Cone-Shaped Brewster Surface Produces Radially Polarized Beam

Breck Hitz

Radially polarized laser beams — in which the electric-field vector is always oriented in the radial direction — may be advantageous for the optical trapping and manipulation of small particles.

Although many techniques for generating radially polarized laser beams, involving both intra- and extracavity optical elements, have been investigated during the past 30 years, they have suffered from undue complexity and/or from low efficiency. Recently, researchers at Tohoku University in Sendai, Japan, demonstrated a simple, intracavity conical Brewster prism that forces a laser to oscillate with radially polarized light.

Figure 1. Two round cones, one convex and the other concave, nested together and forced the laser to oscillate with purely radial polarization. Images ©OSA.

The prism comprised two conical Brewster surfaces, one concave and the other convex, nested against each other (Figure 1). The apex angle of the cones was fabricated such that the radial polarization component of the intracavity beam was incident on the cones’ surfaces at Brewster’s angle. The azimuthal component, on the other hand, was always parallel to the surface. The convex cone had seven layers of alternating high- and low-index thin films, so that light passing through the prism encountered a total of eight Brewster-angle surfaces. The rear surfaces of both conical pieces were antireflection-coated.

The researchers placed the prism inside a diode-/side-pumped Nd:YAG laser from Cutting Edge Optronics of St. Charles, Mo., whose round, cylindrical laser rod measured 2 mm in diameter and 63 mm in length. They obtained 90 mW of radially polarized output through a 98 percent reflecting output coupler.

Figure 2. The unfiltered beam from the laser had a doughnut-shaped intensity profile (a). When viewed through a linear polarizer (orientation indicated by arrows), the intensity profile had two lobes that rotated with the polarizer (b to e). Therefore, the beam’s electric-field vector was always oriented in the radial direction (f).

To verify that the output was radially polarized, the researchers observed its spatial intensity pattern through a linear polarizer. Without the polarizer, the beam was a familiar “doughnut” shape (Figure 2a). When the polarizer was inserted into the beam and rotated, the transmitted intensity pattern indicated that the entire beam was radially polarized (Figures 2b-2e).

The researchers observed that, although the doughnut intensity profile is familiar to laser users everywhere as the conventional TEM₀₁* mode, their laser was not oscillating in that mode. The familiar doughnut mode is a polar (Laguerre-Gaussian) mode that is a linear combination of the rectangular (Hermite-Gaussian) TEM₀₁ and TEM₁₀ modes, each of which is linearly polarized in the same direction and is π/2 out of phase with the other. The instantaneous intensity pattern would oscillate back and forth between shapes that resemble those in Figures 2b and 2d.

The radially polarized doughnut mode observed in these experiments is different. It also can be expressed as a linear combination of the Hermite-Gaussian TEM₀₁ and TEM₁₀ modes, but the modes are polarized orthogonally and are in phase with each other. Thus, the instantaneous shape of the mode would always be a doughnut. For this reason, the researchers adopted the convention of previous investigators and call their mode the R-TEM₀₁* mode, to distinguish it from the conventional, linearly polarized TEM₀₁* mode.