Creating cylindrical vector beams using
spatially-varying birefringent elements

Light can be polarized in an unlimited variety of ways - the familiar linear and circular forms are just special cases of the more general elliptical polarization. Beams of polarized light are typically spatially uniform. In contrast, cylindrical vector beams (CVBs) are spatially inhomogeneous, with a polarization angle that varies continuously with the "clock angle." Certain CVBs can be focused more tightly than spatially homogeneous beams and this advantage has numerous important applications. Birefringence is a property of certain materials in which there are two independent indices of refraction. Such materials can be used to alter the polarization state of light. Birefringence can be an intrinsic property of a material (calcite or cellophane) or can be induced by stress in an otherwise homogeneous material. Certain materials (such as plastic lids or plates) acquire permanent birefringence during their manufacture. Birefringence can be quantified by the relative phase shift it creates in a light beam, which is typically measured in fractions of a wavelength.

This project utilized a stress-engineered birefringent optical element to create CVB's, a technique first proposed by Spilman and Brown (2006). Our element was created by a past LTC student (Jacob Chamoun, 2010). It consists of a plexiglass cylinder within a copper ring, upon which pressure is applied by three equally spaced screws. The applied stress generates rings in the central region of the element whose retardance is proportional to radius. The ring of λ/2 retardance is of special interest since it can be used to create a counterrotating vector beam, which can then be changed to radially or azimuthally polarized light by a λ/2 waveplate.

The light source for our experiments was a linearly polarized 532 nm Nd: YVO₄ laser. Patterns created by the stress-optic in conjunction with additional polarizers were recorded in a CCD camera. In the first part of the experiment, we passed linearly-polarized light through the stress optic and a λ/2 waveplate to create radially and azimuthally polarized beams (depending on the orientation of the waveplate). This result was confirmed by using a linear analyzer to reveal the expected pairs of diametrically-opposed bright lobes. In the second part of the experiment we created a circularly-polarized beam by placing a λ/4 waveplate after the laser in the proper orientation. The light transmitted through the stress optic was analyzed using a pair of MasterImage 3D glasses (in which each lens is an opposite circular polarizer). We observed bright and dark rings with one lens; the pattern was reversed with the other lens.

This work was supported by the Simons Foundation and the Laser Teaching Center.