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The MI gain spectra for the varying strength of quintic nonlinearity for the (a) rectangular and (b) Gaussian response functions with the other parameters as σ = 10, α 1 = 0 P 1 = 1, and P 2 = 0.1.
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A theoretical investigation of the modulational instability (MI) in a composite system with a nonlocal response function is presented. A composite system of silver nanoparticles in acetone is chosen, whose nonlinearity can be delicately varied by controlling the volume fraction of the constituents, thus enabling the possibility of nonlinearity mana...
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... this case is particularly dominated by quintic nonlinearity, it is interesting to understand the strength of quintic nonlinearity in the MI spectrum. Figure 6 shows the evolution of spectral bands with strength of quintic nonlinearity for both cases of nonlocal functions. In both cases, |α 2 | enhance MI by increasing the gain of MI as well as the number of sidebands. ...
Context 2
... Figure 6 shows the evolution of spectral bands with strength of quintic nonlinearity for both cases of nonlocal functions. In both cases, |α 2 | enhance MI by increasing the gain of MI as well as the number of sidebands. In particular, the effect of α 2 is more pronounced in a rectangular function with additional spectral bands of higher gain [ Fig. 6(a)], while the Gaussian function behaves rather in a straightforward way, indicating a monotonous increase of gain with α 2 as shown in Fig. ...
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... 2 | enhance MI by increasing the gain of MI as well as the number of sidebands. In particular, the effect of α 2 is more pronounced in a rectangular function with additional spectral bands of higher gain [ Fig. 6(a)], while the Gaussian function behaves rather in a straightforward way, indicating a monotonous increase of gain with α 2 as shown in Fig. ...
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... Considering the derivatives of Eqs. (9) and (10) with respective to coordinate z, we can obtain the following ordinary differential equations in the k space By solving Eqs. (13) and (14), the solution of random perturbation is obtained with c 1 and c 2 are arbitrary constants, and the eigenvalue is given by It is obvious that no MI exists when 2 < 0 and the plane wave is stable. ...
Modulation instability of one-dimensional plane wave is demonstrated in nonlinear Kerr media with sine-oscillatory nonlocal response function and pure quartic diffraction. The growth rate of modulation instability, which depends on the degree of nonlocality, coefficient of quartic diffraction, type of the nonlinearity and the power of plane wave, is analytically obtained with linear-stability analysis. Different from other nonlocal response functions, the maximum of the growth rate in media with sine-oscillatory nonlocal response function occurs always at a particular wave number. Theoretical results of modulation instability are confirmed numerically with split-step Fourier transform. Modulation instability can be controlled flexibly by adjusting the degree of nonlocality and quartic diffraction.
... Realizing the impact of coupled optical systems in the dynamics of MI, a recent study shows the MI effects in three-core oppositely directed coupler [41] with conventional Kerr-type nonlinearity. Particularly, in a composite system with controllable nonlinearity, the MI is studied with spatial delay [42] in coupled settings with two co-propagating waves. In Kumar et al. [42], the authors employed different classes of nonlocal functions and used the interplay between the competing HONs and nonlocal functions to study the MI. ...
... Particularly, in a composite system with controllable nonlinearity, the MI is studied with spatial delay [42] in coupled settings with two co-propagating waves. In Kumar et al. [42], the authors employed different classes of nonlocal functions and used the interplay between the competing HONs and nonlocal functions to study the MI. The authors argued that both cubic and quintic nonlinearities and its interplay with the nonlocal response function are very crucial in MI dynamics. ...
... In Kumar et al. [42], the authors discusses that in a coupled system, MI is commonly amplified by XPM, particularly in cases of defocusing nonlinearity, where XPM effects are fundamental in initiating MI. The relative magnitude of nonlinearity is another significant factor, either enhancing the gain or introducing new spectral bands. ...
In this paper, the modulational instability of the one-dimensional optical soliton has been studied in the presence of Gaussian and sine oscillatory nonlocal response functions. By properly managing the sign as well as the magnitude of cubic, quintic and septimal nonlinearities and the strength of nonlocal response functions, a remarkable impact on the dynamics of modulational instability has been observed. We have investigated both the symmetric (equal power values for pump and probe beams) and asymmetric (unequal power values for pump and probe beams) cases, in which the asymmetric case shows a reduced bandwidth of MI compared to the symmetric case. Furthermore, our study has revealed the emergence of both type A and type B Akhmediev breathers under specific combinations of higher-order nonlinearities and nonlocal response functions. Specifically, the Gaussian nonlo-cal response function leads to the formation of type A Akhmediev breathers, while the sine oscillatory nonlo-cal response function can give rise to both type A and type B Akhmediev breathers, which depends upon the strength of the nonlocal response function.
... According to Esbensen et al [28], the coexistence of dark and bright spatial solitons in the same medium may be achieved by varying the beam's intensity under a well-controlled balance between focusing and defocusing cubic nonlinearities. Moreover, the crossphase modulation induced spatial MI in a composite medium with a nonlocal nonlinear response was studied [29]. In recent years, localized spatiotemporal solitons were studied in a nonautonomous nonlocal NLS equation [30]. ...
In this work, pure-quartic soliton formation is investigated in the framework of a nonlinear Schrödinger equation with competing Kerr (cubic) and non-Kerr (quintic) nonlocal nonlinearities and quartic dispersion. In the process, the modulational instability (MI) phenomenon is activated under a suitable balance between the nonlocal nonlinearities and the quartic dispersion, both for exponential and rectangular nonlocal nonlinear responses. Interestingly, the maximum MI growth rate and bandwidth are reduced or can completely be suppressed for some specific values of the cubic and quintic nonlocality parameters, depending on the type of nonlocal response. The analytical results are confirmed via direct numerical simulations, where the instability supports the signature of pure-quartic dark and bright solitons. These results may provide a better understanding of pure-quartic solitonic structures for their potential applications in the next generation of nonlinear optical devices.
... can be affected in a nonlinear medium by diverse mechanisms, particularly the nonlocality in nonlinear response, which is an intriguing effect that plays a crucial role in the dynamics of the system [32]. In the temporal domain, MI materializes itself as a result of the interplay between nonlinearity and group-velocity dispersion (GVD): anomalous GVD for self-phase modulation and both anomalous and normal GVD for cross-phase modulation (XPM) [10]. ...
... The problem under consideration is the case in which a coupled NLSE (CNLSE) with higher-order effects [32,44], resulting from two optical beams at different frequencies and the same polarizations, is propagated in a single-mode optical fiber with Kerr nonlinearity, where a time-dependent nonlinear response is incorporated in the system. The governing systems read as ...
... This model of HON was first proposed by Reyna and de Araújo [48] to study experimentally and numerically the nonlinearity management and spatial MI for cubic and quintic nonlinearity for optical beam propagation in metal-dielectric nanocomposites and has been reconsidered very recently by [32] to show the influence of spatial delay on MI in a composite system with controllable nonlinearity. Thus, taking into account the cubic-quintic media, cubic nonlinearity leads to degeneracy of the Townes' solitons, making their propagation stable [49]. ...
We study analytically and numerically the modulation instability (MI) of two incoherently co-propagating optical pulses in nonlinear fiber, taking into account high-order nonlinearity, walk-off effects, delay response time, and cross-phase modulation in several dispersion regimes. We show that higher-order nonlinearity is responsible for superposition of the secondary MI spectrum. We realize that there is a peak located in the emerged Raman band that we call “Raman peak” due to the combined effects of third-order dispersion, delay response time, and the opposite sign of the fourth-order dispersion parameter. These peaks are shifted toward higher frequencies when the walk-off increases.
... Indeed, metal colloids are excellent systems for exploitation of concepts directly related to multidimensionality. Of course there are plenty of possible developments in this area as already pointed out by many authors (see for example: Walasik et al., 2017;Reyna and de Araújo, 2017;Kumar et al., 2018;Trofimov and Lysak, 2018;Kassab and de Araújo, 2019;Ortega et al., 2019, Kartashov et al., 2019, Malomed, 2019. Moreover, with new theoretical advances and the development of nanofabrication techniques exciting challenges and applications are expected for the near future. ...
A review is presented on recent research that demonstrate the control of light-by-light in colloids containing silver-nanospheres (Ag-NS) and gold-nanorods (Au-NR). The presentation is based on experiments performed with pulsed lasers by exploiting the ultrafast electronic nonlinearity of samples exhibiting cubic-quintic nonlinearities. Guiding and confinement of light induced by optical vortex solitons in colloidal suspensions of Ag-NS, and nonlinear processes of light scattering, absorption and refraction in colloids with Au-NR were investigated in the experiments. The results are analyzed by numerical simulations based on modified nonlinear Schrödinger equations. The developments herein discussed are in the forefront of interest for plasmonic applications with metal nanoparticles.
We analyze the modulation instability induced by cross-phase modulation of two co-propagating optical beams in nonlinear fiber with the effect of higher-order dispersion and septic nonlinearity. We investigate in detail the effect of relaxation nonlinear response to the gain spectrum both in normal group velocity dispersion (GVD) and anomalous dispersion regime. We show that the walk-off, the relaxation nonlinear response time as well as the higher-order process particularly influence the generation of the modulation instability gain. Our results shows that the emerging Raman peaks is observable both in the case of weak dispersion and in a higher-order dispersion for mixed GVD regime with slow response time. These Raman peaks are shifted toward higher frequencies with the decrease of their magnitude, when the walk-off increases.
We consider the evolution of light beams in nonlinear Kerr media wherein the beam propagation is governed by the coupled non-paraxial (2+1) dimensional nonlinear Schrödinger equation. In the advent of system failing to obey the slowly varying envelope approximation, the usual paraxial approximation cannot be adopted. Our model equation could potentially serve as a governing model for nano-waveguides and on-chip silicon photonic devices. Using the trial solution method, we derive the different combinations of soliton solutions such as bright–bright, dark–dark, and bright–dark soliton and briefly discuss the characteristics of the soliton. Following the initial discussion on the soliton solution, we extend the study to investigate the modulational instability of the system of equations. We examine the role of the dispersion/diffraction in the instability spectra and demonstrate the different characteristics of the instability bands as a function of system parameters.
