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This invention pertains to a holey fiber and to a fabrication method for making the fiber. The holey fiber can transmit light by total internal reflection or by Bragg diffraction, can be single mode or multimode and can have solid core or a hollow core. The holey fiber has outside diameter typically of 20 microns to 5 mm, a hollow core of a diameter typically of 0.2 micron to 150 microns and longitudinal channels therethrough of a diameter typically of 0.1 micron to 150 microns. The channels are disposed in a desired arrangement with center-to-center distance variation of less than about 2% along the length of the fiber and the cross-section thereof is round that varies less than about 2%.