A passively mode-locked solid-state laser is designed to emit a continuous-wave train (51, 52) of electromagnetic-radiation pulses, the fundamental repetition rate of the emitted pulses exceeding 1 GHz, without Q-switching instabilities. The laser includes an optical resonator (3.1), a solid-state laser gain element (2) placed inside the optical resonator (3.1), a device (1) for exciting said laser gain element (2) to emit electromagnetic radiation having the effective wavelength, and a device (4) for passive mode locking including a saturable absorber. The laser gain element (2) is a laser material with a stimulated emission cross section exceeding 0.8.times.10.sup.-18 cm.sup.2 at the effective wavelength, and is made of Nd:vanadate. The saturable absorber (4) is preferably a semiconductor saturable absorber mirror (SESAM) device. Even higher repetition rates are achieved by operating the laser in the soliton regime. For use in fiber-optical telecommunication, the laser wavelength is preferably shifted to 1.5 .mu.m by use of an optical parametric oscillator. The laser is simple, robust, compact, efficient, and low-cost. It generates a relatively large average power of 100 mW and higher, which is useful for a number of optical probing and detection applications, in a beam (51, 52) that is substantially a fundamental spatial mode.