Parity-time Symmetric Lattices Research Articles

Fundamental and dipole gap solitons and their dynamics in the cubic–quintic fractional nonlinear Schrödinger model with a [formula omitted]-symmetric lattice

The interplay of two linear controlled terms – fractional diffraction and parity-time (PT) symmetric lattice – gives rise to unique and interesting linear Bloch gap structures within where the nonlinear localized gap modes may exist. In this study, we explore the formation and dynamics of one-dimensional gap solitons in the cubic–quintic physical model combining the fractional diffraction and PT symmetric lattice. Two classes of gap solitons, which we name the fundamental gap solitons and dipole ones, are constructed and their stability regions within the first finite gap of the associated linear Bloch spectrum are identified by means of linear-stability analysis and direct perturbed numerical simulations. We stress that the gap solitons are always unstable under the condition of PT symmetry breaking (the imaginary part of which is above 0.5). The excitations of the stable two classes of gap solitons are also investigated by using the adiabatic variation of the system’s parameters. The results predicted here shed some light on soliton physics in physical systems with combined fractional diffraction and PT symmetric lattice and the competing nonlinearities.

Nonlinear conical diffraction in fractional dimensions with a [formula omitted]-symmetric optical lattice

Space-fractional parity-time symmetry, featuring the fractional Laplacian operator rather than the standard operator, continues to be a challenge. This report analytically and numerically assesses the dynamics of wave packets in a space-fractional parity-time symmetric lattice by invoking Kerr nonlinearity. By adjusting the Lévy index, the basic properties of Floquet-Bloch modes in parity-time symmetric optical lattices are examined. It is demonstrated that the width of the first three Floquet-Bloch modes increases as the Lévy index decreases and that the corresponding band structure becomes symmetrically linear. These features result in peculiar properties during propagation, including splitting or diffraction-free propagation, preferential propagation, unidirectional propagation, and phase dislocations. In the two-dimensional fractional case, when the band structure is cone-like, it causes conical diffraction, and non-diffracting propagation occurs when the Floquet-Bloch mode of the upper band is excited by the input beam. Kerr nonlinearity modulates the energy in a certain nonlinear region toward the middle and suppresses the formation of conical diffraction.

Lasing With Resonant Feedback in Weakly Modulated Parity-Time Symmetric Lattices

We report on the lasing action in weakly modulated parity-time (PT) symmetric lattices. At the exceptional point in PT-symmetric lattices, the amplitude and phase of unidirectionally scattered waves are independently and flexibly determined by the PT modulations, thus, providing a distinctive route to construct a lasing mode in finite systems with weakly modulated structures. It is revealed that the resonant feedback mechanism plays a crucial role in building up the lasing action. Our finding would enrich the singularity dynamics in the weakly modulated PT systems.

Discrete multipole dark solitons in saturable nonlinearity media with parity-time symmetric lattices

We investigate numerically the existence and stability of discrete multipole dark solitons in saturable nonlinearity media with parity-time ( $\mathcal{PT}$ ) symmetric lattices. The dipole and triple solitons share the same existence domain associated with the propagation constant, gain-loss coefficient and the degree of saturable nonlinearity. However, the solitons stably propagate in a different area of the aforementioned three parameters. The beam power monotonously increases with the increase of propagation constant and the saturable degree, but gently decreases with the gain-loss coefficient. Moreover, the power of the triple solitons is higher than that of dipole solitons under the same conditions.

Vector solitons in parity-time symmetric lattices with nonlocal nonlinearity

We investigate mixed-gap vector solitons involving incoherently coupled fundamental and dipole components in a parity-time symmetric lattice with nonlocal focusing nonlinearity. The fundamental component exists in the semi-infinite gap with propagation constant μ1 and the dipole component exists in the first gap with propagation constant μ2. We find that the width of the existence domain on μ1 (μ2) for vector solitons shrinks with the growth of nonlocality degree d and expands almost linearly with the increase of μ2 (μ1). In particular, linear stability analyses show that this type of vector solitons are unstable in the high-power region of the dipole component.

Observation of exceptional points in reconfigurable non-Hermitian vector-field holographic lattices.

Recently, synthetic optical materials represented via non-Hermitian Hamiltonians have attracted significant attention because of their nonorthogonal eigensystems, enabling unidirectionality, nonreciprocity and unconventional beam dynamics. Such systems demand carefully configured complex optical potentials to create skewed vector spaces with a desired metric distortion. In this paper, we report optically generated non-Hermitian photonic lattices with versatile control of real and imaginary sub-lattices. In the proposed method, such lattices are generated by vector-field holographic interference of two elliptically polarized pump beams on azobenzene-doped polymer thin films. We experimentally observe violation of Friedel's law of diffraction, indicating the onset of complex lattice formation. We further create an exact parity-time symmetric lattice to demonstrate totally asymmetric diffraction at the spontaneous symmetry-breaking threshold, referred to as an exceptional point. On this basis, we provide the experimental demonstration of reconfigurable non-Hermitian photonic lattices in the optical domain and observe the purest exceptional point ever reported to date.

Control of power in parity-time symmetric lattices

We investigate wave transport properties of parity–time (PT) symmetric lattices that are periodically modulated along the direction of propagation. We demonstrate that in the regime of unbroken PT-symmetry, the system Floquet–Bloch modes may interfere constructively leading to either controlled oscillations or power absorption and unlimited amplification occurring exactly at the phase-transition point. The differential power response is affected by the overlap of the gain and loss system distribution with wave intensity pattern that is formed through Rabi oscillations engaging the coupled Floquet–Bloch modes.

Fundamental solitons in parity-time symmetric lattice with a vacancy defect

We put forward a mechanism for delaying the collapse of the fundamental solitons in nonlinear media whose dynamics is governed by two-dimensional nonlinear Schrödinger (NLS) equation with parity-time symmetric (PT-symmetric) periodic potentials with/without a vacancy defect. We observed that strengthened gain–loss component (imaginary part of the potential) in the periodic lattice impoverish the stability properties of the solitons, on the other hand adding a vacancy defect to the periodic PT-symmetric lattice acts as a delaying mechanism for collapsing solitons.

Diffraction management and soliton dynamics in frequency-chirped ℙT symmetric lattices.

We address two closely related problems: diffraction management and soliton dynamics in parity-time ( ℙT) symmetric lattices with a quadratic frequency modulation. The normal, anomalous, or zero diffraction is possible for narrow beams with a broad band of spatial frequencies. The frequency band of nondiffraction beams can be enlarged by increasing the chirp rate of lattices. Counter-intuitively, the gain-loss component plays the same role as the real part of lattice on the suppression of diffraction, which leads to an effective reduction of critical lattice depth for nondiffraction beams. Additionally, we reveal the existence of a novel type of "bright" solitons in defocusing Kerr media modulated by chirped ℙT lattices. We also demonstrate that lattice chirp can be utilized to suppress the instability of solitons. Our results expand the concept of ℙT symmetry in both linear and nonlinear regimes, and may find interesting optical applications.

Two-dimensional defect solitons in parity-time-symmetric periodic optical lattices

We report on the existence and stability of two-dimensional (2D) fundamental defect solitons (DSs) in parity-time (PT) symmetric periodic optical lattices based on focusing and defocusing nonlinear media, respectively. The stable regions of DSs in focusing and defocusing nonlinear media are calculated for the point defect. With the introduction of gain and loss component, some unique properties of 2D spatial DSs are displayed in such lattice potential. There exists transverse power-flow in the PT symmetric periodic optical lattice, and the DSs in the high power regions are unstable. Some properties in focusing nonlinear media are very different from those in defocusing nonlinear media. DSs in PT symmetric lattices with line defect based on focusing nonlinearity are studied as well.

Discrete solitons in saturable nonlinearity media with parity-time symmetric lattices

We study the existence of discrete solitons in saturable nonlinearity media with parity-time symmetric lattices. We find that there exist two kinds of discrete solitons, they share the same parameters but different energy flows. The degree of saturable nonlinearity can influence the properties of such discrete solitons. Stable discrete solitons are found near the anti-continuum limit.

PTSymmetry with a System of Three-Level Atoms

We show that a vapor of multilevel atoms driven by far-off-resonant laser beams, with the possibility of interference of two Raman resonances, is highly efficient for creating parity-time symmetric profiles of the probe-field refractive index, whose real part is symmetric and imaginary part is antisymmetric in space. The spatial modulation of the probe-field susceptibility is achieved by a proper combination of standing-wave strong control fields and of Stark shifts induced by far-off-resonance laser fields. As particular examples we explore a mixture of isotopes of rubidium atoms and design a parity-time symmetric lattice and a parabolic refractive index with a linear imaginary part.