Characterizing Polarization-maintaining Fibers (PM Fibers)
Real PM fiber cables
Polarization-maintaining fiber cables ideally maintain the linear polarization state of light (linear SOP) that is coupled into the fiber. However, real polarization-maintaining fiber cables can influence the polarization state to a small extent. As a result, the light at the fiber cable exit is then slightly elliptically polarized.
Schematic drawing of a polarization-maintaining fiber cable. Due to the termination of the fiber connector, the polarization state at the cable exit might generally be slightly elliptical.
Definition of Extinction ratio V and PER
The preservation of linear SOPs in polarization-maintaining fiber cables is characterized by an extinction ratio V. This is the fraction of linearly polarized light coupled into the fiber, that is transmitted by a polarizer (analyzer) at the cable end, Pp, versus the fraction Ps blocked by the polarizer.
{!{!{V=\frac{P_p}{P_s}.}!}!}The extinction ratio V is typically expressed as the logarithmic polarization extinction ratio PER:
{!{!{PER=10\ \cdot logV}!}!}The extinction ratio is a measure for the ellipticity η of the light, and it is:
{!{!{V=\cot^2(\eta)}!}!}
Poincaré representation
SOPs can be visualized on the Poincaré sphere, as it is done with the Polarization Analyzer series SK010PA, and as you can see in the figure below. In this representation, linear SOPs are located on the equator of the sphere, and circularly polarized states are located at the two poles of the sphere. Please note that the polarization direction is defined opposite to the direction of porpagation.The expected polarization states at the output of a polarization-maintaining fiber cable may deviate slightly from the equator. The angle of inclination in this representation is the ellipticity η. More information on PM fiber coupling using the Polarization Analyzer can be found here or in an article here.
Poincaré sphere and definition of ellipticity
Poincaré sphere for the representation of arbitrary polarization states. Here, a slightly elliptical polarization state is depicted, as it can occur e.g at the output of a PM fiber cable.
Mean and varying ellipticity
The polarization maintenance of a polarization-maintaining fiber cable is characterized by the ellipticity η. The fiber itself typically has a good polarization maintenance. With this assumption, the ellipticity is affected by the cable ends only, which means that disturbances occur at the terminated connectors of the fiber cable (or at the in- and outcouplers). The ellipticity η consists of two parts, which appear differently in the polarization measurement and which can have different effects when using the fiber cables.
{!{!{\ \eta(t)=\bar{\eta}+\Delta\eta(t)\\ \ \eta(t)=\bar{\eta}+∆\eta\cdot sinβ(t)}!}!}
The first component is the mean ellipticity {!{\bar{\eta}}!} , which can be caused by disturbances (e.g. stress birefringence) at the outcoupling end.
The second component Δη is caused when coupling into the fiber during which the radiation is split between the two main polarization axes of the fiber. Due to a non-constant group delay difference in the two main polarization axes of the fiber, the components coupled into the two polarization axes experience a temporally changing path difference. This path difference can be affected by temperature changes or by bending the fiber. The light exiting the fiber cable then has an arbitrary elliptical SOP.
Assuming that the coherence length of the laser source is large enough, the varying component of the ellipticity Δη can be visualized on the Poincaré sphere and consists of measurement points lying on a circle around the stable ellipticity state
Poincaré plot of an elliptical SOP exiting a PM fiber cable
Poincaré plot of the polarization state at the output of a PM fiber cable. Due to fluctuations (e.g. thermal), the polarization state moves on a circle on the Poincaré sphere. The polarization is quite stabel over time, but clearly elliptical.
Definition of minimum PER
The worst possible SOP (farthest from the equator) in this case is reached when the two components (angles on the Poincaré sphere) add directly to {!{\eta=|\bar{\eta}|+\Delta\eta,}!} resulting in a minimum polarization extinction.
The figure above shows an example of a fiber cable where the polarization is quite stable over time but obviously elliptical. The Figure below shows a fiber with a very good mean PER, but the radius is large which means that the ellipticity varies strongly with time. There are two points crossing the equator, where the SOP is linear, but these states are generally not stable.
Good mean PER but large ellipticity
Good mean PER but large ellipticity. There are two points crossing the equator, where the SOP is linear, but these states are generally not stable.
Reverse measurement
If a fiber cable is examined in the opposite direction (the fiber input is swapped to become the fiber output and thus the fiber output becomes the fiber input), the two components of the ellipticity are also switched.
A small measurement circle with radius {!{\ 2\Delta\eta_a}!} and center far away from equator {!{2\bar{\eta}_a}!}, see below on the left, becomes a large circle with radius {!{2\Delta\eta_b}!} and center close to equator {!{2\bar{\eta}_b}!}, see below on the right. The minimum extinction ratio, calculated from the direct sum of {!{\bar{\eta}}!} and {!{\Delta\eta}!}, is therefore the same for both measurements not taking into consideration measurement errors.