Snell's laws at the interface between nonlinear dielectrics

An equivalent particle theory is developed which is effective in capturing the global behavior of surface waves at the interface between two nonlinear dielectrics.     

A Nonlinear Electric Model of the Transient Photoelectric Current in an Organic Photodiode

One of the possible causes of the degradation of organic photodiodes is explained in terms of a nonlinear resistance–capacitance model. Electronic switches for switching photodiode parameters when light is turned on and off are used as nonlinear elements in the equivalent circuit. The model treats the photodiode as a spatially localized photovoltage generator loaded on a passive four-terminal device connected with the electrodes through passive interface layers. The presence of passive layers that have areas with oppositely directed built-in pulling electric fields is the main cause of the degradation of photodiode characteristics. The proposed equivalent circuit well reproduces the experimental transient and steady-state processes in organic photodiodes and can be useful both for measuring the electrical parameters of photodiodes and for studying the processes leading to their degradation.     

Localization in the model of contacting media with specific nonlinearity and interface interaction

In this paper, we consider the new model of nonlinear contacting media based on nonlinear Schrodinger equation with point potential and term, which is depended stepwise on field amplitude. Such a model theoretically describes a change in properties of the boundary regions along the interface between a Kerr-type crystal with cubic nonlinearity and a nonlinear medium characterized by abruptly change in dielectric constant depending on field amplitude. The short-range local interaction between wave and interface is taken into account by point potential in nonlinear Schrodinger equation. We obtain two new types of localized states characterized by composite structure consisting of three parts of the field distributions. We find exact and approximate solutions of dispersion equations. We described new properties of the spectrum of localized states arising as a result of the interaction of the wave with the interface and the presence of threshold field of the switching between the medium constants. All results are obtained in an analytical form. The proposed theory can be used to describe the propagation features of intense light beams localized along media interfaces in nonlinear optics, and to describe Bose-Einstein condensates with cubic nonlinearity.     

All-optical transistor action with bistable switching in a photonic crystal cross-waveguide geometry

We demonstrate all-optical switching action in a nonlinear photonic crystal cross-waveguide geometry with instantaneous Kerr nonlinearity, in which the transmission of a signal can be reversibly switched on and off by a control input. Our geometry accomplishes both spatial and spectral separation between the signal and the control in the nonlinear regime. The device occupies a small footprint of a few micrometers squared and requires only a few milliwatts of power at a 10-Gbit/s switching rate by use of Kerr nonlinearity in AlGaAs below half the electronic bandgap. We also show that the switching dynamics, as revealed by both coupled-mode theory and finite-difference time domain simulations, exhibits collective behavior that can be exploited to generate high-contrast logic levels and all-optical memory.     

Interactions and switching of spatial soliton pairs in the vicinity of a nonlinear interface

The interaction of spatial soliton pairs with a nonlinear interface was studied theoretically. With mediation of the interface, the two solitons exhibited efficient switching and double switching. A closed-form particlelike model, validated by propagation calculations, yielded the soliton trajectories and switching characteristics.     

Theoretical study of reorientation and torque of liquid crystal molecules under influence of external electric field and experimentally generation of spatial optical soliton beam and getting a sharp switching in chiral nematic liquid crystal

Liquid crystals (LC) are anisotropic materials which experience a torque if an electric field is present. This field can be due to an external voltage or to the presence of a light beam. Reorientation due to light leads to non-linear behavior in the optical behavior. Due to this kind of nonlinearity therefore it is possible to generate optical spatial soliton beam in LC by bias voltage or without it and interestingly chiral nematic liquid crystals has a opportunity to generate spatial optical solitons without the need for a bias voltage. In this paper we also demonstrate that a sharp switching of the helix structure occurs when the spatial soliton is launched in the middle of two regions where soliton generation is favorable. Due to the optical nonlinearity, the helical structure becomes asymmetric and a sharp switching in one direction can be obtained. Moreover, in this paper, the torque and reorientation of the liquid crystal and the change in angular momentum of the light are discussed.     

Distributed optimization for discrete-time multiagent systems with nonconvex control input constraints and switching topologies

This paper addresses the distributed optimization problem of discrete-time multiagent systems with nonconvex control input constraints and switching topologies. We introduce a novel distributed optimization algorithm with a switching mechanism to guarantee that all agents eventually converge to an optimal solution point, while their control inputs are constrained in their own nonconvex region. It is worth noting that the mechanism is performed to tackle the coexistence of the nonconvex constraint operator and the optimization gradient term. Based on the dynamic transformation technique, the original nonlinear dynamic system is transformed into an equivalent one with a nonlinear error term. By utilizing the nonnegative matrix theory, it is shown that the optimization problem can be solved when the union of switching communication graphs is jointly strongly connected. Finally, a numerical simulation example is used to demonstrate the acquired theoretical results.     

Application of the mutual-interaction method to a class of two-scatterer systems: II. Scatterer near an interface

This paper applies the methodology developed in Part I to the problem of a separable scatterer near a dielectric (penetrable) or perfectly conducting (impenetrable) interface. For a penetrable interface, the scatterer may be on either side of the interface (exposed or embedded). As in Part I, the scatterer may also be an active element. Thus, our solutions extend the classic treatments of dipoles radiating near a planar dielectric interface. The mutual-interaction method accommodates a uniform half-space as an equivalent scattering plate of zero thickness that preserves amplitudes and phases of the transmitted and reflected waves. Because this scattering function necessarily includes a Dirac delta function, exact analytic solutions are possible for the class of separable scatterers, which include isotropic scatterers and electric or magnetic dipoles. The results can be interpreted within the context of image theory. Integrals similar to those derived by Sommerfeld must be evaluated to calculate the spatial fields for dielectric media; however, for highly conducting media good approximations are readily obtained.     

Application of the mutual-interaction method to a class of two-scatterer systems: II. Scatterer near an interface

Abstract

This paper applies the methodology developed in Part I to the problem of a separable scatterer near a dielectric (penetrable) or perfectly conducting (impenetrable) interface. For a penetrable interface, the scatterer may be on either side of the interface (exposed or embedded). As in Part I, the scatterer may also be an active element. Thus, our solutions extend the classic treatments of dipoles radiating near a planar dielectric interface. The mutual-interaction method accommodates a uniform half-space as an equivalent scattering plate of zero thickness that preserves amplitudes and phases of the transmitted and reflected waves. Because this scattering function necessarily includes a Dirac delta function, exact analytic solutions are possible for the class of separable scatterers, which include isotropic scatterers and electric or magnetic dipoles. The results can be interpreted within the context of image theory. Integrals similar to those derived by Sommerfeld must be evaluated to calculate the spatial fields for dielectric media; however, for highly conducting media good approximations are readily obtained.     

Surface plasmon-assisted optical switching/bistability at telecommunication wavelengths in nonlinear dielectric gratings

In this paper, we numerically investigate nonlinear optical responses in dielectric gratings coated by flat metallic surface, where the structural parameters are chosen for wavelengths of operation at the telecom regime. The presented designs show the output light reflection with respect to the incident intensity of increasing, decreasing, and non-monotonic belt-shape functions. Nonlinear optical responses including switching and bistability appeared in the telecom region owing to assistance of surface plasmon resonance excited at the metal/dielectric interface, which enhances the diffraction efficiency and induces the momentum matching for the leaky modes of the dielectric grating. This results in electric intensity-effective refractive index dependence enhancement in the Kerr nonlinear media. Our design and investigation of the linear and nonlinear optical responses will provide a general guideline for a hybrid metallic-dielectric structure-based optical switching/bistability device design.     

All-optical polarization switching based on Bragg-spaced quantum dots layers

One kind of Bragg-spaced all-optical switching has been proposed in this paper, and the quantum dots ensembles are used in it as active layers. By one-dimensional photonic crystal theory and transmission matrix method, we have studied the reflectivity stop band and switching effect based on the ac Stark effect. The reflectivity stop band of this switch can be suppressed or recovered, and the circular dichroism and birefringence are induced by a circle-polarized control light, which result in a significant polarization switching effect. This switching structure shows great advantages of lower requirement of pump light intensity, larger contrast ratio than that of Bragg-spaced quantum wells with the same period, especially this switching can be used at room temperature theoretically. So we predict that there are prodigious prospects for its using in high speed optical communications as all-optical switching.     

Investigations on the Capability of the Statistical Extinction Method for the Determination of Mean Particle Sizes in Concentrated Particle Systems

Due to the fast growing number of processes involving particulate systems, simple and robust measurement techniques which enable an inline monitoring of the particle size and their concentration are urgently required, since this ensures control but also process optimization. In this work, an inline measurement technique based on the statistical extinction method is developed that provides a process monitoring for a wide range of particulate processes, such as dispersion processes and spray processes. The method allows the determination of the mean size and concentration for particle systems with the size larger than 1 µm. For this purpose, a light beam illuminates the particle system, whereby the fluctuating light intensity due to the particle movement through the light beam is detected. The statistical fluctuation of the signal can be related to a mean particle size and a particle concentration. Since concentrated particle systems cause effects that additionally influence the signal, such as multiple scattering, approaches are needed to reduce or eliminate these effects. In this work, an approach using a spatial frequency filter is applied. The experimental investigations reveal that the effects can be significantly reduced with the spatial frequency filter.     

Periodic metal-dielectric interfaces for photonic applications

The photonic bandgap properties of periodic interfaces between noble metals and dielectrics exhibiting third-order optical nonlinearity are investigated. Some device configurations aimed at obtaining all-optical switching around 1500 nm are proposed, based either on the excitation of propagating surface plasmons at a sinusoidally modulated interface or on the back-reflection properties of a sawtooth-modulated metal-dielectric interface under normal incidence of the radiation. In the second case, 35% switching of 15-ps 5-nJ input pulses can be obtained using polydiacetylenes as the nonlinear dielectric.     

Switching Dynamic Analysis for Twin-Core Fibre Coupler Using Supermode Theory

Characteristics of optical switching in a twin-core fibre coupler are numerically analysed under short pulse input by using supermode theory. The dynamic nonlinear coupled superlnode equations are derived, The numerical results show that the input pulse width determines the power transfer and the pulse temporal profile in the output ports. The optimal switching characteristics can be obtained by selecting an appropriate initial pulse width. In addition, the switching characteristic curves are insensitive to the input pulse shape for either fundamental soliton pulse or Gaussian pulse input, but sensitive to pulse sharpness. A reduced switching power and a sharper switching transition can be obtained by using the sharp super-Gaussian pulse.     

Excitation of localized spatial structures of different symmetry in a system of two thin films

We consider spatial dissipative solitons arising in the system of two nonlinear thin films which interact resonantly with light. Symmetric and nonsymmetric solitons and methods of their exciting and switching are studied.     

Nonlinear evolution equations for surface plasmons for nano-focusing at a Kerr/metallic interface and tapered waveguide

Maxwell's equations for a metallic and nonlinear Kerr interface waveguide at the nanoscale can be approximated to a (1+1) D Nonlinear Schrodinger type model equation (NLSE) with appropriate assumptions and approximations. Theoretically, without losses or perturbations spatial plasmon solitons profiles are easily produced. However, with losses, the amplitude or beam profile is no longer stationary and adiabatic parameters have to be considered to understand propagation. For this model, adiabatic parameters are calculated considering losses resulting in linear differential coupled integral equations with constant definite integral coefficients not dependent on the transverse and longitudinal coordinates. Furthermore, by considering another configuration, a waveguide that is an M–NL–M (metal–nonlinear Kerr–metal) that tapers, the tapering can balance the loss experienced at a non-tapered metal/nonlinear Kerr interface causing attenuation of the beam profile, so these spatial plasmon solitons can be produced. In this paper taking into consideration the (1+1)D NLSE model for a tapered waveguide, we derive a one soliton solution based on He's Semi-Inverse Variational Principle (HPV).     

Demonstration of an all-optical switching operation using an optical fiber grating coupler

An optical fiber grating coupler (FGC) is a fused optical fiber coupler with a tapered region in which refractive index-modulated gratings are written. In the FGC, the light with specific wavelength satisfying the Bragg condition of the grating can be dropped to one output port and other lights are transmitted to another output port when lights with various wavelengths are launched into the input port. The FGC can operate as an all-optical switch by controlling the Bragg wavelength of the grating using a third order nonlinear optical effect caused by a control light that are launched with a signal light. In this paper, an all-optical switching operation due to a third order nonlinear optical effect in an FGC is first demonstrated for a signal light with 1.55 μm-wavelength to be changed from one port of the FGC to another one by the 720 W peak of a control light from a Nd:YAG laser with 1.06 μm-wavelength. The switching efficiency obtained was 7%. It was clarified that a longer pulse length of the control light compared to the grating length is required to obtain a large Bragg wavelength shift for the switching. It was also clarified that the Bragg wavelength shift is caused by a third order nonlinear effect and a photothermal effect. A contribution of the photothermal effect was estimated. We also estimated the switching efficiency for pump power in the FGC switch.     

Hydrodynamics and Platoon Formation for a Totally Asymmetric Exclusion Model with Particlewise Disorder

We consider a one-dimensional totally asymmetric exclusion model with quenched random jump rates associated with the particles, and an equivalent interface growth process on the square lattice. We obtain rigorous limit theorems for the shape of the interface, the motion of a tagged particle, and the macroscopic density profile on the hydrodynamic scale. The theorems are valid under almost every realization of the disordered rates. Under suitable conditions on the distribution of jump rates the model displays a disorder-dominated low-density phase where spatial inhomogeneities develop below the hydrodynamic resolution. The macroscopic signature of the phase transition is a density discontinuity at the front of the rarefaction wave moving out of an initial step-function profile. Numerical simulations of the density fluctuations ahead of the front suggest slow convergence to the predictions of a deterministic particle model on the real line, which contains only random velocities but no temporal noise.     

Excitation of surface wave beams at the interface between linear and nonlinear media

The spatial evolution of quasi-optical electromagnetic-wave beams propagating in the vicinity of an interface between linear and nonlinear media is studied. It is demonstrated that three-dimensional nonlinear surface beams can efficiently be excited by Gaussian beams of optimal shape, incident onto the nonlinear interface at angles exceeding the total internal reflection angle, and that giant nonlinear Goos-Hänchen effect can result from this process.     

Spatial optical (2+1)‐dimensional scalar‐ and vector‐solitons in saturable nonlinear media

(2+1)‐dimensional optical spatial solitons have become a major field of research in nonlinear physics throughout the last decade due to their potential in adaptive optical communication technologies. With the help of photorefractive crystals that supply the required type of nonlinearity for soliton generation, we are able to demonstrate experimentally the formation, the dynamic properties, and especially the interaction of solitary waves, which were so far only known from general soliton theory. Among the complex interaction scenarios of scalar solitons, we reveal a distinct behavior denoted as anomalous interaction, which is unique in soliton‐supporting systems. Further on, we realize highly parallel, light‐induced waveguide configurations based on photorefractive screening solitons that give rise to technical applications towards waveguide couplers and dividers as well as all‐optical information processing devices where light is controlled by light itself. Finally, we demonstrate the generation, stability and propagation dynamics of multi‐component or vector solitons, multipole transverse optical structures bearing a complex geometry. In analogy to the particle‐light dualism of scalar solitons, various types of vector solitons can ‐ in a broader sense ‐ be interpreted as molecules of light.