The Dark Ages begin about 538 AD. It had absolutely nothing to do with the Ottoman Empire which didn't come around for another 800+ years!
In fact, the Dark Ages are so dark that we know about their "early years" from few sources. One source are ancient Irish royal annals (from which we derive our "King Arthur" stories). Another source are tree rings. The suggestion is that the weather turned very nasty for about a decade. This resulted in the death of almost everybody in Northern and Western Europe as well as the loss of all ancient knowlege. Southern Europe fared better, but "better" does not mean "well", just "better". There was general economic collapse throughout the Mediterranean, Central Asia, Western Europe (to the extent there was any economy at all), China and so on.
Some folks came out of the Dark Ages sooner than others. The Chinese, for example, survived through total collapse for a mere 300 years. Byzentium (the city itself) seems to have had total collapse for only 84 years ~ of course they ended up fairly alone in the world for a long while.
The Western Arabian peninsula seems to have begun recovery within just a few decades! We know they recovered because they had this interesting story about Mohammad and messages from God when they conquered Damascus and kicked out the decadent Persian regime. They then went on to recover as much ancient knowlege as they could, and once contact with India was made, they expanded the scope of the Indian knowledge base (which is, among other things, the number system we now use).
The Ottoman Empire did not yet exist while this recovery was going on.
Finally, about 1000 AD Western Europe recovered economically, but not socially. That's when the Age of Jihad began! Europeans had armed knights who lived under monastic orders (for a start), wore crosses into all battles, etc., etc., etc. It was truly horrible. In the end they conquered just about the whole world. Until oil was discovered in the Middle East most Western Europeans didn't care one way or the other about Islam.