Kerr Nonlinear Waveguides Research Articles

Quantum features of nonlinear coupler with competing nonlinearity

In this work, we examine the quantum features of a multi-waveguide nonlinear coupler exploiting the second-and third-order nonlinearities. The considered system contains four identical channels, each with a single fundamental transverse mode. The essence of this type of nonlinear coupler is to examine the effect of two or more competing nonlinearities on the generated nonclassical features in this class of devices. Here, we consider the case of second harmonic generation, wherein the fundamental harmonic (FH) fields are up-converted in pairs to double-frequency second harmonic (SH) fields, which are then evanescently coupled with the fields from other Kerr nonlinear waveguides. Using the positive P representation of the phase space, the time-evolution of the density matrix could be mapped to the corresponding Fokker–Planck equation of a classical quasiprobability distribution. Using Langevin stochastic equation, an exact representation of the system in phase space led to the demonstration of sub-Poissonian property, squeezing, and entanglement. With more effective squeezing achieved in all channel waveguides, the present system with χ(2)–χ(3) interaction can be a more efficient alternative to other versions of nonlinear couplers such as the quantum optical dimer (QOD) and Kerr nonlinear coupler (KNC). Furthermore, such a structure offers more flexibility in coupled-mode interactions in the form of correlation between the modes in different waveguides. This provides a better mechanism for the generation of enhanced nonclassical effects.

Kerr nonlinear couples

Directional nonlinear couplers composed of two Kerr nonlinear waveguides are studied. Quantum consistent solutions of the equations of motion are obtained showing the collapses and revivals of the field mode amplitudes. The approximate method is also adopted for the contradirectional geometry and the switching accompanied by collapses of the modes is revealed. Kerr couplers with varying linear coefficients arc examined and possible controls of the switching of modes, for instance, digital switching and fast switching are demonstrated. The two-mode squeezing of vacuum fluctuations and the generation of pure states are shown.

Two-color ‘dancing’ light bullets in the graded-index waveguide

The propagation of a spatiotemporal soliton in a focusing quadratic-nonlinear waveguide is theoretically investigated. This soliton is a bound state of localized bunches of light energy at the fundamental frequency and at its second harmonics. It is shown that with anisotropic spatial distribution of the refractive index in the cross section of the waveguide, the soliton trajectory can be a spatial Lissajous figure. Such spatiotemporal solitons are called two-color ‘dancing’ light bullets. Unlike dancing light bullets in a waveguide with Kerr nonlinearity, the stability of the dancing bullets discussed here does not require additional restrictions on their apertures, powers, and temporal durations. In addition, a two-color dancing light bullet can be formed both under anomalous and normal dispersion of group velocity. It also distinguishes a two-color dancing light bullet in a quadratic nonlinear waveguide from a dancing light bullet in a Kerr nonlinear waveguide.

Figure of merit for Kerr nonlinear plasmonic waveguides

AbstractPlasmonic waveguides are promising in many applications because of their subwavelength field confinement, which can strongly enhance light‐matter interactions. Nevertheless, how to efficiently evaluate their Kerr nonlinear performance is still an open question because of the presence of relatively large linear losses. Here a simple and versatile figure of merit (FOM) is proposed for Kerr nonlinear waveguides with linear losses. To derive the FOM, a generalized full‐vectorial nonlinear Schrödinger equation governing nonlinear pulse propagation in a lossy waveguide is developed, and an approximate analytic solution of the degenerate four wave mixing conversion efficiency is derived and validated. The effectiveness of the FOM is verified with an all‐plasmonic and a hybrid‐plasmonic waveguide configuration. Rigorous results show that the optimal waveguide length for the highest conversion efficiency is ln 3 times the attenuation length. At this length, the upper limits of the conversion efficiency and the nonlinear phase shift are determined by the FOM. These results provide fundamental theory and useful guidance in exploring plasmonic waveguides for nonlinear optical applications. image

Stabilizing soliton-based multichannel transmission with frequency dependent linear gain–loss

We report several major theoretical steps towards realizing stable long-distance multichannel soliton transmission in Kerr nonlinear waveguide loops. We find that transmission destabilization in a single waveguide is caused by resonant formation of radiative sidebands and investigate the possibility to increase transmission stability by optimization with respect to the Kerr nonlinearity coefficient γ. Moreover, we develop a general method for transmission stabilization, based on frequency dependent linear gain–loss in Kerr nonlinear waveguide couplers, and implement it in two-channel and three-channel transmission. We show that the introduction of frequency dependent loss leads to significant enhancement of transmission stability even for non-optimal γ values via decay of radiative sidebands, which takes place as a dynamic phase transition. For waveguide couplers with frequency dependent linear gain–loss, we observe stable oscillations of soliton amplitudes due to decay and regeneration of the radiative sidebands.

Cross-talk dynamics of optical solitons in multichannel waveguide systems with a Ginzburg-Landau gain-loss profile

We investigate energy exchange in fast optical soliton collisions in Kerr nonlinear waveguides with weak linear loss, cubic gain, and quintic loss, i.e., with a Ginzburg-Landau (GL) gain-loss profile. We find that the amplitude shift in a single two-soliton collision in the presence of quintic loss is quartic in the initial soliton amplitudes, and that three-soliton interaction gives a significant contribution to the amplitude shift in a three-soliton collision. Moreover, we show that collision-induced dynamics of soliton amplitudes in a two-channel waveguide system with a GL gain-loss profile is described by a Lotka-Volterra (LV) model with quadratic and quartic interaction terms. Using the LV model, we show that linearly stable transmission with equal prescribed amplitudes can be achieved by a proper choice of the time-slot width and the ratio between the cubic gain and quintic loss coefficients. The linear stability of the transmission is confirmed by the numerical solution of a perturbed system of coupled nonlinear Schr\"odinger equations. Further numerical simulations show that transmission in waveguides with a GL gain-loss profile is less susceptible to radiation emission effects compared with waveguides with linear gain and cubic loss.

Effect of Kerr-like medium on a two-level atom in interaction with bimodal oscillators

In this article we study the effect of the Kerr-like medium on a system consisting of two-level atom and two fields injected simultaneously within perfect cavity. We assume that in the presence of the nonlinear Kerr coupler, the atom interacts with each field separately. The present system can be regarded as a co-directional nonlinear coupler composed of two Kerr nonlinear waveguides, where the atom–field interaction plays the role of the energy exchange between the waveguides. The system includes two effective different coupling parameters λ1 and λ2, such that each coupling connects the atom with one of the field mode. Moreover, it includes two different susceptibility factors, one represents self-coupling while the other is responsible for cross-action processes. Under certain conditions, the exact solution of the wavefunction in the Schrödinger picture is obtained and the Husimi quasidistribution is derived. A consideration of some physical phenomena, such as collapses and revivals is given, and the degree of entanglement is also discussed. The system is found to be sensitive to the variation of both mean photon numbers as well as to the Kerr-like medium.

Non-classical behaviour and switching in Kerr nonlinear couplers

Directional nonlinear couplers composed of two Kerr nonlinear waveguides are studied. Quantum consistent solutions of the equations of motion are obtained showing the collapses and revivals of the field mode amplitudes. The approximate method is also adopted for the contradirectional geometry and the switching accompanied by collapses of the modes is revealed. Kerr couplers with varying linear coefficients are examined and possible controls of the switching of modes, for instance, digital switching and fast switching are demonstrated. The two-mode squeezing of vacuum fluctuations and the generation of pure states are shown.

Pump induced normal mode splittings in phase conjugation in a Kerr nonlinear waveguide

Phase conjugation in a Kerr nonlinear waveguide is studied with counter-propagating normally incident pumps and a probe beam at an arbitrary angle of incidence. Detailed numerical results for the specular and phase conjugated reflectivities are obtained with full account of pump depletion. For sufficient strengths of the pump a normal mode splitting is demonstrated in both the specular and the phase conjugated reflectivities of the probe wave. The splitting is explained in terms of a simple model under undepleted pump approximation.

Kerr nonlinear coupler with varying linear coupling coefficient

We investigate a codirectional nonlinear coupler composed of two Kerr nonlinear waveguides. Unlike the conventional device, the linear coupling between the guides is supposed to be a variable function of the propagation distance. We calculate quantum statistical and dynamical properties of the Kerr nonlinear coupler with a coherent input and analyse the influence of coupling variation on oscillations in mean photon number. The possibility to control the switching characteristics and principal squeezing effect by adjusting the form of coupling function is shown.

Quantum statistics and dynamics of Kerr nonlinear couplers

We investigate a codirectional nonlinear coupler composed of two Kerr nonlinear waveguides taking into account linear as well as nonlinear coupling. We calculate quadrature, principal squeezing and integrated intensity variances and quadrature uncertainty product, taking into account effects of transmission of light between waveguides in a closed analytical way in rotating-wave approximation. Incident beams are assumed to be coherent. We show that the coupler can exhibit various quantum properties such as collapses and revivals of oscillations, squeezing of vacuum fluctuations and sub-Poissonian photon statistics in single as well as in compound modes. The field can periodically return to a pure state. The dynamics of energy exchange between waveguides, of self-trapping of beams and collapses and revivals are discussed and a possibility of compensation of nonlinear coupling and self-action processes is demonstrated in competition with linear coupling.