Frequency shifting with local nonlinearity management in nonuniformly poled quadratic nonlinear materials

We show theoretically that the frequency shifts that result from phase-mismatched cascaded processes under conditions of strong group-velocity mismatch can be significantly enhanced by local control of the nonlinearity with propagation. This control is possible with continuous variation of the poling period of quasi-phase-matched structures and can allow one to avoid saturation of the frequency shift. We theoretically demonstrate its applicability to high-quality, efficient frequency shifting of infrared pulses.     

Soliton emission at a phase-mismatch boundary in a quadratic nonlinear film waveguide

We report the experimental demonstration of spatial nonlinear beam displacement caused by an interface between periodically modulated and uniform quadratic nonlinearity. We observe intensity- and phase-mismatch-dependent spatial beam displacement at 1548 nm in lithium niobate waveguides. The device has the potential to provide a soliton-emission-based, ultrafast all-optical switch.     

Phase transitions of nonlinear waves in quadratic waveguide arrays

We study two-color parametric nonlinear modes in waveguide arrays with a quadratic nonlinear response. We predict theoretically and observe experimentally a new type of phase transition manifested in an abrupt power-controlled change of the mode structure from unstaggered to staggered, due to the interplay of localization and synchronization in parametrically driven discrete systems.     

Polymer-based microcavity with photoencoded quadratic nonlinearity

Functional electro-optic polymer thin films embedded in microcavity structures have been poled by an all-optical procedure based on the interference of multiphoton absorption processes. The photoinduced X((2)) tensor was then further addressed at modal resonance for the fundamental wavelength, leading to significant enhancement of the second-harmonic-generation efficiency. An order-of-magnitude enhancement, which is due to electric field resonant conditions inside the microcavity, has been probed by an optical parametric oscillator, in comparison with a single-path thin-film configuration. This configuration opens new perspectives in the realm of nonlinear photonic device processing.     

Propagation of electromagnetic waves in a waveguide with a modulated anisotropic insert

The propagation of transverse electric (TE) and transverse magnetic (TM) waves in a waveguide of arbitrary cross section with an anisotropic periodically space-and time-modulated insert is considered. Under the assumption that the modulation indices are small, analytical expressions for the TE and TM fields in the domain of weak interaction between the signal wave and modulating wave are derived. The frequency near which strong interaction between these waves occurs is found, and specific features of the fields in this domain are revealed.     

Gap soliton in a waveguide array with a saturating defocusing nonlinearity

We investigate radiation of the solitary waves in the first band gap of the waveguide array with a defocusing nonlinearities of different types (Kerr nonlinearity and saturating nonlinearity). We confirm recent findings that gap solitons (GSs) are unstable for their eigenfrequencies around the middle of the band gap for Kerr nonlinearity. The instability is mediated by four-wave mixing process and appears in the form of radiation of solitons into mode continua of the upper and lower bands. We find that this soliton radiation is reduced (and even suppressed completely) in case of a saturating nonlinearity, resulting in substantial stabilization of the GSs.     

Discrete soliton collisions in a waveguide array with saturable nonlinearity

We study the symmetric collisions of two mobile breathers/solitons in a model for coupled wave guides with a saturable nonlinearity. The saturability allows the existence of mobile breathers with high power. Three main regimes are observed: breather fusion, breather reflection and breather creation. The last regime seems to be exclusive of systems with a saturable nonlinearity, and has been previously observed in continuous models. In some cases a “symmetry breaking” can be observed, which we show to be an numerical artifact.     

Molecules with a permanent dipole moment in a periodic medium with quadratic nonlinearity

Nonlinear optical effects in a one-dimensional periodic medium containing spatially oriented molecules of J aggregates of a dye and silver nanoparticles are studied. It is shown that, in such composite medium, the presence of a permanent dipole moment of an exciton transition of molecules of J aggregates results in the appearance of new nonlinear optical properties.     

Traveling waves in a nonlinear medium with cubic nonlinearity

Unlike linear nondispersive media, which allow propagation of wave packets of arbitrary forms, nonlinear media admit only certain profiles of traveling waves. Here we examine media with Duffing oscillators, i.e., with bound electrons for which an equilibrium disturbance causes forces proportional to the first and third powers of deviation. We show that the linearly polarized traveling plane waves such media can transmit have profiles modulated as Jacobi elliptic functions. When discussing propagation across an interface between different media, only incidence from the side of the linear medium is considered. Even in this case, to launch a traveling wave in the nonlinear medium, a severe restriction must be imposed on the incident wave’s amplitude.     

Localized polaritons and second-harmonic generation in a resonant medium with quadratic nonlinearity

We derive model equations for the propagation of ultrashort pulses in materials with resonant linear and quadratic nonlinear responses and find approximate soliton solutions describing all-bright and dark-bright polaritons. We report the specific phase matching condition for efficient 2nd harmonic generation, which involves detuning from the resonance. We also demonstrate that the 2nd harmonic emission by the polaritonic pulses can lead to reduction of their group velocity, having zero as a theoretical limit. Our analytical results are supported by numerical simulations.     

Accumulation of embedded solitons in systems with quadratic nonlinearity

Previous numerical studies have revealed the existence of embedded solitons (ESs) in a class of multiwave systems with quadratic nonlinearity, families of which seem to emerge from a critical point in the parameter space, where the zero solution has a fourfold zero eigenvalue. In this paper, the existence of such solutions is studied in a three-wave model. An appropriate rescaling casts the system in a normal form, which is universal for models supporting ESs through quadratic nonlinearities. The normal-form system contains a single irreducible parameter epsilon, and is tantamount to the basic model of type-I second-harmonic generation. An analytical approximation of Wentzel-Kramers-Brillouin type yields an asymptotic formula for the distribution of discrete values of epsilon at which the ESs exist. Comparison with numerical results shows that the asymptotic formula yields an exact value of the scaling index, -65, and a fairly good approximation for the numerical factor in front of the scaling term.     

Families of spatial solitons in a two-channel waveguide with the cubic-quintic nonlinearity

We present eight types of spatial optical solitons which are possible in a model of a planar waveguide that includes a dual-channel trapping structure and competing (cubic-quintic) nonlinearity. The families of trapped beams include “broad” and “narrow” symmetric and antisymmetric solitons, composite states, built as combinations of broad and narrow beams with identical or opposite signs (“unipolar” and “bipolar” states, respectively), and “single-sided” broad and narrow beams trapped, essentially, in a single channel. The stability of the families is investigated via the computation of eigenvalues of small perturbations, and is verified in direct simulations. Three species-narrow symmetric, broad antisymmetric, and unipolar composite states-are unstable to perturbations with real eigenvalues, while the other five families are stable. The unstable states do not decay, but, instead, spontaneously transform themselves into persistent breathers, which, in some cases, demonstrate dynamical symmetry breaking and chaotic internal oscillations. A noteworthy feature is a stability exchange between the broad and narrow antisymmetric states: in the limit when the two channels merge into one, the former species becomes stable, while the latter one loses its stability. Different branches of the stationary states are linked by four bifurcations, which take different forms in the model with the strong and weak coupling between the channels.     

Optical waveguide with nonlinear walls

The modes of planar waveguides with thin walls, consisting of nonlinear materials, are studied. The dispersion relations are derived and analyzed by analytical and numerical techniques. The effect of modal type conversion is examined. It is shown that the leaky mode can be converted to the virtual one when the field amplitude is varied.     

Transfer matrix method for media with quadratic optical nonlinearity

A transfer matrix method is developed for media containing nonlinear layers. This method can be used to calculate the propagation of light, the electromagnetic field profile, and also second-harmonic generation in layered structures containing a layer exhibiting quadratic nonlinearity. Zh. Tekh. Fiz. 69, 116–117 (April 1999)     

Multiple focused-waves production by parametric mixing in a layer with hysteretic quadratic nonlinearity

Nonlinear scattering of a weak probe wave by a strong pump wave in a layer with nonlinearity hysteresis is analysed. It is demonstrated that a spherical probe wave from a point source after nonlinear process of difference frequency excitation is scattered in several foci. Different foci correspond to different frequencies of the transformed wave spectrum. In the case of a plane pump wave and under the condition that nonlinear scattering proceeds without acoustic mode conversion wave front reversal is possible. To achieve wave front reversal in a layer with hysteretic quadratic nonlinearity the pump wave should have a frequency equal to the frequency of the probe wave or to any of its subharmonics.     

Transport through a network of capillaries from ultrametric diffusion equation with quadratic nonlinearity

This paper is about a novel mathematical framework to model transport (of, e.g., fluid or gas) through networks of capillaries. This framework takes into account the tree structure of the networks of capillaries. (Roughly speaking, we use the tree-like system of coordinates.) As is well known, tree-geometry can be topologically described as the geometry of an ultrametric space, i.e., a metric space in which the metric satisfies the strong triangle inequality: in each triangle, the third side is less than or equal to the maximum of two other sides. Thus transport (e.g., of oil or emulsion of oil and water in porous media, or blood and air in biological organisms) through networks of capillaries can be mathematically modelled as ultrametric diffusion. Such modelling was performed in a series of recently published papers of the authors. However, the process of transport through capillaries can be only approximately described by the linear diffusion, because the concentration of, e.g., oil droplets, in a capillary can essentially modify the dynamics. Therefore nonlinear dynamical equations provide a more adequate model of transport in a network of capillaries. We consider a nonlinear ultrametric diffusion equation with quadratic nonlinearity - to model transport in such a network. Here, as in the linear case, we apply the theory of ultrametric wavelets. The paper also contains a simple introduction to theory of ultrametric spaces and analysis on them.     

Damping of internal soliton modes in media with quadratic nonlinearity

Optical solitons in media with quadratic nonlinearity and frequency dispersion are theoretically analyzed. Internal soliton modes and the rate of their radiative damping as a function of detuning from the phase-matching condition and the nonlinear shift of phase velocity for different soliton dimensions (d=1, 2, 3) are found. The length of a nonlinear medium required to form a stationary soliton is determined.     

基于三角形插片结构的紧凑型波导双工器

为满足高功率微波系统功率容量和紧凑化需求,提出了一种新型波导双工器。选用过模波导进行设计以提高功率容量,引入三角形金属插片结构谐振腔设计滤波器并在其间引入波导弯头以实现紧凑化。采用微波网络方法对滤波器进行理论分析并设计了两个工作在X波段的滤波器,选择终端短路法确定T型结尺寸并组成双工器。利用电磁仿真软件建模优化和仿真模拟,并对实物进行测试。仿真与测试结果表明,该波导双工器单通道工作时的功率容量分别大于0.11 GW和0.12 GW,两个通道的传输效率分别大于83.9%和82.4%,通道间隔离度大于20 dB。此外还可以根据需求增加滤波器阶数和引入更多的波导弯头以提高空间利用率。     

Spontaneous soliton formation with a saturated nonlinearity in a weakly nonlinear medium

We have observed the effect of a saturated nonlinearity on the process of spontaneous soliton formation in a weakly nonlinear medium with absorption. The characteristic properties of the problem are investigated on the basis of a model equation designated as a nonlinear Schrodinger equation with small perturbations describing the saturation of the nonlinearity and the absorption. The stability of the process of decay of the initial pulse is demonstrated by computational methods for a few specific cases. An effect described as an oscillation of the amplitude maximum of the formed pulse has been discovered.V. D. Kuznetsov Siberian Physicotechnical Institute, Tomsk University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 73–76, June, 1995.     

Fano resonance in quadratic waveguide arrays

We study resonant light scattering in arrays of channel optical waveguides in which tunable quadratic non-linearity is introduced as nonlinear defects by periodic poling of single (or several) waveguides in the array. We describe novel features of wave scattering that can be observed in this structure and show that it is a good candidate for observation of Fano resonance in nonlinear optics.