Sequences of picosecond pulses of 1.06-microm Nd:YAG laser radiation with a total energy of approximately 2 mJ are transmitted through a hollow-core photonic-crystal fiber with a core diameter of approximately 14 microm and are focused onto a tooth's surface in vitro to ablate dental tissue. The hollow-core photonic-crystal fiber is shown to support the single-fundamental-mode regime for 1.06-microm laser radiation, serving as a spatial filter and allowing the laser beam's quality to be substantially improved. The same fiber is used to transmit emission from plasmas produced by laser pulses onto the tooth's surface in the backward direction for detection and optical diagnostics.