I’ll try my best to answer you question, please feel free to post more information if I’m off the mark so I (or someone else) can adjust my answer since I’m not sure what you mean by access, distributed, and core “layers”.
You can certainly run fiber between switches, but typically this is done between either backbone switches, when there is greater than 328 feet between switches, or there is a high risk of eletromagnetic interference (like in a manufacturing facility, etc). Many switch makers make switches that have GBIC ports in them, however they generally cost more than a standard switch so you really have to decide if you need fiber.
Additionally, the fiber cables are considerably more expensive when compared to a twisted pair (10/100/1000Mbs) cable of the same length, plus are also more difficult to make on your own.
Additionally, with Cat 6/6e and greater cable you can accomplish the same or greater speeds than fiber.
Typically, if you need faster bandwidth between switches you can also create an access group or trunk that will “bond two cables into one for greater speeds.