We report on a gigahertz self-mode-locked high-order Hermite–Gaussian (HG) $\mathrm{Nd}:\mathrm{Gd}\mathrm{V}{\mathrm{O}}_4$ laser. With a pump power of $2.2\mathrm{W}$ , the average output power for the ${\mathrm{TEM}}_{0,m}$ modes from $m=9$ to $m=0$ are among $350–780\mathrm{mW}$ at a repetition rate of $3.5\mathrm{GHz}$ . The mode-locked pulse width is in the range of $20–25\mathrm{ps}$ for various HG ${\mathrm{TEM}}_{0,m}$ modes. With a simple cylindrical-lens converter, the mode-locked HG beams are converted to generate picosecond optical vortex pulses.

© 2009 Optical Society of America

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