Fig. 1. Evolution of an optical vortex seed with l=1 in a conventional RA and the amplification number kn=4n−3.

Fig. 2. Setup of the proposed RA. QW, quarter-wave plate; QP, Q-plate; OC, optical coupling system; M, plane mirror; CM, concave mirror, R=−1  m; PM, fold mirror, R=0.9  m; PC, Pock cell; BE, beam expander; P, polarizer; PL, pump lens, f=30  cm; CA, convex axicon, base angle of 0.5°; Ti:S, Ti:sapphire, length of 25.4 mm.

Fig. 3. Simulations of laser oscillations from noises with the different ring-shaped pump radii. Expansion ratios are (a) 4, (b) 3.5, and (c) 3.

Fig. 4. Simulation of vortex amplification with different seed energies.

Fig. 5. (a) Ring-shaped pump on one of the Ti:S surfaces, (b) the donut-shaped output from the unseeded RA, (c) the phase structure of our Dammann vortex grating, (d) the corresponding far-field with parallel illumination, and (e) the measured far-field illuminated by the output of the unseeded RA.

Fig. 6. Recorded spatial intensities of the seed with l=1: (a) the seed focused by a cylindrical lens, (b) the output spatial intensity distribution, and (c) the far-field distribution after Dammann vortex grating.

Fig. 7. Recorded spatial intensities of the seed with l=−1: (a) the seed focused by a cylindrical lens, (b) the output spatial intensity distribution, and (c) the far-field distribution after Dammann vortex grating.

Fig. 8. (a) Spatial cross-section intensity of the amplified LG0,1 vortex: the average from the different orientations (black line) and theoretical fitting (dashed red line); (b) the spectral intensity and phase of the amplified LG0,1 pulse; (c) the temporal intensity and phase of the amplified LG0,1 pulse (black and blue lines) and the temporal intensity of corresponding Fourier-transform-limited pulse (red line).