Axially symmetric, polarized laser beams

There are many laser beams which can be referred as axially symmetric, polarized laser beams as shown in Table 1.  In this table, beams are represented by a superposition of a linearly polarized TEM₀₁ and TEM₁₀ modes with orthogonal polarization. By changing the direction of the polarization and the phase shift, many kinds of axially symmetric, polarized beams can be obtained. For example, a radially polarized beam (a) is a superposition of a linearly polarized TEM₀₁ and TEM₁₀ modes with zero phase shift. When the polarization direction of the TEM₀₁ and TEM₁₀ mode beams is rotated by 90 degrees, the beam will be an azimuthally (tangentially) polarized one (i). When the phase shift is p, the beams will be a hybrid mode (c and k). These modes are known as propagating mode (LP₁₁) in an optical fiber. When the phase shift is p/2 or 3p/2, the beam has unique

polarization pattern (b, d, f, h, j and l). The polarization is basically elliptic and the ellipticity changes in the azimuthal direction indicating spatial scattering of the spin angular momentum of light. The beam (e) seems to be be a windmill. Although the beam (g) resembles a Ninja star, this is the same with the beams (c) and (k). Note again that these beams can be generated by a superposition of TEM₀₁ and TEM₁₀ modes with proper polarization and phase shift. Direct generation from a laser cavity is reported for radially and azimuthally polarized beams up to date.

Table 1 Examples of axially symmetric, polarized laser beams.