spacing tuning of the dual-wavelength operations for the photonic generation of
tunable microwave signals, and successfully obtain a signal at 23.10 GHz as a
demonstration.
