Related papers: PT-symmetry in optics beyond the paraxial approxim…
The scattering matrix $S$ obeys the unitary relation $S^\dagger S=1$ in a Hermitian system and the symmetry property ${\cal PT}S{\cal PT}=S^{-1}$ in a Parity-Time (${\cal PT}$) symmetric system. Here we report a different symmetry relation…
Implementation of a parity-time (PT) symmetric microwave photonic system in the optical wavelength space with spatial singularity is proposed. In the proposed PT-symmetric microwave photonic system, the gain and loss modes are confined in a…
In this work we first examine transverse and longitudinal fluxes in a $\cal PT$-symmetric photonic dimer using a coupled-mode theory. Several surprising understandings are obtained from this perspective: The longitudinal flux shows that the…
Over the past decade, parity-time ($\mathcal{PT}$)-symmetric Hamiltonians have been experimentally realized in classical, optical settings with balanced gain and loss, or in quantum systems with localized loss. In both realizations, the…
Parity-time (PT) symmetric systems have two distinguished phases, e.g., one with real energy eigenvalues and the other with complex conjugate eigenvalues. To enter one phase from the other, it is believed that the system must pass through…
Optical systems combining balanced loss and gain profiles provide a unique platform to implement classical analogues of quantum systems described by non-Hermitian parity-time- (PT-) symmetric Hamiltonians and to originate new synthetic…
We observe that the reflection and transmission coefficients of a particle within a double, PT symmetric heterojunction with spatially varying mass, show interesting features, depending on the degree of non Hermiticity, although there is no…
We provide a systematic analysis of a prototypical nonlinear oscillator system respecting PT-symmetry i.e., one of them has gain and the other an equal and opposite amount of loss. Starting from the linear limit of the system, we extend…
The $PT$ symmetric potential $V_0[\cos(2\pi x/a)+i\lambda\sin(2\pi x/a)]$ has a completely real spectrum for $\lambda\le 1$, and begins to develop complex eigenvalues for $\lambda>1$. At the symmetry-breaking threshold $\lambda=1$ some of…
Scattering on the ${\cal PT}$-symmetric Coulomb potential is studied along a U-shaped trajectory circumventing the origin in the complex $x$ plane from below. This trajectory reflects ${\cal PT}$ symmetry, sets the appropriate boundary…
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…
We consider branched quantum wires, whose connection rules provide PT-symmetry for the Schrodinger equation on graph. For such PT-symmetric quantum graph we derive general boundary conditions which keep the Hamiltonian as PT-symmetric with…
A potential scattering theory from deterministic and random $\mathcal{PT}$ collections of particles with gain and loss is introduced and the forms of their structure and pair-structure factors are elucidated. An example relating to light…
Despite its non-Hermitian nature, the transverse optical beam shift exhibits both real eigenvalues and non-orthogonal eigenstates. To explore this unexpected similarity to typical PT (parity-time)-symmetric systems, we first categorize the…
Closed expressions are derived for the pseudo-norm, norm and orthogonality relations for arbitrary bound states of the PT symmetric and the Hermitian Scarf II potential for the first time. The pseudo-norm is found to have indefinite sign in…
Using Maxwell-Bloch equations it has been shown how the superradiance can lead to amplification and gain at a frequency much larger than the pumping frequency. This remarkable effect has been examined in terms of a simpler model involving…
A scalar theory with a preferred reference frame is summarized. To test that theory in celestial mechanics, an "asymptotic" post-Newtonian (PN) scheme has been developed. This associates a conceptual family of self-gravitating systems with…
We discuss a PT-symmetric Hamiltonian with complex eigenvalues. It is based on the dimensionless Schr\"{o}dinger equation for a particle in a square box with the PT-symmetric potential $V(x,y)=iaxy$. Perturbation theory clearly shows that…
We discuss the optical forces exerted on parity-time (PT) symmetric heterostructures under normal incidence of a single and two counter-propagating plane waves. The underlying strategy is through generalized parametric space, stemming from…
With perfectly balanced gain and loss, dynamical systems with indefinite damping can obey the exact PT-symmetry being marginally stable with a pure imaginary spectrum. At an exceptional point where the symmetry is spontaneously broken, the…