Related papers: 2D Solitons in PT-symmetric photonic lattices
The concept of parity-time (PT) symmetry originates from the framework of quantum mechanics, where if the Hamiltonian operator satisfies the commutation relation with the parity and time operators, it shows all real eigen-energy spectrum.…
Canonical quantum mechanics postulates Hermitian Hamiltonians to ensure real eigenvalues. Counterintuitively, a non-Hermitian Hamiltonian, satisfying combined parity-time (PT) symmetry, could display entirely real spectra above some…
We introduce one- and two-dimensional (1D and 2D) models of parity-time ($% \mathcal{PT}$) -symmetric couplers with the mutually balanced linear gain and loss applied to the two cores, and cubic-quintic (CQ) nonlinearity acting in each one.…
Recent progress on nonlinear properties of parity-time ($\cal PT$-) symmetric systems is comprehensively reviewed in this article. $\cal PT$ symmetry started out in non-Hermitian quantum mechanics, where complex potentials obeying $\cal PT$…
In 1998, Carl Bender challenged the perceived wisdom of quantum mechanics that the Hamiltonian operator describing any quantum mechanical system has to be Hermitian. He showed that Hamiltonians that are invariant under combined parity-time…
It is well known that typical PT-symmetric systems suffer symmetry breaking when the strength of the gain-loss terms exceeds a certain critical value. We present a summary of recently published and newly produced results which demonstrate…
Solitons in one-dimensional parity-time (PT)-symmetric periodic potentials are studied using exponential asymptotics. The new feature of this exponential asymptotics is that, unlike conservative periodic potentials, the inner and outer…
Multi-dimensional complex optical potentials with partial parity-time (PT) symmetry are proposed. The usual PT symmetry requires that the potential is invariant under complex conjugation and simultaneous reflection in all spatial…
Non-Hermitian systems based on parity-time (PT) symmetry reveal rich physics beyond the Hermitian regime. So far, realizations of PT-symmetric systems have been limited to the spatial domain. Here we theoretically and experimentally…
The real spectrum of bound states produced by PT-symmetric Hamiltonians usually suffers breakup at a critical value of the strength of gain-loss terms, i.e., imaginary part of the complex potential. On the other hand, it is known that the…
In the past decade, the concept of parity-time ($\mathcal{PT}$) symmetry, originally introduced in non-Hermitian extensions of quantum mechanical theories, has come into thinking of photonics, providing a fertile ground for studying,…
We introduce a two-dimensional (2D) system, which can be implemented in dual-core planar optical couplers with the Kerr nonlinearity in its cores, making it possible to blend effects of the PT symmetry, represented by the balanced linear…
Stability of solitons in parity-time (PT)-symmetric periodic potentials (optical lattices) is analyzed in both one- and two-dimensional systems. First we show analytically that when the strength of the gain-loss component in the PT lattice…
Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc.. The stable solitons have been captured not only…
We prove existence of discrete solitons in infinite parity-time (PT-) symmetric lattices by means of analytical continuation from the anticontinuum limit. The energy balance between dissipation and gain implies that in the anticontinuum…
One of the challenges of the modern photonics is to develop all-optical devices enabling increased speed and energy efficiency for transmitting and processing information on an optical chip. It is believed that the recently suggested…
The recently-developed notion of 'parity-time (PT) symmetry' in optical systems with a controlled gain-loss interplay has spawned an intriguing way of achieving optical behaviors that are presently unattainable with standard arrangements.…
We introduce a 2D network built of $\mathcal{PT}$-symmetric dimers with on-site cubic nonlinearity, the gain and loss elements of the dimers being linked by parallel square-shaped lattices. The system may be realized as a set of…
This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by purely nonlinear lattices (NLs), which represent a spatially periodic modulation of the local strength and sign of…
Non-hermitian, $\mathcal{PT}$-symmetric Hamiltonians, experimentally realized in optical systems, accurately model the properties of open, bosonic systems with balanced, spatially separated gain and loss. We present a family of exactly…