See the sibling comment and my answer. A plane wave can very well be a plane wave "containing" one photon or containing multiple photons or containing a coheren

See the sibling comment and my answer. A plane wave can very well be a plane wave "containing" one photon or containing multiple photons or containing a coherent state. There is a big difference between saying "I can use different sets of creation operators to form a basis for the field operator" (what I think you are saying) and the confounded statement mixing up basis of a Hilbert space with basis of integrable functions of the OP.