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Polarization and Polarimetric Testing

All polarized light can be described in terms of an electric field vector. This vector is a representation of the light’s electric field only (magnetic field is not considered since it is proportional to and in phase with the electric field). For convention, this vector divided into two perpendicular components (x and y) where the third component (z) is simply the direction of wave propagation. When describing polarized light, two characteristics must be observed; First, the relative phase of the two components (x and y), and second, their relative amplitudes. These two characteristics determine the polarization of light.

There are three main types of polarized light. They are linear, circular, and elliptical polarizations.

Linear polarization describes any light where the x-y components are in phase. The relative amplitude of these two components determines the direction of polarization (measured in radians from some reference point). Linear light is most easily obtained through use of a polarizer. The output light will always be linear, independent of input polarization (except in the case of absolute extinction where no output light is observed).

Circular polarized light describes any light where the relative amplitudes are the same and there is a phase shift of exactly ninety degrees. Circular polarization is commonly described as either right-handed or left-handed. This can be visualized by imagining your thumb in the direction of propagation (z direction) and curling your fingers in the direction of the changing field. If this can be done with your right hand, it is obviously right-handed polarization, and left-handed polarization is found similarly. In reality, right-handed and left-handed circular polarizations are virtually the same. One would be concerned only in the case of mathematical convention.

The third type of polarization, Elliptical polarization, describes any polarized light where relative phase and/or amplitude are not equal (excluding the circular and linear polarization cases). Elliptical light can be described as either right handed or left handed in a similar way as circular polarization. But in this case, it is often more important to describe whether the polarization is right handed or left handed. This ellipse can be described as seen in the figure below.

Changes in both phase and relative amplitude can be monitored to characterize materials with variable birefringence. As the relative phase changes, the change can be described as an angle difference. The figure below illustrates a change in phase of the y component relative to the x component. If the relative amplitudes are the same, a full 360 degree shift may be viewed as the light changes through linear, elliptical, and circular polarizations. If the relative amplitudes are unequal, only linear and elliptical light will be observed. In either case, after a full rotation, the light will return to its original state.

The polarimetric testing process can either be done manually with a set of polarizers and waveplates, or electronically with equipment such as the Agilent 8509A/B Lightwave Polarization Analyzer. The latter of which is much easier and more accurate. The Agilent Lightwave Polarization Analyzer (LPA) requires use of fiber-optic cables.

Our testing commonly examines un-jacketed D-fiber coupled into the LPA using a bare-fiber adapter. Circular polarized light is commonly launched into the fiber in order to reduce orientation dependence of the launching end. Also, we are able to easily monitor polarization changes in comparison to the launched circular light. The circular light is obtained through use of a polarizer and a quarter-wave plate preceding the fiber launch. At the detector end of the fiber, however, orientation relative to the analyzer is significant. The LPA will read the x and y values corresponding to horizontal and vertical orientation of the input port, respectively. Therefore, caution must be taken to ensure desired orientation of test material as it is coupled to the LPA.

Throughout polarimetric testing it is important to promote mechanical and thermal stability as the fibers are commonly very sensitive to fluctuation. The effects of the room’s air conditioning can be especially undesirable during testing. To increase thermal stability, a large heat sink such as a metal plate can be used. If the majority of the fiber is in thermal contact with this plate, any fluctuation will be relatively slow and uniform. The fiber may also be covered by another plate or box to protect from changes in the room’s air. Also, it is always wise to allow all equipment to warm up for at least thirty minutes before doing any type of test where high accuracy is desired.

The LPA can output a display as pictured below.

Using the output display, the state of polarization can be monitored in both elliptical and spherical elliptical representations. The poincare sphere on the right is especially useful for polarization monitoring due to its ability to trace changes over time. The trace is marked by a red or blue line and will mark all polarization states recorded. The sphere monitors both relative amplitude and phase difference of the light’s polarization. Common locations are marked in the figure below.

The relative phase of the detected light is displayed as latitude on the sphere with circular polarizations at the poles. The relative amplitude (between x and y components of detected light) is displayed as longitude on the sphere. The four marked meridians correspond to horizontal, vertical, and 45 degree orientations of linear polarized light (at equator).

The polarized light is most easily recorded as Stokes parameters. This is a vector < S0, s1, s2, s3> where:
I=total intensity
p=fractional degree of polarization (DOP)

Using the Stokes Parameters, points on the sphere can be easily recorded and used in calculations. The LPA can also do several calculations automatically such as angle change between given points. For more information on use of the Agilent 8509A/B Lightwave Polarization Analyzer, refer to the manual.

For more on polarization see Wikipedia
This Polarization Calculator converts Jones vectors to Stokes vectors.

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