Birefringent filters utilize changes in the state of polarized light in anisotropic materials to transmit
different intensities of light at certain wavelengths. Such filters are employed in display and color
filtering technology, as well as wavelength division multiplexing systems for optical communications.
Birefringent materials are typically considered to be extremely intricate and expensive, requiring multiple
layers of quartz or other crystals. In contrast, polymer films also exhibit birefringence and can be used
in place of these more expensive materials.
The purpose of my project was to exploit the birefringent properties of low-cost polymer films to create
tuneable filters that effectively transmit various types of polarized light at particular wavelengths. The
material used was "High Performance" Scotch brand clear cellophane packaging tape, whose birefringent
properties are acquired in its manufacturing process when the polymer molecules are aligned in the same
direction. We made samples with 2, 4, 6, 8, and 10 parallel layers of tape and placed these between crossed
and parallel polarizers. We illuminated the samples with a halogen bulb and recorded the transmitted light
with a ThorLabs CSS100 Spectrometer. The observed spectra contain periodic oscillations in which the minima
(for parallel polarizers) or maxima (for crossed polarizers) correspond to the sample being a half-wave
retarder. We were able to determine the order of retardance for these minima by plotting the inverse of
wavelength versus odd integer multiples of pi. The ten-layer sample was determined to be an eighth-order
retarder at 645 nm. The figures below show the transmitted light spectrum for the ten-layer stack between
parallel polarizers and the corresponding inverse wavelength plot.
Now that the birefringent properties of the cellophane tape are known, we can use Jones calculus and
Mathematica to design specialized wavelength-selective filters and other polarization elements such as
quarter- and half-wave plates. The trial-and-error design process involves calculating the effect of
placing various numbers of tape strips at various angles relative to each other.
This work is supported by the Simons Foundation and the Laser Teaching Center.
