Both spellings, fiber and fibre are correct. In United States and countries following the US style of English, it is Optical fiber. In UK and common wealth countries, it is Optical fibre, if you search in the interent, both optical fiber and optical fibre expression can be seen.
If you search in Google, Yahoo or any other search engines for ‘optical fiber’ they will give you mostly the contents written by authors following the US English. On the other hand a search for ‘optical fibre’ will yield results from Common wealth countries. In United Kingdom, technology writers use the term optical fibre. News papers, websites, blogs, magazines and other content generation systems in New Zealand, Australia, South Africa also use the term optical fibre.
Countries ruled by Britain in the past and hence inherited the British system of English in their schools also use the spelling optical fibre following the British style. For example, media in India, Pakistan, Srilanka and Bangladesh in the South Asia, African nations ruled by Britain etc, also use optical fibre.
The influence of United States and the strength of its online and printed media has given popularity to US style of English. Therefore media in many countries such as Japan, China, Vietnam, Oman, UAE, Saudi Arabia etc follow the US style and use the spelling optical fiber.
Technically both fibre and fiber are one material, whether we write fiber or fibre. The base material is Silica. Fortunately spelling of Silica is same in UK and US! We use both fiber and fibre when writing in this site. Our users may write fibre or fiber depending on their convenience and writing practice. Most of the editors here have the practice of following US style and hence you can see most of the content here use the spelling ‘fiber’.