Dr Graham McDonald's Outputs (169)

Relativistic and pseudorelativistic formulation of nonlinear envelope equations with spatiotemporal dispersion. I. Cubic-quintic systems (2018)
Journal Article

A generic envelope equation is proposed for describing the evolution of scalar pulses in systems with spatiotemporal dispersion and cubic-quintic nonlinearity. Our analysis has application, for instance, in waveguide optics where the physical origin... Read More about Relativistic and pseudorelativistic formulation of nonlinear envelope equations with spatiotemporal dispersion. I. Cubic-quintic systems.

On the asymptotic evolution of finite energy Airy wavefunctions (2015)
Journal Article
Chamorro-Posada, P., Sanchez-Curto, J., Aceves, A., & McDonald, G. (2015). On the asymptotic evolution of finite energy Airy wavefunctions. Optics Letters, 40(12), 2850-2853. https://doi.org/10.1364/OL.40.002850

In general, there is an inverse relation between the degree of localization of a wavefunction of a certain class and its transform representation dictated by the scaling property of the Fourier transform. We report that in the case of finite energy A... Read More about On the asymptotic evolution of finite energy Airy wavefunctions.

Gravitational theoretical development supporting MOND (2013)
Journal Article

Conformal geometry is considered within a general relativistic framework. An invariant distant for proper time is defined and a parallel displacement is applied in the distorted space-time, modifying Einstein’s equation appropriately. A particular so... Read More about Gravitational theoretical development supporting MOND.

Spontaneous optical fractal pattern formation (2005)
Journal Article
Huang, J., & McDonald, G. (2005). Spontaneous optical fractal pattern formation. Physical review letters, 94(17), 174101. https://doi.org/10.1103/PhysRevLett.94.174101

We report, for the first time, spontaneous nonlinear optical spatial fractals. The proposed generic
mechanism employs intrinsic nonlinear dynamics both to generate an initial pattern seed and to fill out
structure across decades of spatial scale. W... Read More about Spontaneous optical fractal pattern formation.

Fractal modes in unstable resonators (1999)
Journal Article
Karman, G., Mcdonald, G., New, G., & Woerdman, J. (1999). Fractal modes in unstable resonators. Nature, 402, 138. https://doi.org/10.1038/45960

One of the simplest optical systems, consisting of two mirrors facing each other to form a resonator, turns out to have a surprising property. Here we show that the peculiar eigenmodes of unstable resonators are fractals, a finding that may lead to... Read More about Fractal modes in unstable resonators.

Relativistic and pseudorelativistic formulation of nonlinear envelope equations with spatiotemporal dispersion. II. Saturable systems (2018)
Journal Article

We consider an envelope equation with space-time symmetry for describing scalar waves in systems with spatiotemporal dispersion and a generic saturable nonlinearity. Exact bright and gray solitons are derived by direct integration methods and coordin... Read More about Relativistic and pseudorelativistic formulation of nonlinear envelope equations with spatiotemporal dispersion. II. Saturable systems.

Spontaneous spatial fractal pattern formation in dispersive systems (2017)
Journal Article

We report spontaneous spatial optical fractal patterns in a ring cavity containing a thin slice of diffusive Kerr-type material. The Turing threshold instability condition is derived through linear analysis, and static patterns are found to be descri... Read More about Spontaneous spatial fractal pattern formation in dispersive systems.

Nonlinear Helmholtz wave refraction & Goos-Hänchen shifts in nonparaxial optics : angles and interfaces, solitons and Snell's law (2015)
Presentation / Conference Contribution

The interaction of self-localized waves with an abrupt interface is a problem of fundamental importance in many branches of physics, engineering, and applied mathematics. Waveguide optics, for instance, is dominated in an essential way by such consid... Read More about Nonlinear Helmholtz wave refraction & Goos-Hänchen shifts in nonparaxial optics : angles and interfaces, solitons and Snell's law.

Unstable resonators with polygon and von Koch-type boundary conditions : virtual source modelling of fractal eigenmodes (2015)
Presentation / Conference Contribution

We will report on our latest research into modelling fractal lasers (linear systems that involve geometrically-unstable resonators with inherent magnification), and propose two new classes of cavity configuration. These devices are of fundamental the... Read More about Unstable resonators with polygon and von Koch-type boundary conditions : virtual source modelling of fractal eigenmodes.

Diffraction of Weierstrass scalar fractal waves by circular apertures : symmetry and patterns, complexity and dimension (2015)
Presentation / Conference Contribution

The diffraction of plane waves from simple hard-edged apertures constitutes a class of boundary value problem that is well understood in optics, at least within the scalar approximation. Similarly, the diffraction of such waves from fractal apertures... Read More about Diffraction of Weierstrass scalar fractal waves by circular apertures : symmetry and patterns, complexity and dimension.

Vector dark solitons in systems with spatiotemporal dispersion and cubic nonlinearity : solutions and stability, transformations and relativity (2015)
Presentation / Conference Contribution

The origin of conventional models for nonlinear optical pulse propagation lies in the ubiquitous slowly-varying envelope approximation (SVEA) accompanied by a Galilean boost to a local-time frame. While such a near-universal procedure typically resul... Read More about Vector dark solitons in systems with spatiotemporal dispersion and cubic nonlinearity : solutions and stability, transformations and relativity.

Diffraction of optical Weierstrass waves by simple apertures : circular symmetry and fractal dimension (2015)
Presentation / Conference Contribution

Multi-Turing instabilities & spontaneous patterns in discrete nonlinear systems : simplicity and complexity, cavities and counterpropagation (2015)
Presentation / Conference Contribution

Alan Turing's profound insight into morphogenesis, published in 1952, has provided the cornerstone for understanding the origin of pattern and form in Nature. When the uniform states of a nonlinear reaction-diffusion system are sufficiently stressed,... Read More about Multi-Turing instabilities & spontaneous patterns in discrete nonlinear systems : simplicity and complexity, cavities and counterpropagation.

Helmholtz non-paraxial beam propagation method: An assessment (2014)
Journal Article

We present a performance evaluation of a non-paraxial beam propagation method suitable for the study of Helmholtz solitons. The analysis aims to determine the accuracy limits of the numerical scheme in terms of the maximum propagation angle addressab... Read More about Helmholtz non-paraxial beam propagation method: An assessment.

Single interfaces and coupled-waveguide arrays: off-axis nonparaxial analyses (2014)
Presentation / Conference Contribution

We report on our most recent results concerning arbitrary-angle spatial soliton
refraction at the interface between dissimilar dielectrics, each of which comprises
both X(3)and X(5) susceptibilities. Attention is also paid to the oblique injectio... Read More about Single interfaces and coupled-waveguide arrays: off-axis nonparaxial analyses.

Efficient parallel implementation of the nonparaxial beam propagation method (2014)
Journal Article
Sanchez-Curto, J., Chamorro-Posada, P., & McDonald, G. (2014). Efficient parallel implementation of the nonparaxial beam propagation method. Parallel Computing, 40(8), 394-407. https://doi.org/10.1016/j.parco.2014.06.003

An efficient parallel implementation of a nonparaxial beam propagation method for the numerical study of the nonlinear Helmholtz equation is presented. Our solution focuses on minimizing communication and computational demands of the method which are... Read More about Efficient parallel implementation of the nonparaxial beam propagation method.

Widely varying giant Goos–Hänchen shifts from airy beams at nonlinear interfaces (2014)
Journal Article
Chamorro-Posada, P., Sánchez-Curto, J., Aceves, A., & McDonald, G. (2014). Widely varying giant Goos–Hänchen shifts from airy beams at nonlinear interfaces. Optics Letters, 39(6), 1378-1381. https://doi.org/10.1364/OL.39.001378

We present a numerical study of the giant Goos–Hänchen shifts (GHSs) obtained from an Airy beam impinging on a nonlinear interface. To avoid any angular restriction associated with the paraxial approximation, the analysis is based on the nonlinear He... Read More about Widely varying giant Goos–Hänchen shifts from airy beams at nonlinear interfaces.

Refraction at interfaces with X(5) nonlinearity: Snell’s law & Goos-Hänchen shifts (2013)
Presentation / Conference Contribution

In this presentation, we give the first detailed overview of spatial soliton refraction at the planar interface between materials whose nonlinear polarization has contributions from both X(3)and X(5)susceptibilities [1]. The governing equation is of... Read More about Refraction at interfaces with X(5) nonlinearity: Snell’s law & Goos-Hänchen shifts.

Diffraction of fractal light: New frontiers for the mathematics of edge waves (2013)
Presentation / Conference Contribution

The diffraction pattern produced by a plane wave (i.e., a perfectly uniform wavefront) scattering from an infinite hard edge is well-described by the Fresnel integral [1]. Such one-dimensional (1D) edge waves [see Fig. 1(a)] turn out to be truly elem... Read More about Diffraction of fractal light: New frontiers for the mathematics of edge waves.

Ultrabroad-band Raman light: Linear detuning & gain suppression (2013)
Presentation / Conference Contribution

Ultrabroad-band multifrequency Raman generation is a (laser-driven) resonant-symmetric two-colour pumping technique for exciting polychromatic light beams that are characterized by potentially very wide “top-hat” temporal bandwidths [1]. The spectra... Read More about Ultrabroad-band Raman light: Linear detuning & gain suppression.