Adrian Sheppard

Collisions, steering, and guidance with spatial solitons

By colliding two self-guided beams (solitons), we generate one, two, three, four, or possibly more stable solitons for a broad class of nonlinear material that spans threshold to power-law nonlinearities. This reproduction is shown to depend critically on beam stability, on the standard waveguide parameter V, and on a scaled angular beam separation theta/theta(c). The beams can also annihilate one another or create a stable beam from two unstable beams. Beam steering is possible by differentially changing soliton power or phase. Also, the colliding solitons induce versatile optical devices for the switching and steering of small-signal beams.

Bound-vector solitary waves in isotropic nonlinear dispersive media

On the basis of a simple analysis of the coupled nonlinear Schrodinger equations that govern pulse propagation in isotropic nonlinear dispersive media, we show the existence of a novel class of bound-vector solitary waves. These solitary waves are novel in exhibiting elliptical polarization that varies across the pulse and evolves periodically during propagation while the pulse intensity envelope remains unchanged. Simple physical arguments allow us to understand the existence and the features of these particular solutions.

Polarization domain walls in diffractive or dispersive Kerr media

A novel type of vector dark solitary wave is shown to exist in Kerr materials. These solitary waves consist of localized structures separating adjacent regions (or domains) of different polarization eigenstates of the Kerr medium.

Bimodal counterpropagating spatial solitary-waves

Abstract A simple analysis of the standard coupled nonlinear Schrodinger equations for counterpropagating beams reveals the existence of a new class of spatial solitary waves in Kerr media. These solitary waves are bound states of two counterpropagating fields that constitute the fundamental and second modes of the waveguiding structure they induce. For certain parameters they represent two distinct, parallel self-guided beams. The existence and the features of these particular solutions are explained on the basis of simple physical arguments.

Imaged-based multiscale network modelling of microporosity in carbonates

Abstract Diagenetic changes such as cementation or dissolution have a strong control on carbonate pore structure, and often disconnect the original intergranular pore space. Spatial distribution of submicron porosity (microporosity) that develops in the process, as well as its influence on flow properties, is difficult to image and characterize. Yet, a petrophysically rigorous pore-scale model that accounts for submicron porosity interconnectivity would help in the understanding and development of carbonate reservoirs dominated by microporosity. We present algorithms to geometrically match pore–throat networks from two separate length scales that can be extracted directly from three-dimensional (3D) rock images, or be constructed to match the relevant measured properties. We evaluate the combined influence of cementation and dissolution using a Bentheimer Sandstone sample, as well as image-identified microporosity on flow transport properties in an Estaillades Limestone sample.

Nonparaxiality stabilizes three-dimensional soliton beams in Kerr media.

On the basis of simple physical arguments involving energy flows and power invariants, we show that nonparaxiality stabilizes (1+2D) soliton beams in Kerr media.

The elliptically polarized fundamental vector soliton of isotropic Kerr media

Abstract A bifurcation analysis of the incoherently coupled nonlinear Schrodinger equations describing light propagation in isotropic Kerr media reveals the existence of a continuous family of elliptically polarized vector solitons. The polarization state varies across the profile of the solitons. During propagation the polarization ellipse at each point of the profile rotates at a constant rate depending on the degree of ellipticity of the soliton.

Polarization-domain solitary waves of circular symmetry in Kerr media.

We present a new class of dark circularly symmetric solitary wave in bulk, self-defocusing Kerr media. The waves comprise two orthogonally polarized fields mutually guiding each other and forming separate polarization domains. The stability of these new solutions and the dynamics of related structures are briefly investigated.

Devices written by colliding spatial solitons: a coupled mode theory approach

Abstract The waveguides induced by interacting solitons (both bright and dark) are of great interest as potential all-optical devices. Devices induced by two distinct Kerr solitons are examined and expressions for the soliton separation throughout the interaction are obtained. Linear coupler theory is applied to these new expressions to calculate the behaviour of small signal beams guided by one of the solitons before the collision. In the case of equal signal and pump wavelengths the junctions are shown to exhibit the same remarkable properties observed in recent numerical studies.

Extended modulational instability and new type of solitary wave in coupled nonlinear Schrödinger equations

Abstract We investigate the dynamics of the incoherently coupled nonlinear Schrodinger equations describing the propagation of two waves interacting through a third order nonlinearity. We show that the phenomenon of extended modulational instability induced by incoherent coupling is associated with the existence of a new type of solitary wave. This solitary wave consists of a bound state of two interacting semi-infinite symmetric kink waves.