Spin-optical solitons in liquid crystals

© 2020 American Physical Society. In the framework of nonlinear spin optics, we investigate self-confined light beams in reorientational nematic liquid crystals. Using modulation theory and numerical experiments, we analyze spatial solitary waves supported by the geometric phase arising in a uniaxial when subject to a nonlinear modulation of its optic axis distribution. Spin evolution and optical reorientation in an index-homogeneous medium give rise to a longitudinally periodic, transversely inhomogeneous potential able to counteract the diffraction of a polarized bell-shaped beam, generating a spin-optical solitary wave. Spin-optical solitary waves evolve in polarization and have an oscillatory character in amplitude, size, and ellipticity

Whitham Shocks and Resonant Dispersive Shock Waves Governed by the Higher Order Korteweg-de Vries Equation

The addition of higher order asymptotic corrections to the Korteweg-de Vries equation results in the extended Korteweg-de Vries equation. These higher order terms destabilise the dispersive shock wave solution, also termed an undular bore in fluid dynamics, and result in the emission of resonant radiation. In broad terms, there are three possible dispersive shock wave regimes: radiating dispersive shock wave (RDSW), cross-over dispersive shock wave (CDSW) and travelling dispersive shock wave (TDSW). While there are existing solutions for the RDSW and TDSW regimes obtained using modulation theory, there is no existing solution for the CDSW regime. Modulation theory and the associated concept of a Whitham shock are used to obtain this CDSW solution. In addition, it is found that the resonant wavetrain emitted by the extended Korteweg-de Vries equation with water wave coefficients has a minimal amplitude. This minimal amplitude is explained based on the developed Whitham modulation theory.Comment: To appear in the Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science

Special Issue on Light Beams in Liquid Crystals

The study of propagating light beams in liquid crystals, i [...

Dispersive shock waves for the Boussinesq Benjamin-Ono equation

In this work, the dispersive shock wave (DSW) solution of a Boussinesq Benjamin–Ono (BBO) equation, the standard Boussinesq equation with dispersion replaced by nonlocal Benjamin–Ono dispersion, is derived. This DSW solution is derived using two methods, DSW fitting and from a simple wave solution of the Whitham modulation equations for the BBO equation. The first of these yields the two edges of the DSW, while the second yields the complete DSW solution. As the Whitham modulation equations could not be set in Riemann invariant form, the ordinary differential equations governing the simple wave are solved using a hybrid numerical method coupled to the dispersive shock fitting which provides a suitable boundary condition. The full DSW solution is then determined, which is found to be in excellent agreement with numerical solutions of the BBO equation. This hybrid method is a suitable and relatively simple method to fully determine the DSW solution of a nonlinear dispersive wave equation for which the (hyperbolic) Whitham modulation equations are known, but their Riemann invariant form is not

Interactions of self-localized optical wavepackets in reorientational soft matter

The interaction of optical solitary waves in nematic liquid crystals, nematicons and vortices, with other nematicons and localised structures, such as refractive index changes, is reviewed. Such interactions are shown to enable simple routing schemes as a basis for all-optical guided wave signal manipulation

Multihump thermo-reorientational solitary waves in nematic liquid crystals: Modulation theory solutions

The propagation of light-induced thermo-reorientational solitary waves in nematic liquid crystals is studied using numerical solutions of the full governing equations and variational approximations. These thermo-reorientational solitary waves form as the nonlocal refractive index response to extraordinarily polarized light beams is both self-focusing via the induced rotation of the constituent molecules and self-defocusing owing to the temperature increase through optical absorption. These competing nonlinearities can lead to the formation of one- and two-dimensional multihumped solitary and ring-shaped waves at high enough optical powers with a volcano profile on the plane transverse to propagation. The variational solutions for these self-localized structured beams are in remarkably good agreement with full numerical solutions of the governing equations

Interaction of internal solitary waves with long periodic waves within the rotation modified Benjamin–Ono equation

The interaction of a solitary wave with a long background periodic wave in a deep ocean is studied within the framework of the rotation modified Benjamin-Ono equation. Using a multiple scales analysis, we find stationary and nonstationary solutions for a Benjamin-Ono soliton trapped within a long sinusoidal wave. We show that the radiation losses experienced by the soliton and caused by the Earth’s rotation can be compensated by energy pumping from the background wave. However, the feedback of the soliton on the background wave eventually leads to the destruction of the coherent structure and energy dispersion in a quasi-random wave field. Estimates of the characteristic parameters of the soliton dynamics are presented for real oceanic conditions

The Físchlár-News-Stories system: personalised access to an archive of TV news

The “Físchlár” systems are a family of tools for capturing, analysis, indexing, browsing, searching and summarisation of digital video information. Físchlár-News-Stories, described in this paper, is one of those systems, and provides access to a growing archive of broadcast TV news. Físchlár-News-Stories has several notable features including the fact that it automatically records TV news and segments a broadcast news program into stories, eliminating advertisements and credits at the start/end of the broadcast. Físchlár-News-Stories supports access to individual stories via calendar lookup, text search through closed captions, automatically-generated links between related stories, and personalised access using a personalisation and recommender system based on collaborative filtering. Access to individual news stories is supported either by browsing keyframes with synchronised closed captions, or by playback of the recorded video. One strength of the Físchlár-News-Stories system is that it is actually used, in practice, daily, to access news. Several aspects of the Físchlár systems have been published before, bit in this paper we give a summary of the Físchlár-News-Stories system in operation by following a scenario in which it is used and also outlining how the underlying system realises the functions it offers

Solitary wave propagation and steering through light-induced refractive potentials

The steering of a self-guided beam in a dye-doped nematic liquid crystal caused by an external illumination (control beam) that induces changes in the refractive index of the medium is theoretically analyzed. The interaction between the control beam and the dye molecules modifies the anchoring of the nematic molecules, so changing the director orientation in the bulk of the medium. Beam evolution is investigated by use of a modulation theory approach. It is found that the beam trajectory is independent of the beam profile, as long as this profile is self-similar. Solutions obtained from the modulation theory approach are in excellent agreement with numerical solutions