  We show that confluent Darboux-Crum transformations with emergent Jordan
states are an effective tool for the design of optical systems governed by the
Helmholtz equation under the paraxial approximation. The construction of
generic, asymptotically real and periodic, $PT$-symmetric systems with local
complex periodicity defects is discussed in detail. We show how the decay rate
of the defect is related with the energy of the bound state trapped by the
defect. In particular, the bound states in the continuum are confined by the
periodicity defects with power law decay. We show that these defects possess
complete invisibility; the wave functions of the system coincide asymptotically
with the wave functions of the undistorted setting. The general results are
illustrated with explicit examples of reflectionless models and systems with
one spectral gap. We show that the spectral properties of the studied models
are reflected by Lax-Novikov-type integrals of motion and associated
supersymmetric structures of bosonized and exotic nature.
