We demonstrate an efficient transformation of a linearly polarized Gaussian beam to a radially or an azimuthally polarized doughnut (0,1)* Laguerre-Gaussian beam of high purity. We use a spatially variable retardation plate, composed of eight sectors of a lambda/2 retardation plate, to transform a linear polarization distribution to radial/azimuthal distribution. We transformed an Nd:YAG Gaussian beam with M(2)=1.3 to a radially and azimuthally polarized (0,1)* Laguerre-Gaussian beams with M(2)=2.5 and degree of radial/azimuthal polarization of 96-98%.

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We develop a round-trip matrix diagonalization method for quantitative description of selection of radially or azimuthally polarized beams by birefringence-induced bifocusing in a simple laser resonator. We employ different focusing between radially and tangentially polarized light in thermally stressed laser rods to obtain low-loss stable oscillation in a radially polarized Laguerre-Gaussian, LG(0,1)*, mode. We derive a free-space propagator for the radially and azimuthally polarized LG(0,1)* modes and explain basic principles of mode selection by use of a round-trip matrix diagonalization method. Within this method we calculate round-trip diffraction losses and intensity distributions for the lowest-loss transverse modes. We show that, for the considered laser configuration, the round-trip loss obtained for the radially polarized LG(0,1)* mode is significantly smaller than that of the azimuthally polarized mode. Our experimental results, obtained with a diode side-pumped Nd:YAG rod in a flat-convex resonator, confirm the theoretical predictions. We achieved a pure radially polarized LG(0,1)* beam with M(2)=2.5 and tens of watts of output power.

Intra-cavity binary phase elements are incorporated into a-switched Nd : YAG laser resonator to obtain efficient high-order transverse mode selection. The resonator configuration is analyzed using the propagation-matrix diagonalization method and the Fox-Li algorithm, and a simple model for predicting the relative output powers of the selected modes is developed. The predicted results are verified experimentally with binary phase elements for selecting the TEM 01 , TEM 02 and TEM 03 , degenerate Laguerre-Gaussian modes. The output energy per pulse was 15 mJ for the TEM 01 , 16.5 mJ for TEM 02 and 18.3 mJ for TEM 03 , all higher than the 10mJ for the TEM 00. The performance in-switched operation was found to be similar to that in free-running operation. The numerical calculations, experimental procedure and experimental results are presented.

A simple, robust, and efficient method to produce either radially or azimuthally polarized output beam from a fiber laser is presented. Experimental results reveal that polarization purity of 90% or better can be obtained