Slow-light optical bullets in arrays of nonlinear Bragg-grating waveguides

We demonstrate that propagation direction and velocity of optical pulses can be controlled independently in the structures with multiscale modulation of the refractive index in transverse and longitudinal directions. We reveal that, in arrays of waveguides with phase-shifted Bragg gratings, the refraction angle does not depend on the speed of light, allowing for efficient spatial steering of slow light. In this system, both spatial diffraction and temporal dispersion can be designed independently, and we identify the possibility for self-collimation of slow light when spatial diffraction is suppressed for certain propagation directions. We also show that broadening of pulses in space and time can be eliminated in nonlinear media, supporting the formation of slow-light optical bullets that remain localized irrespective of propagation direction.     

Interface discrete light bullets in waveguide arrays

We analyze spatiotemporal light localization at the interface separating two different periodic photonic lattices. We demonstrate the existence of a novel class of continuous-discrete spatiotemporal solitons propagating along the interface, including hybrid staggered-unstaggered discrete light bullets with tails belonging to spectral gaps of different types.     

Shaping and switching of polychromatic light in arrays of periodically curved nonlinear waveguides

We overview our recent theoretical results on spatio-spectral control, diffraction management, and broadband all-optical switching of polychromatic light in periodically curved one and two dimensional arrays of coupled optical waveguides. In particular, we show that polychromatic light beams and patterns produced by white-light and supercontinuum sources can experience wavelength-independent normal, anomalous, or zero diffraction in specially designed structures. We also demonstrate that in the nonlinear regime, it is possible to achieve broadband all-optical switching of polychromatic light in a directional waveguide coupler with special bending of the waveguide axes. Our results suggest novel opportunities for creation of all-optical logical gates and switches which can operate in a very broad frequency region, e.g., covering the entire visible spectrum. Presented at 9-th International Workshop on Nonlinear Optics Applications, NOA 2007, May 17–20, 2007, Świnoujście, Poland     

Elliptic X-shaped light bullets

Elliptic X-shaped light bullets, which are generated as nondiffraction elliptic Bessel-like beams with central humps of elliptical shape during the propagation of asymmetric input ultrashort pulses in normal dispersive quadratic media, are demonstrated to be quite stable against wave-packet breakup due to asymmetric input or anisotropic diffraction. Walking elliptic X-shaped light bullets can be observed without spatial wave-packet breakup for strongly coupled fundamental-wave and second-harmonic ultrashort pulses with nonvanishing group-velocity mismatch.     

Spontaneously generated X-shaped light bullets

We observe the formation of an intense optical wave packet fully localized in all dimensions, i.e., both longitudinally (in time) and in the transverse plane, with an extension of a few tens of fsec and microns, respectively. Our measurements show that the self-trapped wave is an X-shaped light bullet spontaneously generated from a standard laser wave packet via the nonlinear material response (i.e., second-harmonic generation), which extend the soliton concept to a new realm, where the main hump coexists with conical tails which reflect the symmetry of linear dispersion relationship.     

空间诱导产生艾里-贝塞尔光弹研究

利用波动方程,研究了脉冲贝塞尔光束在自由空间传输时的空间诱导群速度色散(SIGVD)效应. 结果表明,三阶SIGVD能使脉冲贝塞尔光束的时域逐渐演化为艾里分布. 由于艾里-贝塞尔光弹是一种新奇的时、空都不扩展的局域波包, 能在光与物质相互作用的很多应用领域发挥作用.因此,本文提出了 通过色散管理技术补偿二阶SIGVD,利用三阶SIGVD在自由空间产生艾里-贝塞尔光弹的方案. 为分析这种光弹的时空传输特性,数值模拟了它在色散介质中的传输情况. 结果表明,这种光弹能在色散介质中保持空域不衍射、时域不色散的稳定传输.     

Spontaneously generated walking X-shaped light bullets

In quadratic nonlinear media with normal dispersion and nonvanishing group velocity mismatch between fundamental wave and second-harmonic pulses, the wave packets of two harmonics can be locked together in propagation in the form of walking X-shaped light bullets. The output wave packets are developed into X-shaped light bullets with significant group delay time due to mutual dragging and significant shifting in spatiotemporal spectrum due to delayed nonlinear phase shift. We also show that spontaneously generated phase-front tilting can balance the dragging force induced by group velocity mismatch and lead to zero-velocity walking X-shaped light bullets.     

Optical light bullets in a pure Kerr medium

We show that small negative fourth-order dispersion can arrest spatiotemporal collapse of ultrashort pulses with anomalous dispersion in a planar waveguide with pure Kerr nonlinearity, resulting in (2 + 1)D optical bullets. Similarly to solitons, these bullets undergo elastic collisions. Since these bullets can self-trap from noisy Gaussian input beams and propagate without any power losses, this result may be used to realize experimentally stable, nondissipative optical bullets.     

Two-dimensional light bullets in an array of carbon nanotubes

The problem of the propagation of two-dimensional solitary electromagnetic waves in an array of carbon nanotubes has been considered. The electromagnetic field and the electron system of carbon nanotubes have been treated on the basis of the Maxwell’s equations and the Boltzmann kinetic equation in the relaxation-time approximation, respectively. The derived effective equation has been analyzed and the state of the electromagnetic field that is localized in two spatial dimensions has been found.     

Few-cycle light bullets created by femtosecond filaments

We report a generic mechanism of light bullet formation during the filamentation of femtosecond pulses. This mechanism is tested for gaseous and dense media. It allows the production of robust, sub-10 fs structures of light with no post-compression stage. By coupling an infrared pump with a seed beam, tunable pulses with durations down to a few femtoseconds can be generated by parametric processes.     

Anomalous Bloch oscillations in arrays of coupled waveguides

Anomalous Bloch oscillations in arrays of coupled waveguides have been investigated using two different approaches: multiple scattering formalism and coupled-mode model. Both approaches are shown to yield identical results. Formulas for the parameters of the coupled-mode model are derived. An analytical expression for the optical beam path is obtained, and the condition for the existence of anomalous Bloch oscillations is found.     

Nonlinear surface waves in arrays of curved waveguides

We study both theoretically and experimentally the nonlinear surface waves at the edge of curved waveguide arrays with a surface defect. We show that the nonlinear coupling between different linear modes supported by the array can lead to beam switching to different output waveguides with increasing of the nonlinearity strength. Our experimental observations are in good agreement with the numerical modelling.     

Acoustical scattering by arrays of cylinders in waveguides

Multiple scattering of acoustic waves in a planar horizontal waveguide by finite-length cylinders is considered. Cylinder height equals the waveguide depth, and both are vertically constrained by the pressure-release boundaries. An analytically exact solution is obtained via normal mode expansion method in conjunction with the concept of the T matrix. The problem is decomposed into an infinite number of two-dimensional multiple scattering problems, modulated by waveguide mode shapes. Examples are presented for an isovelocity waveguide in which the medium is uniform and the waveguide depth is constant. It is found that, in numerical computations, including one or two evanescent modes captures the essence of the evanescent modes. Multiple scattering in the waveguide is compared with the corresponding two-dimensional case. It is concluded that, in low frequencies, the wave patterns in the two cases are very similar, with a shift in the frequency. The similarity diminishes when there are multiple propagating modes. Despite the mode mixing, some key features in the scattering as observed in the two-dimensional problem remain observable in the waveguide case.     

Diffraction engineering in arrays of photonic crystal waveguides

Light propagation in uniform arrays of photonic crystal waveguides is studied. We demonstrate that, in stark contrast to the case of conventional waveguide arrays, diffraction can be tailored both in magnitude and sign by varying only the spacing between adjacent waveguides. Diffraction management in ultracompact arrays of straight photonic crystal waveguides is demonstrated by solving Maxwell's equations through the time-domain finite-element method.     

Semidiscrete composite solitons in arrays of quadratically nonlinear waveguides

We demonstrate that an array of discrete waveguides on a slab substrate, both featuring chi2 nonlinearity, supports stable solitons composed of discrete and continuous components. Two classes of fundamental composite soliton are identified: ones consisting of a discrete fundamental-frequency (FF) component in the waveguide array, coupled to a continuous second-harmonic (SH) component in the slab waveguide, and solitons with an inverted FF/SH structure. Twisted bound states of the fundamental solitons are found, too. In contrast with the usual systems, the intersite-centered fundamental solitons and bound states with the twisted continuous components are stable over almost the entire domain of their existence.     

Spatiotemporal airy light bullets in the linear and nonlinear regimes

We demonstrate the realization of intense Airy-Airy-Airy (Airy(3)) light bullets by combining a spatial Airy beam with an Airy pulse in time. The Airy(3) light bullets belong to a family of linear spatiotemporal wave packets that do not require any specific tuning of the material optical properties for their formation and withstand both diffraction and dispersion during their propagation. We show that the Airy(3) light bullets are robust up to the high intensity regime, since they are capable of healing the nonlinearly induced distortions of their spatiotemporal profile.     

Polarization conversion of light in thin-film waveguides

Polarization conversion in optical waveguides on birefringent substrates is discussed with the aid of a coupled wave model. Structures are described which tolerate large thickness variations (up to 45%) while achieving the phase matching necessary for high conversion efficiency. Polarization conversion is experimentally demonstrated in two such arrangements using ADP substrates and organic polymer films. Conversion efficiencies in excess of 98% have been obtained.     

Discrete diffraction in two-dimensional arrays of coupled waveguides in silica

The propagation of light in 5 x 5 and 7 x 7 cubic lattices of evanescently coupled waveguides is investigated for the first time, to the authors' knowledge. The results reveal ideal discrete diffraction and demonstrate the excellent quality of the waveguide arrays, which were manufactured in fused silica by femtosecond-laser-induced refractive-index modifications.     

Discrete light bullets in two-dimensional photonic lattices: Collision scenarios

We report systematic results of collisions between discrete spatiotemporal optical solitons in two-dimensional photonic lattices. We show that the outcomes of collisions strongly depend on the initial soliton parameters, such as their input amplitudes (energies) and their transverse velocities. Four generic outcomes are identified in the study of collisions between discrete light bullets located in the corner, at the edge, and in the center of the photonic lattice: (a) merger of both low and high amplitude solitons into a single one, at small values of the kick parameter (soliton transverse velocity), (b) spreading of low amplitude solitons at intermediate values of the kick parameter, (c) bouncing of high amplitude solitons at intermediate values of the kick parameter, which is accompanied by a sharp modification of input soliton transverse velocities, and (d) quasi-elastic (symmetric) interactions of both low and high amplitude solitons at large values of the kick parameter.