The field of applicability of the concept of PT-symmetry of
differential operators (where, say, P is parity and T is complex
conjugation) has recently been successfully extended to classical
optics, both theoretically and experimentally.  The text shows that
the quantum-theoretical ``ancestors" of these models may still offer
useful methodical hints in the new setting. Among them the author
emphasizes the profit gained by the transition to isospectral
selfadjoint operators. This degenerates here to the mere complex
shift of the argument in Bloch functions.  In the case under
consideration (taken from Ref. [8]), this simplifies the picture.
Besides this formal advantage the sinusoidal setup is shown to
exhibit also specific phenomenological merits - its most remarkable
properties (like birefringence) are shown weakening when one moves
away from the sinusoidal shape.

MR2823453 Jones, H. F. Use of equivalent Hermitian Hamiltonian for
$PT$-symmetric sinusoidal optical lattices. J. Phys. A 44 (2011),
no. 34, 345302, 10 pp. 81Qxx (81Vxx)