Pattern matching operators a index

Hi

I'm developing a new type for character string, like varchar. I wrote
operators for btree and so forth.
I wonder how pattern matching operators using btree index, because btree
operator class ony knows about >, >=, <=, and = operators, but operators
for pattern matching, such as LIKE, are not known for btree access method.

Now my question is:
Is Postgre using btree for pattern matching query for varchar or other
character string types?

If it does, how i implement it for my new type?

Regards,
Soroosh