Ole Bang

Exploiting discreteness for switching in waveguide arrays

A new approach to multiport switching in arrays of nonlinear waveguides is proposed. Whereas other schemes have relied on suppressing the inherent transverse discreteness of these arrays, this approach takes advantage of that feature. One of the effects of discreteness is to keep intense beams trapped in a single waveguide for the length of the array. Switching may be achieved by use of a controlled perturbation to displace such a trapped beam in the transverse direction. This displacement is quantized to an integer number of waveguides, thus permitting unambiguous selection of the output channel.

Dynamical equations for wave packets in materials with both quadratic and cubic response

The dynamical equations that govern the interaction between a weakly modulated plane wave and its second harmonic are derived for materials with asymmetric crystal structure, in which the effects of both the quadratic and the cubic nonlinear susceptibility tensors must be considered. Unlike in the case of pure quadratic nonlinearity, the equations for wave packets that describe temporal and spatial solitary waves do not have the same form unless the crystal structure of the material is nearly centrosymmetric, such that the lowest-order quadratic and cubic nonlinear terms balance. For lossless materials and nonresonant conditions the Hamiltonian structure of the equations is discussed, conserved quantities described, and a stable one-parameter family of bright ground-state solitary wave solutions found numerically for fixed material parameters.

Nonlinear phase shift and all-optical switching in quasi-phase-matched quadratic media.

Recently it was shown that in quasi-phase-matched quadratic media the average intensities are subject to an induced Kerr effect. We analytically study the influence of this induced cubic nonlinearity on the amplitude and phase modulation of the fundamental wave and predict efficient all-optical switching.

Bright spatial solitons in defocusing Kerr media supported by cascaded nonlinearities

We show that resonant wave mixing that is due to quadratic nonlinearity can support stable bright spatial solitons, even in the most counterintuitive case of a bulk medium with defocusing Kerr nonlinearity. We analyze the structure and stability of such self-guided beams and demonstrate that they can be generated from a Gaussian input beam, provided that its power is above a certain threshold.

Exploiting Discreteness for Switching in Arrays of Nonlinear Waveguides

A new approach to multiport switching in arrays of nonlinear waveguides is proposed. While other schemes have relied on suppressing the inherent transverse discreteness, this approach takes advantage of this feature of the array. One of the effects of discreteness is to keep intense beams trapped in a single waveguide for the length of the array. Switching may be achieved by using a controlled perturbation to displace such a trapped beam in the transverse direction. This displacement is quantized to an integer number of waveguides, thus allowing unambiguous selection of the output channel.

Wave collapse in bulk media with quadratic and cubic responses

The mutual influence of quadratic and cubic nonlinearities on the propagation of coupled fundamental and second harmonic waves in optical media is studied. Particular attention is paid to the self-focusing of CW Gaussian beams in bulk media. Such beams are found to self-focus until collapse, whenever their power exceeds a threshold value. We determine this threshold power and find its dependence on the strength of the quadratic and cubic nonlinearities and on the phase mismatch.

Effect of a fluctuating phase mismatch on spatial solitons in quadratic media.

We investigate the evolution of self-guided beams in a chi((2)) medium with a fluctuating phase mismatch between the fundamental wave and its second harmonic, as may occur in particular when the quasi-phase-matching technique is applied. We show that the fluctuations reduce the phase correlation and act as an effective loss to solitary waves.

Robustness of quadratic solitons with periodic gain

We address the robustness of quadratic solitons with periodic non-conservative perturbations. We find the evolution equations for guiding-center solitons under conditions for second-harmonic generation in the presence of periodic multi-band loss and gain. Under proper conditions, a robust guiding-center soliton formation is revealed.

Large amplitude spatial fluctuations in the boundary region of the Bose–Einstein condensate in the Gross–Pitaevskii régime

The Gross–Pitaevskii regime of a Bose–Einstein condensate is investigated using a fully non-linear approach. The confining potential first adopted is that of a linear ramp. An infinite class of new analytical solutions of this linear ramp potential approximation to the Gross–Pitaevskii equation is found which are characterised by pronounced large-amplitude oscillations close to the boundary of the condensate. The limiting case within this class is a nodeless ground state which is known from recent investigations as an extension of the Thomas–Fermi approximation. We have found the energies of the oscillatory states to lie above the ground state energy but recent experimental work, especially on spatially confined superconductors, indicates that such states may be easily occupied and made manifest at finite temperatures. We have also investigated their stability using a Poincare section analysis as well as a linear perturbation approach. Both these techniques demonstrate stability against small perturbations. Finally, we have discussed the relevance of these quasi-one-dimensional solutions in the context of the fully three-dimensional condensates. This has been argued on the basis of numerical work and asymptotic approximations.

Multi-component optical solitary waves

We discuss several novel types of multi-component (temporal and spatial) envelope solitary waves that appear in fiber and waveguide nonlinear optics. In particular, we describe multi-channel solitary waves in bit-parallel-wavelength fiber transmission systems for high-performance computer networks, multi-color parametric spatial solitary waves due to cascaded nonlinearities of quadratic materials, and quasiperiodic envelope solitons due to quasi-phase-matching in Fibonacci optical superlattices.