I work with customers in the US and am asleep during most of their work hours.  In general customers should know when they can and can't get ahold of you.

You don't need to mention you are a night owl, but you should set expectations regarding your availability.  For example, "My office hours are from 11am to 9pm" is fine.

I wouldn't mention your waking cycle.  There could be all kinds of reasons for keeping non-traditional working hours.