Band-specific phase engineering for curving and focusing light in waveguide arrays

Band specific design of curved light caustics and focusing in optical waveguide arrays is introduced. Going beyond the discrete, tight-binding model, which we examined recently, we show how the exact band structure and the associated diffraction relations of a periodic waveguide lattice can be exploited to phase-engineer caustics with predetermined convex trajectories or to achieve optimum aberration-free focal spots. We numerically demonstrate the formation of convex caustics involving the excitation of Floquet-Bloch modes within the first or the second band and even multi-band caustics created by the simultaneous excitation of more than one bands. Interference of caustics in abruptly autofocusing or collision scenarios are also examined. The experimental implementation of these ideas should be straightforward since the required input conditions involve phase-only modulation of otherwise simple optical wavefronts. By direct extension to more complex periodic lattices, possibilities open up for band specific curving and focusing of light inside 2D or even 3D photonic crystals

Non-Hermitian control of optical turbulence in systems with fractional dispersion

We show an efficient mechanism to control optical turbulence in systems with different dispersion laws, including parabolic, sub-diffractive, hyper-diffractive or general fractional dispersion. The method is based on the modification of the energy cascade through spatial scales leading to turbulence: a non-Hermitian spatio-temporal periodic potential allows unidirectional coupling between modes in the excitation process. We prove a significant increase and reduction of the energy flow in turbulent states, by either condensing the excitation towards small wave-numbers or affecting the energy transfer towards large wave-number. The study is based on the complex Fractional Ginzburg–Landau equation, a universal model for pattern formation and turbulence in a wide range of systems. The enhancement or reduction of turbulence is indeed dependent on the imposed direction of the energy flow, controlled by the phase shift between the real and imaginary parts of the temporal oscillation of the non-Hermitian potential.Peer ReviewedPostprint (published version

Three-dimensional Gross-Pitaevskii solitary waves in optical lattices: stabilization using the artificial quartic kinetic energy induced by lattice shaking

In this Letter, we show that a three-dimensional Bose-Einstein solitary wave can become stable if the dispersion law is changed from quadratic to quartic. We suggest a way to realize the quartic dispersion, using shaken optical lattices. Estimates show that the resulting solitary waves can occupy as little as $\sim 1/20$-th of the Brillouin zone in each of the three directions and contain as many as $N = 10^{3}$ atoms, thus representing a \textit{fully mobile} macroscopic three-dimensional object.Comment: 8 pages, 1 figure, accepted in Phys. Lett.

Raman Solitons in Nanoscale Optical Waveguides, with Metamaterials, Having Polynomial Law Nonlinearity Using Collective Variables

A mathematical analysis is conducted to illustrate the controllability of the Raman soliton self-frequency shift with polynomial nonlinearity in metamaterials by using collective variable method. The polynomial nonlinearity is due to the expanding nonlinear polarization P NL in a series over the field E up to the seventh order. Gaussian assumption is selected to these pulses on a generalized mode. The numerical simulation of soliton parameter variation is given for the Gaussian pulse parameters

Analysis of Optical Pulse Propagation with ABCD Matrices

We review and extend the analogies between Gaussian pulse propagation and Gaussian beam diffraction. In addition to the well-known parallels between pulse dispersion in optical fiber and CW beam diffraction in free space, we review temporal lenses as a way to describe nonlinearities in the propagation equations, and then introduce further concepts that permit the description of pulse evolution in more complicated systems. These include the temporal equivalent of a spherical dielectric interface, which is used by way of example to derive design parameters used in a recent dispersion-mapped soliton transmission experiment. Our formalism offers a quick, concise and powerful approach to analyzing a variety of linear and nonlinear pulse propagation phenomena in optical fibers.Comment: 10 pages, 2 figures, submitted to PRE (01/01

Dynamical stabilization of matter-wave solitons revisited

We consider dynamical stabilization of Bose-Einstein condensates (BEC) by time-dependent modulation of the scattering length. The problem has been studied before by several methods: Gaussian variational approximation, the method of moments, method of modulated Townes soliton, and the direct averaging of the Gross-Pitaevskii (GP) equation. We summarize these methods and find that the numerically obtained stabilized solution has different configuration than that assumed by the theoretical methods (in particular a phase of the wavefunction is not quadratic with $r$). We show that there is presently no clear evidence for stabilization in a strict sense, because in the numerical experiments only metastable (slowly decaying) solutions have been obtained. In other words, neither numerical nor mathematical evidence for a new kind of soliton solutions have been revealed so far. The existence of the metastable solutions is nevertheless an interesting and complicated phenomenon on its own. We try some non-Gaussian variational trial functions to obtain better predictions for the critical nonlinearity $g_{cr}$ for metastabilization but other dynamical properties of the solutions remain difficult to predict