Compound-photonic structures with gain and loss1 provide a powerful platform for testing various theoretical proposals on non-Hermitian parity–time-symmetric quantum mechanics2–5 and initiate new possibilities for shaping optical beams and pulses beyond conservative structures. Such structures can be designed as optical analogues of complex parity–timesymmetric potentials with real spectra. How...

The PT-symmetric square well problem is considered in a SUSY framework when the coupling strength lies below the critical value where PT symmetry becomes spontaneously broken. We find SUSY partner potentials to exist admitting a hierarchy with energy levels depicting an unbroken SUSY situation. Such a hierarchy is a PT-symmetric analogue of the family of sec2-like potentials, to which it reduce...

We introduce here the concept of acoustic parity-time (PT ) symmetry and demonstrate the extraordinary scattering characteristics of the acoustic PT medium. On the basis of exact calculations, we show how an acoustic PT -symmetric medium can become unidirectionally transparent at given frequencies. Combining such a PT -symmetric medium with transformation acoustics, we design two-dimensional sy...

We demonstrate that light propagation in waveguide arrays that include PT-symmetric structures can exhibit strongly nonlocal sensitivity to topology of the array at fixed other parameters. We consider an array composed of lossless waveguides, that includes a pair of PT-symmetric waveguides with balanced gain and loss, and reveal that PT-symmetry breaking thresholds are different for planar and ...

The characteristic anti-linear (parity/time reversal, PT) symmetry of non-Hermitian Hamiltonians with real energies is presented as a source of two new forms of solvability of Schrödinger’s bound-state problems. In detail we describe (1) their very specific semi-exact solvability (SES) and (2) their innovated variational tractability. SES technicalities are discussed via charged oscillator exam...

We study the effect of localized modes in lattices of size N with parity-time (PT) symmetry. Such modes are arranged in pairs of quasidegenerate levels with splitting delta approximately exp(-N/xi) where xi is their localization length. The level "evolution" with respect to the PT breaking parameter gamma shows a cascade of bifurcations during which a pair of real levels becomes complex. The sp...

By rearrangements of waveguide arrays with gain and losses one can simulate transformations among parity-time (PT-) symmetric systems not affecting their pure real linear spectra. Subject to such transformations, however, the nonlinear properties of the systems undergo significant changes. On an example of an array of four waveguides described by the discrete nonlinear Schrödinger equation with...

For the one-dimensional nonlinear Schrödinger equations with parity-time (PT) symmetric potentials, it is shown that when a real symmetric potential is perturbed by weak PT-symmetric perturbations, continuous families of asymmetric solitary waves in the real potential are destroyed. It is also shown that in the same model with a general PT-symmetric potential, symmetry breaking of PT-symmetric ...

Parallels between the concepts of symmetry, supersymmetry and (recently introduced) PT −symmetry are reviewed and discussed, with particular emphasis on the new insight in quantum mechanics which is rendered possible by their combined use.

We study complexified Harmonic Oscillator with a position dependent mass, referred to in the present paper as Exotic Oscillator (EO), in arbitrary dimensions. The real space EO has an interesting dynamics: in the equation of motion the full Hamiltonian operator appears in place of the frequency parameter in a Harmonic Oscillator. We reveal some generic features in the constraint structure of th...