Stefano Trillo

Soliton switching in fiber nonlinear directional couplers

We predict all-optical switching of solitons between the two linear modes of a nonlinear coherent coupler made from a dual-core fiber operating in the anomalous dispersion regime.

Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications

We present an overview of nonlinear phenomena related to optical quadratic solitons—intrinsically multicomponent localized states of light, which can exist in media without inversion symmetry at the molecular level. Starting with presentation of a few derivation schemes of basic equations describing three-wave parametric wave mixing in di7ractive and=or dispersive quadratic media, we discuss their continuous wave solutions and modulational instability phenomena, and then move to the classi8cation and stability analysis of the parametric solitary waves. Not limiting ourselves to the simplest spatial and temporal quadratic solitons we also overview results related to the spatio-temporal solitons (light bullets), higher order quadratic solitons, solitons due to competing nonlinearities, dark solitons, gap solitons, cavity solitons and vortices. Special attention is paid to a comprehensive discussion of the recent experimental demonstrations of the parametric solitons including their interactions and switching. We also discuss connections of quadratic solitons with other types of solitons in optics and their interdisciplinary signi8cance. c

Third-order three-wave mixing in single-mode fibers: exact solutions and spatial instability effects

Exact solutions are presented to the steady-state coupled-mode equations that govern the nonlinear parametric interaction of a central-frequency wave with a pair of upshifted and downshifted sidebands in isotropic single-mode optical fibers. This solution accounts for pump depletion as well for as a possible phase mismatch among the waves. The existence is predicted of eigensolutions propagating unchanged along the fiber, which may be either spatially stable or spatially unstable, depending on the total power and the propagation-constant mismatch. The presence of spatially unstable eigensolutions dramatically affects the power exchange among the three waves. The physical implications of this instability for the frequency-conversion process, as well as its potential application to all-optical switching, are discussed.

Experimental observation of polarization instability in a birefringent optical fiber

We present the first experimental demonstration of spatial instability in the nonlinear evolution of the state of polarization of an intense light beam in a birefringent Kerr‐like medium. As the peak power crosses the threshold for the instability, we observed strong intensity‐dependent power transfer between the two counter‐rotating circularly polarized waves propagating along a birefringent optical fiber. The experimental results agree well with the theory.

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.

Dissipative modulation instability in a nonlinear dispersive ring cavity

Abstract We investigate the modulational instability in a synchronously pumped nonlinear dispersive ring cavity. The infinite-dimensional Ikeda map which describes the evolution of the field in the cavity is reduced to a partial derivative equation which allows for analytical developments. We show that, owing to the dissipative nature of the problem, the physics of modulational instability in the ring is fundamentally different from the usual modulational instability in a nonlinear dispersive fiber. In particular, we predict the formation of stable temporal dissipative structures for both the normal and the anomalous dispersion regime of the fiber.

Optical solitary waves induced by cross-phase modulation.

We show that an optical pulse can propagate undistorted as a bright solitary wave in the normal dispersion regime when it couples through cross-phase modulation to a dark pulse in the anomalous dispersion regime.

All-optical signal reshaping via four-wave mixing in optical fibers

A new scheme for all-optical signal reshaping is proposed and demonstrated. The strongly depleted mixing between a CW pump and a noisy nonreturn-to-zero (NRZ) signal in a common fiber can provide wavelength-converted signals exhibiting excellent intensity-noise cancellation. Numerical simulations confirm almost complete suppression of intensity fluctuations, simultaneously occurring at several different wavelengths.

Shocks in nonlocal media

We investigate the formation of collisionless shocks along the spatial profile of a Gaussian laser beam propagating in nonlocal nonlinear media. For defocusing nonlinearity the shock survives the smoothing effect of the nonlocal response, though its dynamics is qualitatively affected by the latter, whereas for focusing nonlinearity it dominates over filamentation. The patterns observed in a thermal defocusing medium are interpreted in the framework of our theory.

Nonlinear nonreciprocity in a coherent mismatched directional coupler

The analytical solution is given for the nonlinear propagation in a linearly mismatched directional coupler taking into account an arbitrary nonuniform nonlinearity. The effect of mismatching which causes nonreciprocal nonlinear switching of the device is analyzed in detail.