This project was motivated by an interest in polymers and the many connections between polymers and optics, and specifically polarized light. Polymer materials consist of long chain molecules, which are often arranged in some specific way, such as parallel to each other. These specific molecular arrangements create birefringence, an effect in which the material's refractive index can vary with its orientation with respect to incident polarized light. It follows that birefringent materials can alter the polarization of transmitted light, creating elliptical or circular light from linear polarized light for example. Light is "polarized" when the E-field vector of the transverse EM wave moves in a specific pattern that repeats with the frequency of the light. (Since this frequency is extremely high, only the recurring pattern is detectable, not the individual oscillations.) The most general pattern is an ellipse, and this form of light is said to be elliptically polarized. Special cases of elliptical light are circular polarized light and linear polarized light, which is the most common and familiar form. The polarization ellipse can be descibed by the phase difference between x and y components, which is 0 degrees for linear light and 90 degrees for circular.

We started by studying how elliptically polarized light can be created, described and analyzed. We set up a simple computer model in a spreadsheet program to aid in visualizing elliptically polarized light and to show how it can be analyzed by passage through a rotatable linear polarizer. The formulae used were derived using the Jones matrix theory of polarized light, and the results were plotted in polar coordinates. The model was tested by creating a specific form of elliptically polarized light (45 degree phase shift), analyzing this with the rotating polarizer, and comparing the result to the prediction. The controlled phase shift was created by total internal reflection (TIR) at an angle of incidence near 54 degrees, within an inexpensive ($10) 45-45-90 glass prism. (Two such prisms can replace a Fresnel rhomb, a specialized and expensive optical element for creating circular polarized light.) As shown in the Figure, our measurement (data points) is in excellent agreement with the calculated prediction (solid line).

The next phase of the project will utilize similar measurements and analysis to characterize the optical retardance (phase shift) of various polymeric thin films.