2020, Lühder, Tilman A.K., Schaarschmidt, Kay, Goerke, Sebastian, Schartner, Erik P., Ebendorff-Heidepriem, Heike, Schmidt, Markus A.

Efficient supercontinuum generation demands for fine-tuning of the dispersion of the underlying waveguide. Resonances introduced into waveguide systems can substantially improve nonlinear dynamics in ultrafast supercontinuum generation via modal hybridization and formation of avoided crossings. Using the example of exposed core fibers functionalized by nanofilms with sub-nanometer precision both zero-dispersion and dispersive wave emission wavelengths are shifted by 227 and 300 nm, respectively, at tuning slopes higher than 20 nm/nm. The presented concept relies on dispersion management via induced resonances and can be straightforwardly extended to other deposition techniques and film geometries such as multilayers or 2D materials. It allows for the creation of unique dispersion landscapes, thus tailoring nonlinear dynamics and emission wavelengths and for making otherwise unsuitable waveguides relevant for ultrafast nonlinear photonics. © 2020 The Authors. Published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

2003, Bandelow, Uwe, Demircan, Ayhan, Kesting, Martin

We solve numerically a generalized nonlinear Schroedinger equation by using a pseudospectral method. Integration is performed by using an eight-order Runge-Kutta scheme. The numerical method therefore differs from the commonly used split-step method. Effects such as the impact of group velocity dispersion (GVD) up to fourth-order dispersion, self phase modulation (SPM), self-steepening and intrapulse Raman scattering can be investigated with the code. Examples for the above effects are demonstrated, as well as their interplay in the context of soliton propagation and sub-picosecond pulses.

2017, Slavcheva, Gabriela, Koleva, Mirella V., Pimenov, Alexander

We have developed a model of the nonlinear polariton dynamics in realistic 3D non-planar microcavity wires in the driven-dissipative regime [15]. We find that the typical microcavity optical bistability evolves into multi-stability upon variation of the model parameters. The origin of the multi-stability is discussed in detail. We apply linear perturbation analysis to modulational instabilities, and identify conditions for localisation of composite multi-mode polariton solitons in the triggered parametric oscillator regime. Further, we demonstrate stable polariton soliton propagation in tilted and tapered waveguides, and determine maximum tilt angles for which solitons are still found. Additionally, we study soliton amplitude and velocity dependence on the wire width, with a view towards device applications.

2016, Buller, J.V.T., Cerda-Méndez, E.A., Balderas-Navarro, R.E., Biermann, K., Santos, P.V.

Exciton-polariton systems can sustain macroscopic quantum states (MQSs) under a periodic potential modulation. In this paper, we investigate the structure of these states in acoustic square lattices by probing their wave functions in real and momentum spaces using spectral tomography. We show that the polariton MQSs, when excited by a Gaussian laser beam, self-organize in a concentric structure, consisting of a single, two-dimensional gap-soliton (GS) state surrounded by one dimensional (1D) MQSs with lower energy. The latter form at hyperbolical points of the modulated polariton dispersion. While the size of the GS tends to saturate with increasing particle density, the emission region of the surrounding 1D states increases. The existence of these MQSs in acoustic lattices is quantitatively supported by a theoretical model based on the variational solution of the Gross–Pitaevskii equation. The formation of the 1D states in a ring around the central GS is attributed to the energy gradient in this region, which reduces the overall symmetry of the lattice. The results broaden the experimental understanding of self-localized polariton states, which may prove relevant for functionalities exploiting solitonic objects.

2019, Bandelow, Uwe, Amiranashvili, Shalva, Pickartz, Sabrina

We prove theoretically, that the evolution of optical solitons can be dramatically influenced in the course of nonlinear interaction with much smaller group velocity matched pulses. Even weak pump pulses can be used to control the solitons, e.g., to compensate their degradation caused by Raman-scattering.

2018, Ankiewicz, Adrian, Bandelow, Uwe, Akhmediev, Nail

We derive the new infinite Sasa-Satsuma hierarchy of evolution equations using an invariant densities approach. Being significantly simpler than the Lax-pair technique, this approach does not involve ponderous 3 x3 matrices. Moreover, it allows us to explicitly obtain operators of many orders involved in the time evolution of the Sasa-Satsuma hierarchy functionals. All these operators are parts of a generalized Sasa-Satsuma equation of infinitely high order. They enter this equation with independent arbitrary real coefficients that govern the evolution pattern of this multi-parameter dynamical system.

2012, Bandelow, Uwe, Akhmediev, Nail N.

We present the lowest order rogue wave solution of the Sasa-Satsuma equation (SSE) which is one of the integrable extensions of the nonlinear Schrödinger equation (NLSE). In contrast to the Peregrine solution of the NLSE, it is significantly more involved and contains polynomials of fourth order rather than second order in the corresponding expressions. The correct limiting case of Peregrine solution appears when the extension parameter of the SSE is reduced to zero.

2015, Slavcheva, Gabriela, Gorbach, Andrey V., Pimenov, Alexander, Vladimirov, Andrei G., Skryabin, Dmitry

Nonlinear polaritons in microcavity waveguides are demonstrated to exhibit multi-stable behaviour and rich dynamics, including filamentation and soliton formation. We find that the multi-stability originates from co-existense of different transverse modes of the polaritonic waveguide. Modulational stability and conditions for multi-mode polariton solitons are studied. Soliton propagation in tilted, relative to the pump momentum, waveguides is demonstrated and a critical tilt angle for the soliton propagation is found.