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Exact soliton solutions of the nonlinear Helmholtz equation: communication (2002)
Journal Article
Chamorro-Posada, P., McDonald, G., & New, G. (2002). Exact soliton solutions of the nonlinear Helmholtz equation: communication. Journal of the Optical Society of America B, 19(5), 1216-1217. https://doi.org/10.1364/JOSAB.19.001216

Exact analytical soliton solutions of the nonlinear Helmholtz equation are reported. A lucid generalization of paraxial soliton theory that incorporates nonparaxial effects is found.

Diffractive origin of fractal resonator modes (2001)
Journal Article
New, G., Yates, M., Woerdman, J., & Mcdonald, G. (2001). Diffractive origin of fractal resonator modes. Optics Communications, 193(1-6), 261-266. https://doi.org/10.1016/S0030-4018%2801%2901237-8

The modes of unstable optical resonators possess fractal character. In this paper, the fundamental question of how and why fractals originate in one of the simplest linear optical systems is addressed. The answer is related to the fact that unstabl... Read More about Diffractive origin of fractal resonator modes.

Non-paraxial beam propagation methods (2001)
Journal Article
Chamorro-Posada, P., Mcdonald, G., & New, G. (2001). Non-paraxial beam propagation methods. Optics Communications, 192(1-2), 1-12. https://doi.org/10.1016/S0030-4018%2801%2901171-3

Exact analytical results are employed in the testing of split-step and finite difference approaches to the numerical solution of the non-paraxial non-linear Schrodinger equation. It is shown that conventional split-step schemes can lead to spurious o... Read More about Non-paraxial beam propagation methods.

Transverse effects in multifrequency Raman generation (2000)
Journal Article
Syed, K., Mcdonald, G., & New, G. (2000). Transverse effects in multifrequency Raman generation. Journal of the Optical Society of America B, 17(8), 1366-1375. https://doi.org/10.1364/JOSAB.17.001366

The theory of ultrabroadband multifrequency Raman generation is extended, for the first time, to allow for beam-propagation effects in one and two transverse dimensions. We show that a complex transverse structure develops even when diffraction is ne... Read More about Transverse effects in multifrequency Raman generation.

Kaleidoscope laser (2000)
Journal Article
Mcdonald, G., Karman, G., New, G., & Woerdman, J. (2000). Kaleidoscope laser. Journal of the Optical Society of America B, 17(4), 524-529. https://doi.org/10.1364/JOSAB.17.000524

We report the first calculations of mode patterns of unstable-cavity lasers with truly two-dimensional transverse geometries. A detailed account of numerical techniques, incorporating a nonorthogonal beam-propagation method, and results for cavities... Read More about Kaleidoscope laser.

Propagation properties of nonparaxial spatial solitons (2000)
Journal Article
Chamorro-Posada, P., Mcdonald, G., & New, G. (2000). Propagation properties of nonparaxial spatial solitons. Journal of Modern Optics, 47(11), 1877-1886. https://doi.org/10.1080/09500340008232440

We present an analysis and simulation of the non-paraxial nonlinear Schroedinger equation. Exact general relations describing energy flow conservation and transformation invariance are reported, and then explained on physical grounds. New instabiliti... Read More about Propagation properties of nonparaxial spatial solitons.

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.

Excess noise in low Fresnel number unstable resonators (1999)
Journal Article
Mcdonald, G., New, G., & Woerdman, J. (1999). Excess noise in low Fresnel number unstable resonators. Optics Communications, 164(4-6), 285-295. https://doi.org/10.1016/S0030-4018%2899%2900194-7

Numerical calculations of excess noise factors in low Fresnel number unstable resonators are described in detail. Computed mode profiles in one transverse dimension together with associated Petermann K-factors are presented; dynamical considerations... Read More about Excess noise in low Fresnel number unstable resonators.

Fast algorithm for studying the evolution of optical solitons under perturbations (1999)
Journal Article
Chamorro-Posada, P., Mcdonald, G., New, G., & Fraile-Pelaez, F. (1999). Fast algorithm for studying the evolution of optical solitons under perturbations. IEEE Transactions on Magnetics, 35(3), 1558-1561. https://doi.org/10.1109/20.767268

A numerical algorithm is proposed for computing the eigenvalues of the linear scattering problem associated with the nonlinear Schrodinger equation. The numerical method allows a fast calculation of the dynamical evolution of the properties of optica... Read More about Fast algorithm for studying the evolution of optical solitons under perturbations.

Excess-noise dependence on intracavity aperture shape (1999)
Journal Article
Karman, G., Mcdonald, G., Woerdman, J., & New, G. (1999). Excess-noise dependence on intracavity aperture shape. Applied Optics, 38(33), 6874-6878. https://doi.org/10.1364/AO.38.006874

In lasers with nonorthogonal eigenmodes the excess-noise factor K can be large, especially in unstable-cavity lasers with hard-edged intracavity apertures. To the best of our knowledge, we report the first detailed study of the dependence of K on ape... Read More about Excess-noise dependence on intracavity aperture shape.

Non-paraxial solitons (1998)
Journal Article
Chamorro-Posada, P., Mcdonald, G., & New, G. (1998). Non-paraxial solitons. Journal of Modern Optics, 45(6), 1111-1121. https://doi.org/10.1080/09500349808230902

In this paper, we propose the use of ultranarrow soliton beams in miniaturized nonlinear optical devices. We derive a nonparaxial nonlinear Schrödinger equation and show that it has an exact non-paraxial soliton solution from which the paraxial solit... Read More about Non-paraxial solitons.

Nonlinear competing processes in multifrequency Raman generation (1998)
Journal Article
Mcdonald, G., Chan, Y., New, G., Losev, L., & Lutsenko, A. (1998). Nonlinear competing processes in multifrequency Raman generation. Journal of Modern Optics, 45(6), 1099-1110. https://doi.org/10.1080/09500349808230901

We investigate the extent to which the Raman generation of ultrabroad-band light will be affected by nonlinear competing processes. The model equations are generalized to incorporate an off-axis competing signal and a quantitative study is undertaken... Read More about Nonlinear competing processes in multifrequency Raman generation.

On the generation of ultra-broad bandwidth light in air at atmospheric pressure (1997)
Journal Article
atmospheric pressure. Journal of Physics B: Atomic, Molecular and Optical Physics, 30(21), L719-L725. https://doi.org/10.1088/0953-4075/30/21/002

We predict that ultra-broadband light consisting of over 150 distinct frequencies of comparable energy can be generated in air at atmospheric pressure by stimulated Raman scattering using resonant symmetric pumping. Nanosecond input pulses and the hi... Read More about On the generation of ultra-broad bandwidth light in air at atmospheric pressure.

Nondiffracting beams: travelling, standing, rotating and spiral waves (1996)
Journal Article
Chávez-Cerda, S., Mcdonald, G., & New, G. (1996). Nondiffracting beams: travelling, standing, rotating and spiral waves. Optics Communications, 123(1-3), 225-233. https://doi.org/10.1016/0030-4018%2895%2900538-2

A reformulation of nondiffracting beams, based on more general (travelling wave) solutions of the nonparaxial wave equation, is presented. Zero order nondiffracting beams are found to be radial standing waves arising from counterpropagating zero orde... Read More about Nondiffracting beams: travelling, standing, rotating and spiral waves.

Ultrabroad-bandwidth multifrequency Raman soliton pulse trains (1995)
Journal Article
McDonald, G. (1995). Ultrabroad-bandwidth multifrequency Raman soliton pulse trains. Optics Letters, 20(8), 822-824. https://doi.org/10.1364/OL.20.000822

I have discovered that in the coherent regime of ultrabroad-bandwidth Raman generation, a large number of long-lived soliton pulse trains are spontaneously generated. This novel solution of the dispersionless and highly transient regime, involving mo... Read More about Ultrabroad-bandwidth multifrequency Raman soliton pulse trains.

Ultrabroad-bandwidth multifrequency Raman generation (1994)
Journal Article
Mcdonald, G., New, G., Losev, L., Lutsenko, A., & Shaw, M. (1994). Ultrabroad-bandwidth multifrequency Raman generation. Optics Letters, 19(18), 1400-1402. https://doi.org/10.1364/OL.19.001400

We report on the modeling of transient stimulated rotational Raman scattering in H2 gas. We predict a multifrequency output, spanning a bandwidth greater than the pump frequency, that may be generated without any significant delay with respect to the... Read More about Ultrabroad-bandwidth multifrequency Raman generation.

Pattern formation in a passive Kerr cavity (1994)
Journal Article
Scroggie, A., Firth, W., Mcdonald, G., Tlidi, M., Lefever, R., & Lugiato, L. (1994). Pattern formation in a passive Kerr cavity. Chaos, Solitons and Fractals, 4(8-9), 1323-1354. https://doi.org/10.1016/0960-0779%2894%2990084-1

Analytical and numerical investigations of a cavity containing a Kerr medium are reported. The mean field equation with plane-wave excitation and diffraction is assumed. Stable hexagons are dominant close to threshold for a self-focusing medium. B... Read More about Pattern formation in a passive Kerr cavity.

Switching dynamics of spatial solitary wave pixels (1993)
Journal Article
Mcdonald, G., & Firth, W. (1993). Switching dynamics of spatial solitary wave pixels. Journal of the Optical Society of America B, 10(6), 1081-1089. https://doi.org/10.1364/JOSAB.10.001081

Separatrices and scaling laws in the switching dynamics of spatial solitary wave pixels are investigated. We show that the dynamics in the full model are similar to those in the plane-wave limit. Switching features may be indicated and explained by t... Read More about Switching dynamics of spatial solitary wave pixels.

Self-sustained modelocking using induced nonlinear birefringence in optical fibres (1993)
Journal Article
Langridge, P., Mcdonald, G., Firth, W., & Wabnitz, S. (1993). Self-sustained modelocking using induced nonlinear birefringence in optical fibres. Optics Communications, 97(3-4), 178-182. https://doi.org/10.1016/0030-4018%2893%2990136-S

A numerical study of self-sustained mode locking due to optically induced nonlinear birefringence is presented. The model incorporates a polarizer, a gain medium, a half-wave plate and a single-mode passive fibre in a ring cavity configuration. The... Read More about Self-sustained modelocking using induced nonlinear birefringence in optical fibres.