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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 soliton is recovered in the appropriate limit. The physical and mathematical geometry of the non-paraxial soliton is explored through the consideration of dispersion relations, rotational transformations and approximate solutions. We highlight some of the unphysical aspects of the paraxial limit and report modifications to the soliton width, the soliton area and the soliton (phase) period which result from the breakdown of the slowly varying envelope approximation

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We construct combined electric and magnetic field variables which independently represent energy flows in the forward and backward directions respectively, and use these to re-formulate Maxwell's equations. These variables enable us to not only judge the effect and significance of backwardtravelling field components, but also to discard them when appropriate. They thereby have the potential to simplify numerical simulations, leading to potential speed gains of up to 100% over standard FDTD or PSSD simulations. We present results for various illustrative situations, including an example application to second harmonic generation in periodically poled lithium niobate. These field variables are also used to derive both envelope equations useful for narrow-band pulse propagation, and a second order wave equation. Alternative definitions are also presented. Phys. Rev. A72, 063807 (2005) Published as

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We present a comprehensive framework for treating the nonlinear interaction of few-cycle pulses using an envelope description that goes beyond the traditional SVEA method. This is applied to a range of simulations that demonstrate how the effect of a χ (2) nonlinearity differs between the many-cycle and few-cycle cases. Our approach, which includes diffraction, dispersion, multiple fields, and a wide range of nonlinearities, builds upon the work of Brabec

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