Creating Circularly-Polarized Light with a
Readily-available Birefringent Polymer

The immediate motivation for this project was the need to create circularly polarized light in the near-infrared (780 nm) for use in a device to lock the frequency of a diode laser to atomic transitions in rubidium. Commercial waveplates are available for this purpose, but they typically cost many hundreds of dollars and must be purchased for specific wavelengths. We demonstrate that it's possible to create useful waveplates for any desired wavelength simply by suitably orienting a thin sheet of the readily-available birefringent polymer cellophane with respect to the incident beam of light.

Waveplates (also called retarders) create a phase shift between orthogonal components E_x and E_y of the electric field vector E; birefringent materials are used because they have different indices of refraction for different components of E. Circularly polarized light results if E_x and E_y have equal magnitude and differ in phase by exactly π/2, or 90 degrees. Other waveplates with a π phase shift are very useful for changing the orientation of polarized light. The retardance (phase shift in radians) of a birefringent material is given by Γ = 2π Δn t / λ, where Δn is the birefringence value, t is the thickness, and λ is the wavelength of the incident light. Retardance values greater than 2π are equivalent to values between 0 and 2π. The "order" of the waveplate refers to the additional multiples of 2π degrees, and generally the lowest possible order is most desirable. The birefringence of cellophane is due to the fact that its long cellulose molecules are aligned along a single axis of symmetry (the optical axis) in the manufacturing process. The two indices of refraction are the extraordinary index (n_e) for light parallel to the optical axis, and the ordinary index (n_o) for light perpendicular to it. In the case of cellophane, n_e > n_o and the birefringence Δn = n_e - n_o is positive.

The figure below summarizes our experiment. The light source was a HeNe laser (633 nm) linearly polarized at 45° to the horizontal. A cellophane sample obtained from a local florist was mounted on a rotator (horizontal rotation axis) which sat on a small horizontal turntable (vertical axis). The tuning angle is the rotation about the vertical axis, which can be set with the upper rotator to coincide with either the o-axis of the cellophane (solid points on the graph) or the e-axis (open points). Retardances were determined through the relationship Γ = 2*atan(√(I₁/I₂)), where I₁ and I₂ are intensities measured through an analyzer set either perpendicular or parallel to the incident light, respectively, as described by A. Márquez et.al. (J.Mod.Opt., 10 March 2005). The creation of accurate circularly polarized light at a tuning angle of 42° was confirmed by observing that light reflected back through the cellophane sample was totally absorbed in the initial linear polarizer. The "horn" shape of the graph results from two competing effects: 1) the effective thickness of the sample increases as it's rotated, which increases retardance, and 2) the effective index of refraction decreases for rotations about the o-axis, but is unchanged for rotations about the e-axis. The solid lines are calculated from the expressions of Hale and Day (Applied Optics, 15 Dec. 1988) with index n = 1.38 and order m = 1 (total retardance = 550°).