A method of making an optical fiber preform includes depositing silica glass soot on the inside of a substrate tube via a chemical vapor deposition operation. The silica glass soot is consolidated into silica glass under controlled conditions such that the consolidated silica glass on the interior of the substrate tube contains a non-periodic array of gaseous voids in a cladding region of the optical fiber preform. The optical fiber preform may be used to produce an optical fiber having a core and a cladding containing voids formed from the gaseous voids of the cladding region of the optical fiber preform. The core of the optical fiber has a first index of refraction and the cladding has a second index of refraction less than that of the core.