PURPOSE: To enable efficient and low-cost polishing by contacting a polishing mixture in the form of a liquid slurry containing abrasive particles while subjecting it to agitation, with an optically transparent surface which defines a cavity or a wall in an optical waveguide included in a small planar optical device.

CONSTITUTION: This apparatus has a pulse generator 10, in response to a generated pulse, and a transducer 8 disposed in the base of a tank 6 is vibrated to vibrate a liquid L in the tank 6. A container 2 where a planar optical device D for precise polishing is disposed is arranged in the tank 6, and to hold the container 2 in contact state at the bottom of the tank 6, a weighty cover 4 is disposed on the container 2. A polishing mixture P in the form of liquid slurry containing polishing abrasive particles, which is subjected to high intensity positive displacement and ultrasonic condition caused in the liquid L, is put in the container 2, and the surface is polished by contact of the polishing mixture P.