We investigate the collision dynamics of discrete soliton (DS) pair in a realistic semi-infinite nonlinear waveguide array (WA) in the context of \textit{diffractive resonant radiation} (DifRR). Depending on the initial amplitude ($A_0$) and wavenumber ($k_0$), a co-moving pair of identical DSs either collide elastically or merge to form a discrete \textit{breather}. For large amplitude and small wavenumber, DSs form a bound state and do not interact .
We map the domain of interaction by iterative simulation and present a phase plot in ($A_0$-$k_0$) parameter space.
A variational technique is developed where the interaction term is considered as perturbation. A proper choice of Lagrangian density and the \textit{ansätz} function followed by the Ritz optimization leads us to a set of ordinary differential equations that describe the collision mechanism. The analytical result corroborate well with numerical data.
We further investigate the role of initial phase detuning between two identical DS and observe a periodic energy exchange during their interaction.
Varied degree of energy exchange occurs when two DS with different wavenumbers collide which results in three distinct output states accompanied by DifRR generation.
Extending our investigation to a more generalized condition by taking different amplitudes and wavenumber of DS pair, we find an unique secondary radiation in $k$-space which is originated due to the collision of solitons.
The nature of this collision mediated secondary radiation is found to be different from usual DifRR.
Our results shed light on the interesting aspects of the collision dynamics of DS pair in nonlinear WA and useful in understanding the complex mechanism.
We consider light pulses in a circular array of $2N$ coupled nonlinear optical waveguides. The waveguides are either hermitian or alternate gain and loss in a $\mathcal{PT}$-symmetric fashion. Simple patterns in the array include a ring of $2N$ pulses travelling abreast, and a breather -- a string of pulses where all even and all odd waveguides flash in turn. In addition, the structure displays solitons gyrating around the necklace by switching from one waveguide to the next. Some of the gyrating solitons are stable while other ones are weakly unstable and evolve into gyrating multiflash strin…
We analyse Raman-induced self-frequency shift in two-component solitons supported by both quadratic and cubic nonlinearities. Treating Raman terms as a perturbation, we derive expressions for soliton velocity and frequency shifts of the fundamental frequency and second harmonic soliton components. We find these predictions compare well with simulations of soliton propagation. We also show that Raman shift can cause two-component solitons to approach the boundary of their own existence and subsequently trigger soliton instabilities. In some cases these instabilities are accompanied by an almost…
We address the formation of \{chi}(2) topological edge solitons emerging in topologically nontrivial phase in Su-Schrieffer-Heeger (SSH) waveguide arrays. We consider edge solitons, whose fundamental frequency (FF) component belongs to the topological gap, while phase mismatch determines whether second harmonic (SH) component falls into topological or trivial forbidden gaps of the spectrum for SH wave. Two representative types of edge solitons are found, one of which is thresholdless and bifurcates from topological edge state in FF component, while other exists above power threshold and emanat…
We present a design and protocol to achieve an essential feature of an optical transistor, namely the amplification of input signal with the use of discrete solitons in waveguide arrays. We consider the scattering of a discrete soliton by a reflectionless potential in the presence of a control soliton. We show that at the sharp transition region between full reflectance and full transmittance, the intensity of the reflected or transmitted soliton is highly sensitive to the intensity of the control soliton. This suggests a setup of signal amplifier. For realistic purposes, we modulate the param…
We report a detailed study on soliton steering dynamics in a parity-time-symmetric directional coupler in the femtosecond domain, which requires incorporation of higher-order perturbative effects such as third-order and fourth-order dispersions, self-steepening, and intrapulse Raman scattering. With a high gain/loss, the combination of all these effects is found to stabilize the soliton pulse evolution in the coupler from the chaotic behavior of unperturbed evolution. This work demonstrates that efficient soliton steering can be achieved at very low critical power and a relatively higher gain/…
Enhancement of transmission quality in soliton-based optical waveguide systems by frequency dependent linear gain-loss and the Raman self-frequency shift
This paper deals with the temporal nonlinear dynamics of plasmon-solitons in a plasmonic waveguide. Duffing equation is recognized as the temporal part of the nonlinear amplitude equation governing the plasmonic waveguide. It is shown that Duffing oscillator waveforms stand for the temporal nonlinear dynamics of plasmon-soliton waves. The exchange of Lorentz-type bright and dark solitons energies gives rise to a Fano resonance. It is thus shown that the interaction of solitons and the formation of plasmon-solitons is inherently nonlinear. It is accordingly indicated that the nonlinear modulati…
Heat-induced soliton self-frequency redshift in the ultrafast nonlinear dynamics of active plasmonic waveguides
我们研究了在有源等离子体激元波导中发射的光的超快非线性动力学，该有源等离子体激元波导由两个硅层夹在一个金薄膜中组成，并且浸没在外部泵浦的Al $_2$ O $_3$：Er $^{3+}$中。我们通过一个广义的立方Ginzburg-Landau方程来模拟这种耗散系统中的光传播，该方程考虑了活性介质的放大效应以及金的吸收和热调制非线性效应。我们发现，加热严重影响时间耗散孤子在这样的等离子体波导中的传播，通过产生孤子自频率红移伴随着孤子减速在时域。采用半解析变分法，推导了一组脉冲参数的耦合微分方程，计算了自感红移的依赖关系。这些方程通过简单的时间和频率偏移的近似解析表达式提供了对复杂的非线性动力学的物理洞察。这样的分析预测被发现与直接数值模拟的广义立方Ginzburg-Landau方程非常吻合。我们的研究结果提供了一个普遍的理解，在金基有源等离子体波导的超快非线性动力学，特别是传播光脉冲的光谱整形特性。
We present a design and protocol to add binary numbers using discrete solitons in waveguide arrays. We show that the nonlinear interaction between discrete solitons in waveguide arrays can be exploited to design half and full adders. By modulating the separation between waveguides and introducing control solitons, we achieve the performance of an XOR gate. We construct the half and full adders using the XOR gate together with the previously-designed OR and AND gates. To facilitate the experimental realization, we calculate the profile of separations between the waveguides that will lead to the…
We consider a two-dimensional nonlinear waveguide with distributed gain and losses. The optical potential describing the system consists of an unperturbed complex potential depending only on one transverse coordinate, i.e., corresponding to a planar waveguide, and a small non-separable perturbation depending on both transverse coordinates. It is assumed that the spectrum of the unperturbed planar waveguide features an exceptional point (EP), while the perturbation drives the system into the unbroken phase. Slightly below the EP, the waveguide sustains two-component envelope solitons. We derive…
