A collimated light beam parallel to the axis of a fused-quartz cylinder impinging on a 90° apex angle concave cone cut in a quartz rod is transformed into a cylindrical wave by total internal reflection. A thin metal film at the quartz-air interface enables excitation of the plasmon mode at the air side that can polarize the cylindrical wave and/or has the potential to monitor physical, chemical, or biological quantities or events at the inner wall of the cone. The present Letter first analyzes the plasmon coupling mechanism and conditions. It then describes the diamond-grinding technique achieving a smooth cone wall and the finest possible tip. The experimental evidence of the polarization conversion is brought on a diamond-grinded section of fused-silica rod and gold coating of the concave wall.