A fiber ring laser was characterized in order to determine the possibility of the ring laser gyroscope using a rare-earth doped fiber laser. The fiber ring laser was constructed with $Nd^{3+}$-doped fiber and a 15:85 directional coupler at 1060nm. $Ar^+$ laser with 514.5nm wavelength was used as a pumping source and the lasing center wavelength was 1064nm. Above the threshold absorbed pump power of 19mW the slope efficiency of 2.5% was obtained, and the continuous wave laser action was observed in both CW (clockwise) and CCW(counterclodkwise) direction with stable output power. Inhomogeneous line broadening in $Nd^{3+}$-doped fiber made this laser operated in multiple longitudinal modes with the total linewidth of 15nm for the absorbed pump power of about 60mW. A simple laser cavity theory shows that the laser oscillating in each direction has two orthogonal elliptically polarized eigenmodes, whose oscillating frequencies are shifted from each other due to the random birefringence induced in the laser fiber. The CW and CCW laser have the longitudinal modes at the same frequencies and the state of polarization is the complex conjugates with each other in Jones vector notation. The rf beat frequency spectrum of 28.7 MHz and its higher harmonics (LMB : Longitudinal Mode Beating) was observed and that matched well with the spacings between the adjacent longitudinal modes from a resonator of 7.2m in length. Using a polarizer that makes two orthogonal polarized modes interfere with each other, the new beat signals (PMB : Polarization Mode Beating) were observed in pairs at symmetric positions around LMB signals. The frequency of the PMB signals was sensitive to environmental perturbations. To observe the correlation between the CW and CCW lasers, the two laser signals were interfered using and additional 50:50 directional coupler at 1060nm. The PMB signals were observed without a polarizer at the same frequencies as those observed for CW (or CCW) laser with a polarizer. This results confirms that the lasers oscillating in both directions have the same longitudinal frequencies for corresponding polarization states. It can also be concluded that the two lasers oscillating in opposite directions can lase simultaneously at similar frequencies with different polarization states.
