The polarization properties, such as the output polarization angle and polarization mode beat frequency, of a fiber laser in response to circular birefringences induced by twist or axial magnetic field are investigated experimentally and theoretically.
In case of twisted fiber laser, the directions and frequencies of two laser eigen-polarization modes are found to evolve in a much more complicated way as a function of the twist rate compared to the well known case of polarization evolution in a twisted passive optical fiber.
The basic difference between the two cases comes from the fact that a fiber laser with a linear cavity formed by two mirrors has to satisfy an additional condition that the state of polarization(SOP) must come back to the original SOP after a complete round trip inside the cavity.
Twisting a fiber induces reciprocal circular birefringence, and if the fiber has intrinsic linear birefringence as is usually the case, it results in a general elliptical birefringence. Their polarization eigenmodes for laser conditions are obtained simply by Jones vector calculus. Under reciprocal birefringence, the fiber laser consists of two orthogonal linear polarization eigenmodes. The polarization eigenmodes are all linear for any twist angle, and were experimentally observed. As twist angle increases, their beat frequency(PMB) decreases with a periodic dependence on the twist angle.
Nd and Er doped fiber laser were constructed and analyzed on the polarization properties. From the analysis of experimental data, the Nd doped fiber was found to have small intrinsic linear birefringence (β$\simeg$1.8 rad/m), and Er doped fiber was found to have large one (β\simeg100 rad/m). The proportionality constant relating the twist rate and the induced circular birefringence was deduced from the experimental results as 0.15+-0.01, and agreed with published values. For a fiber with uniform birefringence, the polarization angles of eigenmode rotate at a lower rate compared to the twist angle, and the difference in the rotation angles of fiber and eigenmodes becomes 90 degree at periods wherever PMB disappears. At high twist rates, they follow 54% of twist rates.
The existence of short untwisted fiber sections with linear birefringence at the ends of the fiber laser cavity causes a significant change in the characteristics of the fiber laser. Modified solutions predict only small corrections for PMBs. The polarizations angles are quite different from those without the untwisted sections. They do not rotate linearly with fiber twist at 54% of twist angle but go through abrupt change when the polarization eigenmodes return back to original directions. At high rotation rates, they follow the twist angle with an average slope of 1. This modified model explains experimental data very well.
Axial magnetic field induces circular birefringence in optical fibers resulting in the rotation of polarization angle for a linearly polarized input (Faraday effect). Unlike the case of twist induced circular birefringence, Faraday effect introduces non-reciprocal phase shift between the counter propagating optical waves in the fiber. This non-reciprocal Faraday effect makes their polarization eigenmodes elliptical at the location of the mirrors in the existence of an intrinsic linear birefringence in the fiber. Their PMB frequencies vary as a function of the magnetic field strength, which can be utilized for magnetic field or current sensing with frequency readout. In the Nd doped fiber laser with small linear birefringence, polarization eigenmodes became elliptic and their PMB frequencies changed in proportion to magnetic field magnitude. When the fiber was twisted, the magnetic field induced PMB frequency changes increased with periodic peakings. Main axis of elliptic polarization eigenmodes reduced close to linear polarization axis without field, but show the periodic behavior similar to PMB changes for twist angle.
