Nonlinear photonics with metallic nanostructures on top of dielectrics and waveguides

We review recent experimental and theoretical studies of the ultrafast and nonlinear optical response of metallic nanostructures on top of dielectric substrates and slab waveguides where plasmon hybridization is a key ingredient. In a first three-pulse all-optical control experiment a hybrid plasmonic mode is turned on or off only a few tens of femtoseconds after its excitation. A second experiment concentrates on the origin of the nonlinear response in a metallo-dielectric photonic crystal structure. We show that the shape of the nonlinear optical spectra provides unambiguous information about the nonlinear optical contribution of the metallic as well as the dielectric part of the structure. Furthermore, we discuss the influence of slow-light on the nonlinear response. All experimental results agree perfectly with numerical scattering matrix calculations as well as simulations based on a classical harmonic oscillator model.     

Effect of multiphoton absorption and free carriers in slow-light photonic crystal waveguides

We examine the effects of multiphoton absorption, free carriers, and disorder-induced linear scattering in slow-light photonic crystal waveguides. We derive an analytic formulation for self-phase modulation including the group velocity scaling of the nonlinear phase shift in materials limited by three-photon absorption as a representative nonlinear process. We investigate the role of free carriers and derive an approximate critical intensity at which these effects begin to strongly modify the optical field. This critical intensity is employed to determine an optimal group index for the self-phase modulation in the slow-light devices. These observations are confirmed with numerical modeling.     

Localization of nonlinear excitations in curved waveguides and chains of nonlinear oscillators

It is shown that the interplay of curvature and nonlinearity in systems with finite curvature: bent waveguides, curved chains of nonlinear oscillators, etc can lead to the qualitative effects, such as symmetry breaking of the nonlinear excitations and their trapping by the bending. The finite curvature of the waveguide with infinite hard walls (Dirichlet boundary conditions) provides a stabilizing effect on otherwise unstable localized states of repelling nonlinear Schr?dinger excitations. The number of quanta which the curved waveguide can bind monotonically increases when the radius of curvature decreases. In the waveguides with Neumann boundary conditions at the confining walls the curved region might manifest itself as a two-hump potential barrier with interbarrier space acting as a potential valley. A threshold character of the scattering process, i.e. transmission, trapping, or reflection of the moving nonlinear excitation passing through the bending, is demonstrated.     

Nonlinear wave interactions in patterned Silica and AlGaAs waveguides

We study nonlinear interactions between discrete optical solitons that propagate in different regimes of diffraction, and the nonlinear scattering of dispersive waves by local optical potentials. It is well known in optics that when linear coherent waves meet, they interfere without interactions. Linear waves also scatter through local optical structures not exchanging any power with the guided modes of these structures. As a focusing Kerr nonlinearity is present, such linearly-inhibited phenomena can exist. Our studies are performed in silica and AlGaAs nonlinear waveguides, excited by ultra-short pulses in the near infrared. Presented at 9-th International Workshop on Nonlinear Optics Applications, NOA 2007, May 17–20, 2007, Świnoujście, Poland     

Superfluidity of coherent light in self-focusing nonlinear waveguides

We establish the superfluidity theory of coherent light in waveguides made of nonlinear polar crystals.It is found that the pairing state of photons in a nonlinear polar crystal is the photonic superfluid state.The photon-photon interaction potential is an attractive effective interaction by exchange of virtual optical phonons.In the traveling-wave pairing state of photons,the photon number is conserved,which is similar to the Bose-Einstein condensation(BEC) state of photons.In analogy to the BCS-BEC crossover theory of superconductivity,we derive a set of coupled order parameter and number equations,which determine the solution of the traveling-wave superfluid state of photons.This solution gives the critical velocity of light in a self-focusing nonlinear waveguide.The most important property of the photonic superfluid state is that the system of photon pairs evolves without scattering attenuations.     

Nonlinear theory of soliton-induced waveguides

We develop a nonlinear theory of soliton-induced waveguides that describe a finite-amplitude probe beam guided by a spatial dark soliton in a saturable nonlinear medium. We suggest an effective way to control the interaction of these soliton-induced waveguides and also show that, in sharp contrast with scalar dark solitons, the dark-soliton waveguides can attract each other and even form stationary bound states.     

Interference effect in scattering loss of high-index-contrast planar waveguides caused by boundary reflections

We present theoretical and experimental results on an interference effect caused by boundary reflections on the optical scattering loss in high-index-contrast planar waveguides. Analytical expressions for the polarization-dependent scattering loss are derived using a surface Green's function. For high-index-contrast waveguides of submicrometer dimensions a significant deviation from accepted theory arises, including scattering loss suppression owing to a thin-film interference effect. Our theoretical predictions are confirmed by loss measurements on silicon-on-insulator channel waveguides.     

Scattering from Spatially Localized Chaotic and Disordered Systems

A version of scattering theory that was developed many years ago to treat nuclear scattering processes, has provided a powerful tool to study universality in scattering processes involving open quantum systems with underlying classically chaotic dynamics. Recently, it has been used to make random matrix theory predictions concerning the statistical properties of scattering resonances in mesoscopic electron waveguides and electromagnetic waveguides. We provide a simple derivation of this scattering theory and we compare its predictions to those obtained from an exactly solvable scattering model; and we use it to study the scattering of a particle wave from a random potential. This method may prove useful in distinguishing the effects of chaos from the effects of disorder in real scattering processes.     

Quantum routing of few photons using a nonlinear cavity coupled to two chiral waveguides

We investigate few-photon scattering properties in two one-dimensional waveguides chirally coupled to a nonlinear cavity. The quantum states of scattered few photons are solved analytically via a real-space approach, and the solution indicates the few-photon reflection and transmission properties. When inputting two photons of equal energy to resonate with the cavity, the propagation characteristics of the two photons will be interesting, which is different from the previous anti-bunching effects with a quantum emitter. More importantly, when the total energy of the two incident photons equals the energy of a nonlinear cavity accommodating two photons, influence of the bound state will become larger to result in disappearance of antibunching effect. However, the bound state has no effect on probability of routing to another waveguide.     

Optical vortex solitons and soliton clusters in photonic crystal fibres

We study higher-order nonlinear modes in the form of vortex solitons and soliton clusters propagating in the waveguides created in photonic crystal fibers made of a material with the focusing Kerr nonlinearity. We find numerically different families of such nonlinear modes with a nontrivial topology and study their bifurcations. We also study the soliton stability to propagation. We demonstrate that waveguides in photonic crystal fibers may support a variety of soliton clusters with the symmetries that may differ from the lattice symmetry. We also discuss briefly the case of a dual-core coupler created by two neighboring cores in a photonic crystal fiber and find numerically the profiles of symmetric and asymmetric nonlinear modes.     

Self-Phase modulation in nonlinear 2-D plasma waveguides

Pulse propagation equation of 2-D nonlinear dispersion plasma waveguides is strictly educed from the wave equation. The nonlinear coefficient is defined, simplified and used to assess and compare the nonlinear characteristic of three popular 2-D plasma waveguides: the metal stripe, the V-groove on a metal surface and the triangular metal wedge. SPM (Self-Phase Modulation) of three 2-D plasma waveguides is predicted and discussed. The results indicate that the propagation distance is enough to observe SPM phenomenon in 2-D plasma waveguides. Both V-groove and Ag stripe are suitable for constructing nonlinear optical devices.     

Nanohybrids investigation by waveguide SNOM illumination mode

We demonstrate how optical waveguides can serve as a high resolution illumination source to image hybrid nano-objects in near field optical microscopy. Nanohybrid particles deposited on the surface of glass waveguides are imaged in terms of topography, scattering and fluorescence.     

Theory of nonlinear dispersive waves and selection of the ground state

A theory of time-dependent nonlinear dispersive equations of the Schr?dinger or Gross-Pitaevskii and Hartree type is developed. The short, intermediate and large time behavior is found, by deriving nonlinear master equations (NLME), governing the evolution of the mode powers, and by a novel multitime scale analysis of these equations. The scattering theory is developed and coherent resonance phenomena and associated lifetimes are derived. Applications include Bose-Einstein condensate large time dynamics and nonlinear optical systems. The theory reveals a nonlinear transition phenomenon, "selection of the ground state," and NLME predicts the decay of excited state, with half its energy transferred to the ground state and half to radiation modes. Our results predict the recent experimental observations of Mandelik et al. in nonlinear optical waveguides.     

Scattering at sidewall roughness in photonic crystal slabs

We have simulated the effect of sidewall roughness in photonic-crystallike structures with different vertical refractive-index contrast. We treated the scattering off a sidewall irregularity as a radiating dipole excited by the incident waveguide mode. We show that the loss that is due to this scattering is significantly larger for structures with a low refractive-index contrast (such as GaAs/AlGaAs waveguides) than for structures with a high vertical index contrast (such as silicon-on-insulators and membranes).     

Coherent transport of matter waves

A transport theory for atomic matter waves in low-dimensional waveguides is outlined. The thermal fluctuation spectrum of magnetic near fields leaking out of metallic microstructures is estimated. The corresponding scattering rate for paramagnetic atoms turns out to be quite large in micrometer-sized waveguides (approx. 100 /s). Analytical estimates for the heating and decoherence of a cold atom cloud are given. We finally discuss numerical and analytical results for the scattering from static potential imperfections and the ensuing spatial diffusion process. Received: 17 July 2000 / Published online: 30 November 2000     

屏蔽光伏孤子诱导的非线性光波导

从理论上研究了由一维稳态屏蔽光伏孤子诱导的非线性波导,结果表明在加偏压的光伏光折变晶体中,例如铌酸锂,无论是明孤子还是暗孤子都能诱导出非线性波导.推导出了在一般条件和低振幅条件下探测光束满足的波方程.     

Analysis and design of efficient coupling in photonic crystal circuits

A rigorous analysis and design of efficient coupling from photonic crystal (PhC) waveguides into conventional dielectric waveguides is reported. Closed-form expressions for the reflection and transmission matrices that completely characterize the scattering that occurs at the interface are derived based on an eigenmode expansion technique and a Bloch basis. Analytic expressions are used to analyze the reflection into PhC waveguides. We obtain that negligible reflection can be achieved by choosing a certain interface within a PhC unit cell. Furthermore, analytic expressions are used to design a novel and compact coupler structure in order to achieve high coupling efficiency when broad dielectric waveguides are considered. Thereby, transmission efficiencies near 100 from the fundamental guided Bloch mode into the fundamental waveguide mode are achieved.     

Controlled switching of discrete solitons in waveguide arrays

We suggest an effective method for controlling nonlinear switching in arrays of weakly coupled optical waveguides. We demonstrate digitized switching of a narrow input beam for as many as 11 waveguides in the engineered waveguide arrays.     

Self-trapping of one-dimensional and two-dimensional optical beams and induced waveguides in photorefractive KNbO(3)

We demonstrate self-trapping of one-dimensional and two-dimensional optical beams in a photorefractive KNbO(3) crystal. We study the waveguides induced by the self-trapped beams for prospective applications of tunable nonlinear frequency conversion in soliton-induced waveguides.