Creating unconventionally polarized beams using stress birefringent wave plates

Jacob Chamoun, Cornell University
Marty Cohen and John Noe
Laser Teaching Center
Department of Physics and Astronomy
Stony Brook University

This project investigated the use of a wave plate with spatially varying birefringence to produce cylindrical vector beams (CVB's), as suggested by the work of Spilman and Brown [1]. Birefringence is a property of materials in which incident polarized light is decomposed into two orthogonally polarized components - the ordinary and extraordinary ray - upon entry into the material. Because each ray travels at a different speed, a phase shift is incurred upon exiting the material. If the shift is 180 degrees, the material constitutes a half-wave plate and will rotate the polarization of linearly polarized light. In stress-induced birefringence, the fast and slow axes line up with the directions of principle stress, so a planar, inhomogeneous stress pattern can produce a wave plate whose fast axis orientation varies in space. These wave plates can be used to create unconventional polarization states, including cylindrical vector beams. CVB's are propagating solutions to the vector paraxial Helmholtz equation which contain a central polarization singularity. Such beams are of both theoretical and practical interest.

Spilman and Brown [1] mention a "discrete" wave plate composed of an angular arrangement of 8 half-wave plate wedges such that the fast axis rotates or "counterrotates" [1] at half the rate of the azimuthal angle. We made several such plates using birefringent transparency film and observed that the discrete wave plates rotated linearly polarized light in a way consistent with a discrete approximation to radially or azimuthally polarized light. Next, we built a stress-optical element (SOE) based on the previous work [1,2] to apply adjustable compressive stresses at 120o intervals around the perimeter of a 1/2 in. diameter, 3/8 in. thick plexiglass window. Spilman and Brown [1] calculated that such a stress pattern would produce a counterrotating fast axis - the continuous analog to the discrete plate - which could be used to produce a truly radial or azimuthally polarized beam. We chose plexiglass over glass [1,2] because its stress-optic coefficient is higher, so less compression is needed.

When we used an expanded green (532 nm) laser beam to illuminate our SOE between linear or circular polarizers, interesting polarization structures appeared. Between circular polarizers, the SOE exhibited a single dark ring of half-wave retardance. With the ring isolated by an annular mask, exposing the SOE to linearly polarized illumination and analyzing with a linear analyzer produced dark lobes that rotated with the analyzer, indicating the presence of a polarization vortex. A series of images of the SOE between various combinations of polarizer and analyzer were taken with a consumer camera and analyzed in MATLAB to extract the spatial pattern of Stokes parameters. This analysis confirmed that there is an annular region of counterrotating linear polarization at the half-wave radius. We are currently taking additional images with a more appropriate computer-based camera.

This work was supported by the National Science Foundation (Phy-0851594).

[1] A. K. Spilman, T. G. Brown, Appl. Opt. 46, 61-66 (2007)

[2] A. K. Spilman, "Stress-engineered optical elements". PhD thesis. University of Rochester. (2007)