A radially polarized beam was generated in a microchip Nd:YVO4 laser by shaping the pump profile to be a group of focused plane waves, the directions of which are located on a conical surface. The oblique incident pump beam induces thermal lensing combined with birefringence to distinguish the radial ray from the azimuthal ray to achieve radial polarization. The average contrast ratio was 23.6 when the pump power was between 3.06 and 4.27 W.

We find that soft-aperture Kerr-lens mode locking (SAKLM) in a Ti:sapphire laser always takes place around certain discrete cavity configurations accompanied by peculiar beam patterns. By correlating the superposition of proper transverse modes to the observed beam patterns and fitting the beat frequencies to the resonance equation, we discovered that the patterns for SAKLM are formed by phase locking of the fundamental mode with specific degenerate transverse modes that occur near different degenerate cavity configurations. As predicted by the stability analysis, period-3 and period-2 SAKLM does occur around the 1/3-and 1/4degenerate cavity configurations, which cannot be fully explained in terms of total mode locking of TEM 00 and TEM 01 modes.

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We determined theoretically that the nonlinear dynamics of a Gaussian beam is configuration dependent in a general cavity. This prediction was confirmed by numerical simulation in a Kerr-lens mode-locked cavity for which the self-focusing effect is considered the nonlinear source in both the spatial and the temporal domains. Period doubling, tripling, and quadrupling can occur in these configurations with the products of generalized cavity G parameters equal to 1/2, 1/4 (or 3/4), and (2 Ϯ ͱ2)/4, respectively. The dynamic behavior of the cavity beam will become irregular if the nonlinear effect is further increased.

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