Julio Sánchez-Curto

Helmholtz solitons at nonlinear interfaces.

The evolution of Helmholtz solitons at the interface separating two Kerr-type media is described by means of a generalized nonlinear Helmholtz equation. The bright soliton solution for this equation and arbitrary media properties are presented. Numerical simulations show that, when there is only mismatch in the linear refractive index, Helmholtz solitons behave according to Snells law. Also, the general reflection and refraction properties of optical solitons show features that cannot be captured in the paraxial theory.

Dark solitons at nonlinear interfaces

The refraction of dark solitons at a planar boundary separating two defocusing Kerr media is simulated and analyzed, for the first time (to our knowledge). Analysis is based on the nonlinear Helmholtz equation and is thus valid for any angle of incidence. A new law, governing refraction of black solitons, is combined with one describing bright soliton refraction to yield a generalized Snells law whose validity is verified numerically. The complexity of gray soliton refraction is also analyzed, and illustrated by a change from external to internal refraction on varying the soliton contrast parameter.

Nonlinear interfaces: intrinsically nonparaxial regimes and effects

The behaviour of optical solitons at planar nonlinear boundaries is a problem rich in intrinsically nonparaxial regimes that cannot be fully addressed by theories based on the nonlinear Schrodinger equation. For instance, large propagation angles are typically involved in external refraction at interfaces. Using a recently proposed generalized Snells law for Helmholtz solitons, we analyse two such effects: nonlinear external refraction and total internal reflection at interfaces where internal and external refraction, respectively, would be found in the absence of nonlinearity. The solutions obtained from the full numerical integration of the nonlinear Helmholtz equation show excellent agreement with the theoretical predictions.

Giant Goos–Hänchen shifts and radiation-induced trapping of Helmholtz solitons at nonlinear interfaces

Giant Goos-Hänchen shifts and radiation-induced trapping are studied at the planar boundary separating two focusing Kerr media within the framework of the Helmholtz theory. The analysis, valid for all angles of incidence, reveals that interfaces exhibiting linear external refraction can also accommodate both phenomena. Numerical evidence of these effects is provided, based on analytical predictions derived from a generalized Snells law.

Widely varying giant Goos–Hänchen shifts from Airy beams at nonlinear interfaces

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 Helmholtz equation. We report the existence of nonstandard nonlinear GHSs displaying an extreme sensitivity to the input intensity and the existence of multiple critical values. These intermittent and oscillatory regimes can be explained in terms of competition between critical coupling to a surface mode and soliton emission from the refracted beam component and how this interplay varies with localization of the initial Airy beam.

Helmholtz solitons at nonlinear interfaces

The evolution of Helmholtz solitons at the interface separating two Kerr-type media is described by means of a generalized nonlinear Helmholtz equation. The bright soliton solution for this equation and arbitrary media properties are presented. Numerical simulations show that, when there is only mismatch in the linear refractive index, Helmholtz solitons behave according to Snells law. Also, the general reflection and refraction properties of optical solitons show features that cannot be captured in the paraxial theory.

On the asymptotic evolution of finite energy Airy wave functions.

In general, there is an inverse relation between the degree of localization of a wave function 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 Airy wave packets a simultaneous increase in their localization in the direct and transform domains can be obtained as the apodization parameter is varied. One consequence of this is that the far-field diffraction rate of a finite energy Airy beam decreases as the beam localization at the launch plane increases. We analyze the asymptotic properties of finite energy Airy wave functions using the stationary phase method. We obtain one dominant contribution to the long-term evolution that admits a Gaussian-like approximation, which displays the expected reduction of its broadening rate as the input localization is increased.

On a faster parallel implementation of the split-step Fourier method

A new parallel implementation of the split-step Fourier method is presented. The computational core of our scheme focuses on the parallelization of the whole linear step using a combination of fast cyclic convolutions and fast Fourier transforms. For all problems and cluster sizes tested, our method exhibits better performance than conventional parallel implementations of the split-step Fourier method using state-of-the art parallel fast Fourier transforms.

Efficient parallel implementation of the nonparaxial beam propagation method

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 dependent on a nonparaxiality parameter. Performance tests carried out on different types of parallel systems behave according theoretical predictions and show that our proposal exhibits a better behavior than those solutions based on the use of conventional parallel fast Fourier transform implementations. The application of our design is illustrated in a particularly demanding scenario: the study of dark solitons at interfaces separating two defocusing Kerr media, where it is shown to play a key role.

From Maxwell's equations to new families of Helmholtz solitons

In this presentation, we give an overview of new results in Helmholtz soliton theory. Firstly, fundamental considerations are made in terms of new contexts for Helmholtz solitons that arise directly from Maxwells equations. We will then explore applications involving a variety of different material interfaces and the role of Helmholtz solitons in these configurations. Finally, specific new families of solutions arising from the generalisation of the Manakov equation will be reported.