  The broken and unbroken phases of PT and supersymmetry in optical systems are
explored for a complex refractive index profile in the form of a Scarf
potential, under the framework of supersymmetric quantum mechanics. The
transition from unbroken to the broken phases of PT-symmetry, with the merger
of eigenfunctions near the exceptional point is found to arise from two
distinct realizations of the potential, originating from the underlying
supersymmetry. Interestingly, in PT-symmetric phase, spontaneous breaking of
supersymmetry occurs in a parametric domain, possessing non-trivial shape
invariances, under reparametrization to yield the corresponding energy spectra.
One also observes a parametric bifurcation behaviour in this domain. Unlike the
real Scarf potential, in PT-symmetric phase, a connection between complex
isospectral superpotentials and modified KdV equation occurs, only with certain
restrictive parametric conditions. In the broken PT-symmetry phase,
supersymmetry is found to be intact in the entire parameter domain yielding the
complex energy spectra, with zero-width resonance occurring at integral values
of a potential parameter.
