Discrete X-wave formation in nonlinear waveguide arrays

Radial Structure of OAM-Carrying Fundamental X-Waves

We investigate the spectral degree of freedom of OAM-carrying localized waves and its influence on their transverse intensity distribution. In particular, we focus our attention on exponentially decaying spectra, which are very tightly connected to fundamental X-waves; we then show how it is possible to structure their transverse intensity distribution, thus creating a radial structure similar to that of Bessel beams.

Spatiotemporal optical dark X solitary waves

We introduce spatiotemporal optical dark X solitary waves of the (2+1)D hyperbolic nonlinear Schrödinger equation (NLSE), which rules wave propagation in a self-focusing and normally dispersive medium. These analytical solutions are derived by exploiting the connection between the NLSE and a well-known equation of hydrodynamics, namely the type II Kadomtsev-Petviashvili (KP-II) equation. As a result, families of shallow water X soliton solutions of the KP-II equation are mapped into optical dark X solitary wave solutions of the NLSE. Numerical simulations show that optical dark X solitary waves may propagate for long distances (tens of nonlinear lengths) before they eventually break up, owing to the modulation instability of the continuous wave background. This finding opens a novel path for the excitation and control of X solitary waves in nonlinear optics.

Effect of Orbital Angular Momentum on Nondiffracting Ultrashort Optical Pulses

We introduce a new class of nondiffracting optical pulses possessing orbital angular momentum. By generalizing the X-wave solution of the Maxwell equation, we discover the coupling between angular momentum and the temporal degrees of freedom of ultrashort pulses. The spatial twist of propagation invariant light pulse turns out to be directly related to the number of optical cycles. Our results may trigger the development of novel multilevel classical and quantum transmission channels free of dispersion and diffraction. They may also find application in the manipulation of nanostructured objects by ultrashort pulses and for novel approaches to the spatiotemporal measurements in ultrafast photonics.

Spectral pulse transformations and phase transitions in quadratic nonlinear waveguide arrays

We study experimentally and numerically the dynamics of a recently found topological phase transition for discrete quadratic solitons with linearly coupled SH waves. We find that, although no stationary states are excited in the experimental situation, the generic feature of the phase transition of the SH is preserved. By utilizing simulations of the coupled mode equations we identify the complex processes leading to the phase transition involving spatial focusing and the generation of new frequency components. These distinct signatures of the dynamic phase transition are also demonstrated experimentally.

Interaction dynamics of X-waves in waveguide arrays

The interaction dynamics of X-waves in an AlGaAs waveguide array is theoretically considered. The nonlinear discrete diffraction dynamics of a waveguide arraymediates the generation of spatio-temporal X-waves from pulsed initial conditions. The interactions between co-propagating and counter-propagating X-waves are studied. For the co-propagating case, the initial phase relation between the X-waves determine the attractive or repulsive behavior of the X-wave interaction. For the counter-propagating case, the collisions between X-waves generate a nonlinear phase-shift. These dynamics show that X-waves interact in a manner similar to solitons.

Nonlinear spectrum broadening of femtosecond laser pulses in photorefractive waveguide arrays

In photorefractive waveguide arrays, the process and extent of spectral broadening of femtosecond laser pulse caused by self-phase modulation are studied theoretically and experimentally. The threshold of self-phase modulation is more than two times larger than the common threshold in a bulk sample, which affects the extent of spectral broadening dramatically. The coupling length and the ratio between the common threshold and the input peak intensity of the femtosecond laser pulse are the two key parameters dominating these phenomena. The experimental results confirm the theoretical expectation.

Spatio-temporal X-wave

We introduce an illumination configuration which is a spatiotemporal analog of a non-diffracting X-wave. By interfering multiple ultrashort converging plane waves, we generate a tight central spot at which a transform limited ultrashort pulse is formed. Outside this tight focus a spatiotemporal speckle field with longer duration and reduced peak power is created. We investigate this spatiotemporal X-wave configuration analytically, numerically, and experimentally demonstrate the effect using two photon excitation fluorescence.

Observation of three-dimensional discrete-continuous x waves in photonic lattices

We report on the generation of three-dimensional discrete X waves in a femtosecond laser-written waveguide array. Our measurements constitute the first experimental observation of temporally localized three-dimensional discrete-continuous entities. The X waves spontaneously emerge from a single-site excitation due to the discrete diffraction of the lattice and the normally dispersive as well as cubically nonlinear properties of the fused silica used as host material.

Tunneling mediated by 2D+1 conical waves in a 1D lattice

The propagation of 2D+1 wave packets in 1D band gap systems shows that the interplay of periodicity and nonlinearity leads to the spontaneous formation of fast and slow conical localized waves. Such nonlinear tunneling has features that differ on the two edges of the band gap and it is characterized by the competition of bullets and nonlinear X waves.

Nonlinear femtosecond pulse reshaping in waveguide arrays

We observe nonlinear pulse reshaping of femtosecond pulses in a waveguide array owing to coupling between waveguides. Amplified pulses from a mode-locked fiber laser are coupled to an AlGaAs core waveguide array structure. The observed power-dependent pulse reshaping agrees with theory, including shortening of the pulse in the central waveguide.