Doan Quang Tri | Search arXiv

arXiv2026

Re-entrant parity-time phase transitions in locally coupled ring resonators

We investigate two parity-time-symmetric ring resonators coupled over a finite angular region described by a super-Gaussian profile. In the linear regime, analytical spectra are obtained in the homogeneous-coupling and fixed-amplitude narrow-contact limits, while the finite-width problem is treated numerically. Local coupling introduces nonzero spatial Fourier components that mix angular harmonics and lift the degeneracy of counterpropagating modes, resolving each excited doublet into parity-dependent branches. Collisions among these branches generate multiple exceptional-point boundaries and disconnected broken-PT domains. The resulting phase diagrams exhibit re-entrant unbroken-broken-unbroken transitions when the gain-loss strength, coupling width, or peak coupling amplitude is varied. The numerical spectra continuously recover both analytical limits. In the nonlinear regime, selected ground and excited linear modes are used as seeds for adiabatic propagation into finite-amplitude Kerr waveforms that remain dynamically persistent over the simulated observation interval for finite ranges of nonlinear strength. These results show that the spatial profile of inter-resonator coupling provides a geometric means of controlling multimode PT transitions and selecting dynamically accessible nonlinear waveforms in coupled-ring systems.

nlin.PS↗

arXiv2026

Stability and Interaction Dynamics of Solitons in Spatially Engineered High-Order Nonlinear Media

We study spatial solitons and their interaction dynamics in nonlinear optical media with spatially engineered refractive index and competing cubic-quintic (CQ) nonlinear profiles, using the variational approximation (VA), the hybrid variational approximation (HVA), and direct numerical simulations. The model was implemented in a symmetric step-index planar dielectric waveguide with a core exhibiting competing CQ nonlinearity and cladding layers possessing only a cubic nonlinear response. For stationary states, the Gaussian VA predicts two types of $N(μ)$ characteristic curves, where $N$ is soliton norm and $μ$ is propagation constant, separated by a boundary surface in parameter space, and numerical calculations reveal the same two types. Below this surface, the VA agrees with the numerical results mainly at low powers, while pronounced deviations in the profile and stability appear at high powers. Above the surface, the variational and numerical curves retain the same qualitative form, and a super-Gaussian ansatz accurately describes the high-power flat-top solitons. Soliton collisions produce four post-interaction regimes: Oscillation, Molecular, Splitting, and Breakup. The HVA reproduces the first three over a broad power range, including collisions involving flat-top solitons. Its main limitation arises in the Breakup regime, where strong radiation leaves the guiding region and cannot be represented by the adopted HVA ansatz. Nevertheless, for solitons associated with the second type of characteristic curves, the HVA still captures the breakup dynamics qualitatively. Thus, the HVA provides an efficient description of complex soliton interactions at a substantially lower computational cost than direct numerical simulations.

nlin.PS↗