Polarimetric fiber laser sensors.

Rare-earth-doped fibers have been extensively investigated for their applications to optical amplifiers and fiber lasers. The Er-doped fiber amplifiers are about to be implemented in practical communication systems.' On the other hand, current use of fiber lasers is relatively limited, although their potential as light sources for telecommunications and fiber-optic sensors is considered to be significant. One example of fiber laser applications is the amplified spontaneous emission source with broad bandwidth and stable optical spectrum ideal for fiber-optic gyroscopes. 2 Many other forms of the fiber lasers have also been investigated, such as single-frequency lasers,3 mode-locked lasers with femtosecond pulse width,4 and wavelength-tunable lasers.5 In this Letter we propose and demonstrate a new use of the fiber laser as a fiber sensor based on the beating of two mutually orthogonal eigenpolarization modes in the fiber laser cavity. The change in the birefringence of the laser fiber in response to the external perturbations directly translates into a change in the beat frequency of the two polarization modes. The measurement of the beat frequency can be made by using a conventional frequency counter, which leads to a straightforward electronic signal processing. This approach avoids complicated electronic signal processing required for conventional interferometric sensors,6'7 in which the optical phase shift information has to be extracted from the direct intensity output having a sinusoidal dependence on the phase shift. Although the polarization behavior of a laser with anisotropic cavity can be complicated owing to the gain medium, most of the features of our interest could be explained from the polarization properties of a passive cavity.8 Assuming no polarizationselective components and no nonreciprocal components inside the Fabry-Perot-type cavity with mirrors at each end, we can represent the Jones matrix of the cavity for one round trip as ATA in a laboratory frame, where A represents the propagation of light in one direction along the fiber cavity with random birefringence and AT represents the transpose matrix of A. As expected, two orthogonal eigenpolarization states with different eigenvalues can be obtained for the cavity matrix ATA. In this case the light beams in the eigenpolarization states return to their original polarization states after a complete round trip, and the eigenvalues represent corresponding resonance frequencies. It is interesting to note that the two eigenpolarization states are found to be linearly polarized at the mirror position. Figure 1 shows the longitudinal mode lines for each polarization mode and their beat frequencies, where c is the velocity of light in a vacuum, L is the cavity length, M and N are integers, and nx and ny are the effective refractive indices of the two (X and Y) eigenpolarization modes. In general, the two effective refractive indices for the eigenpolarization modes are different, which results in differences in resonance frequencies and their longitudinal mode spacing. Polarization mode beat (PMB) frequencies appear at the symmetric places A ppol and Apo A vpol around adjacent longitudinal