Intrapulse Raman Scattering Research Articles

(Invited) Kink solutions of the complex cubic– quintic Ginzburg-Landau equation in the presence of intrapulse Raman scattering

We present a study of solutions of the complex cubic–quintic Ginzburg-Landau equation (CCQGLE) and CCQGLE perturbed with the term responsible for the intrapulse Raman scattering (IRS). In both cases, using the method of first-order autonomous sub-equations, novel exact kink and antikink solutions have been identified. These solutions are represented in explicit analytic form. The numerical investigation of the influence of the IRS on the shape, amplitude, and velocity of the right side of the observed "front" CCQGLE solution revealed a good correlation with the identical features predicted by the newly discovered exact kink solution.

Modeling of the effects of intrapulse Raman scattering on dissipative solitons in a mode-locked fiber laser.

The effects of intrapulse Raman scattering (IRS) on dissipative solitons in a mode-locked fiber laser are studied numerically. This research contributes to understanding the impact of IRS on the stability of pulsating soliton solutions of the complex cubic-quintic Ginzburg-Landau equation (in the anomalous dispersion region). It is found that IRS causes an additional loss on the pulse and leads to balance between dissipative effects to generate stable dissipative solitons. The regions of parameters where stationary, pulsating, and chaotic solitons are generated are depicted considering IRS and without it. Regarding the results, the region of the existence of stable solitons becomes larger in the presence of IRS. There is an important trade-off between output pulse energy and laser stability by increasing the IRS parameter. IRS can transform pulsating solitons into stable solitons for a wide range of parameter values. However, the pulse energy is reduced. The bifurcation diagram shows that period doubling and period quadrupling do not occur in the presence of IRS.

Diverse Forms of Breathers and Rogue Wave Solutions for the Complex Cubic Quintic Ginzburg Landau Equation with Intrapulse Raman Scattering

This manuscript consist of diverse forms of lump: lump one stripe, lump two stripe, generalized breathers, Akhmediev breather, multiwave, M-shaped rational and rogue wave solutions for the complex cubic quintic Ginzburg Landau (CQGL) equation with intrapulse Raman scattering (IRS) via appropriate transformations approach. Furthermore, it includes homoclinic, Ma and Kuznetsov-Ma breather and their relating rogue waves and some interactional solutions, including an interactional approach with the help of the double exponential function. We have elaborated the kink cross-rational (KCR) solutions and periodic cross-rational (KCR) solutions with their graphical slots. We have also constituted some of our solutions in distinct dimensions by means of 3D and contours profiles to anticipate the wave propagation. Parameter domains are delineated in which these exact localized soliton solutions exit in the proposed model.

Attitude of the Modulation Instability gain in Oppositely Directed Coupler with the effects of the Intrapulse Raman Scattering and Saturable Function

To establish the effects of the Higher-Order Dispersion (HOD) and Raman Scattering (RS) on Modulation Instability (MI) in the presence of the Saturable Function (SF), it is used the Coupled Nonlinear Schrödinger Equation (CNLSE) which describes pulses propagating in a higher optical beam in oppositely guided coupler. It has been shown through the MI gain spectra the power of the SF in the presence of HOD and Raman effects (RE). By utilizing the HOD with the saturable nonlinearity (SN), it is formed three sides lobes and some new MI bands emerged. On the same way, it is observed that the RE have more potency in the presence of saturable parameter (SP) in the normal and anomalous dispersion regime. It is important to mention that by varying the SF, third-order dispersion (TOD) and Group Velocity Dispersion (GVD) in the absence of Raman parameter (RP) it is obtained three sides lobes which is an supplementary results compare to Alves et al. (2020), Guérin et al. (1995) and Mohamadou et al. (2010). These results could be important to stress the dynamics of the MI in optical fibers such as optical amplification of poor signal, supercontinuum generation, data transmission and signal processing system and very fast transmission signal and so on.

Dynamics of a chirped Airy pulse in a dispersive medium with higher-order nonlinearity

Chirp can control the dynamics of the Airy pulse, making it an essential factor in pulse manipulation. Finite energy chirped Airy pulses (FECAPs) have potential applications in underwater optical communication and imaging. Hence, it is critical to study the propagation of FECAPs. We present a numerical investigation of the propagation dynamics of a FECAP in a dispersive and highly nonlinear medium. The nonlinearity under study includes self-phase modulation (SPM), self-steepening (SS), as well as intra-pulse Raman scattering (IRS) terms. We have observed soliton shedding, and the chirp parameter is demonstrated to have a considerable impact on the pulse dynamics. In particular, the emergent soliton does not propagate in a straight path; instead, depending on the sign of the chirp parameter, it delays or advances in time. Furthermore, it has been established that the chirp can be employed as an alternate control parameter for spectral manipulation. The results of our study may have implications in supercontinuum generation and for producing tunable sources.

Engineering chirped Lambert W-kink signals in a nonlinear electrical transmission network with dissipative elements

The dynamics of modulated waves in a nonlinear discrete transmission network with dissipative elements are investigated analytically. The generalized cubic-quintic Ginzburg-Landau (GCQ-GL) equation with intrapulse Raman scattering (IRS) terms governing spatially damped slowly modulated wave propagation is derived. Considering modulated Stokes wave propagating in the network, we investigate their baseband modulational instability (MI) and show that there are significant changes for the bandwidth frequency where the network may exhibit baseband MI. We show that the MI growth rate increases with the propagating frequency. The analytical chirped Lambert W-kink soliton-like solution of the derived GCQ-GL equation is presented and used to analyze the dissipative effects on chirped Lambert W-kink signals propagating through our network system. We show that the amplitude decreases both in space and time, while the width and the velocity remains constant when the Lambert W-kink signal propagates along the dissipative network. The effects of the cubic-Raman contributions on (i) the propagating frequency, (ii) the baseband MI, as well as (iii) the dynamics of Lambert W-kink signals are also investigated. In particular, our results reveal that a decrease in the cubic-Raman contributions enhances the baseband MI. The results of this paper may be useful for theoretical study of the propagation of ultrashort pulses in a single-mode optical fiber, as well as for experimental realization of undistorted transmission of optical pulses in optical fibers and further understanding their optical transmission properties.

Periodic Solutions of the Complex Cubic-Quintic Ginzburg–Landau Equation in the Presence of Higher-Order Effects

We have studied numerically the influence of intrapulse Raman scattering (IRS) and self-steepening (SS) on the period-2 pulsating solution of the complex cubic-quintic Ginzburg–Landau equation. A cascade of transformations of the numeric solutions under the influence of SS is reported, which includes the existence of: period-1 solutions, chaotic solutions, period–doubling transformation leading to the appearance of pulsating solutions with many periods, then period–halved transformation, periodic in t and x solutions and, finally, uniformly translating fronts. We have shown that by increasing the IRS parameter, the period-4 pulsating solution related to the SS can be successfully transformed into a period-2, period-1 pulsating solutions and, finally, into a stationary solution.

Influence of the higher-order effects on the solutions of the complex cubic–quintic Ginzburg–Landau equation

ABSTRACT The influence of intrapulse Raman scattering (IRS), self-steepening (SS) and third-order of dispersion (TOD) on the solutions of the complex cubic–quintic Ginzburg–Landau equation is studied by means of bifurcation analysis of the dynamical model. The numerical bifurcation diagram of the amplitude of the solution with respect to the nonlinear gain has revealed a cascade of bifurcations that leads to chaotic behaviour. We have found that the IRS leads to the larger shifts in positions and widths of the zones with different types of solutions in comparison to the influence of SS and TOD. Using numerical bifurcation diagrams of the amplitude of the solution with respect to the parameter describing IRS the following types of transformations have been identified: (a) from chaotic into two-periodic solution; (b) from two-periodic into a limit cycle; and (c) from a limit cycle into a stationary solution.

Numerical investigation on the dynamic propagation of finite-energy Airy pulses in photonic crystal fibre

ABSTRACTWe report on numerical analysis of the dynamic propagation of finite-energy Airy pulses (FEAPs) in photonic crystal fibre (PCF) at 835 nm wavelength. We focus on the influence of self-phase modulation (SPM), intrapulse Raman scattering (IRS), as well as self-steepening (SS) on the dynamic propagation of FEAPs under three circumstances, i.e. SPM alone affected, and the combined effect of the first two or all three mentioned above. Furthermore, the influence of the truncation coefficient and initial frequency chirp is discussed in detail. Our results demonstrate that the FEAP can slow down gradually with the increase of the peak power during propagation, while higher-order nonlinear effects, such as IRS and SS, are beneficial for widening and flatting the supercontinuum (SC); the SC becomes wider with decreasing the truncation coefficient; compared to negative initial chirp, positive initial chirp can enhance SC generation, i.e. leading to a broader SC.

Stability and variational analysis of cavity solitons under various perturbations

We theoretically investigate the dynamics and stability of a temporal cavity soliton (CS) excited inside a silicon-based microresonator that exhibits free-carrier generation as a result of two-photon absorption (TPA). The optical propagation of the CS is modeled through a mean-field Lugiato-Lefever equation (LLE) coupled with an ordinary differential equation accounting for the generation of free carriers owing to TPA. The CS experiences several perturbations (like intrapulse Raman scattering (IRS), TPA, free-carrier absorption (FCA), free-carrier dispersion (FCD), etc.) during its round-trip evolution inside the cavity. We develop a full variational analysis based on a Ritz optimization principle which is useful in deriving simple analytical expressions describing the dynamics of individual pulse parameters of the CS under perturbation. TPA and FCA limit the efficient comb generation and modify the stability condition of the CS. We determine the critical condition of stability modified due to TPA and derive closed-form expressions of the saturated amplitude and width of stable CS. We perform detailed modulation-instability analysis and obtain stability condition against perturbations of steady-state solution of LLE. The CS experiences FCD which leads to a temporal acceleration resulting in spectral blueshift. Exploiting the variational analysis, we estimate these temporal and spectral shifts. We also include IRS in our perturbation theory and analytically estimate the frequency redshifting. Finally, we study the effect of pump-phase-modulation on a stable CS. All our analytical results are found to be in good agreement with the data obtained from the full numerical solution of LLE.

Intrapulse Raman scattering and dissipative solitons with extreme spikes

We have studied numerically the influence of intrapulse Raman scattering (IRS) on the dissipative solitons with extreme spikes (DSES). The following scenarios of the influence of IRS have been identified. In the anomalous dispersion regime, there has been found a transformation of the single spike DSES and pulsating in x and t DSES into Raman dissipative solitons. We should mention a good performance of the finite-dimensional system in the description of all pulse parameters in the first case. In the other scenario, the DSES moving with fixed velocity pulsating in x and t transforms into single spike DSES moving with fixed velocity. We have also observed a transformation of double spike DSES into single spike moving DSES as well as a transformation of a single spike DSES into a single spike moving DSES accompanied by the change in the period of the spikes appearance. In the normal dispersion regime, we have found a transformation of a single spike DSES into a single spike moving DSES and the change of the period of the spikes appearance. For a large strength of IRS, an appearance of a chaotic DSES has been observed.

Study on the impact of high-order effects on the evolution of a trapped soliton pumped by a high-power pulse

We theoretically and numerically investigate the influence of high-order effects on a trapped soliton pumped by a high-power pulse during nonlinear propagation. According to the moment method, some evolution rules of a trapped soliton are found in the presence of high-order effects by theoretically analyzing five moment parameters. Further, the temporal and spectral evolutions of a trapped soliton are numerically studied in details. It is demonstrated that the third-order dispersion (TOD) only affects the center position of a trapped soliton, but it does not change the spectrum structure. The intrapulse Raman scattering (IRS) causes a trapped soliton to red-shift and modifies the spectrum structure, thus the asymmetric oscillation structure is generated in the lagging edge of a spectrum. The self-steepening (SS) mainly changes the distribution of red-shifted components, however, it has little effect on the blue-shifted spectrum. Moreover, suppression or enhancement of the Raman-induced frequency shift (RIFS) affected by TOD and SS is also discussed.

On the efficiency of different numerical methods for the calculation of intrapulse Raman scattering of optical solitons

In this paper we compare the performance of different numerical methods for the calculation of the asymptotic evolution of soliton self-frequency shift in the presence of intrapulse Raman scattering (IRS) in optical fibers. First we have calculated the order of global accuracy for the fundamental soliton and the second-order bound state of the unperturbed nonlinear Schrodinger equation for the following numerical methods: the simple split step (SS) method, the full SS method, the reduced SS method, the reduced SS method with fourth order Runge–Kutta (RK4), the Blow–Wood method, the fourth order Runge–Kutta in the interaction picture (RK4IP) method and the Agrawal SS method with one and two iterations. We have shown that the asymptotic evolution of soliton self-frequency shift in the presence of IRS in optical fiber can be best described by the Agrawal SS method (compared to the Blow–Wood method and the RK4IP method). The obtained numerical results for the soliton position and frequency are in agreement with the predictions for these parameters according to the perturbation theory. We have shown that in the presence of IRS the fundamental soliton quickly develops an oscillating tail on its left. The generated tail hardly influences the soliton propagation at large distances. At large distances the form of the soliton gradually becomes asymmetric. The increase of the frequency resolution leads to a notable increase of the maximum propagation distance of the numerical soliton under the influence of IRS.

Cross-phase modulation instability in an elliptical birefringent positive-negative index coupler with self-steepening and intrapulse Raman Scattering effects

In this paper, we investigate the modulational instability (MI) in an elliptical birefringent positive-negative index coupler. Also, we derive the general expression for instability gain by taking into account cross-phase modulation (XPM), self-steepening (SS) and intrapulse Raman scattering. The instability gain is attained. Using standard linear stability analysis, particularly, we study different configurations of the birefringence with self-steepening or intrapulse Raman scattering effects on MI for both normal and anomalous group velocity dispersion regimes. We observe that the instability gain exhibits significant changes due to the effects of the cross-phase modulation. Finally, we show that efficient control of the MI can be realized by adjusting the self-steepening and intrapulse Raman scattering term, even in the presence of different configurations of the birefringence.

Combined influence of third order dispersion (TOD) and intra-pulse Raman scattering (IRS) on initially phase imparted solitons

The temporal shifts caused by the combined influence of Third Order Dispersion (TOD) and Intra-pulse Raman scattering (IRS) on initially phase imparted soliton pulses is demonstrated analytically and numerically. Further the effects are realized in a 160 Gbps, single channel telecommunication system. The phase (ψ) characteristics of soliton with respect to initial relative spacing (qo) is governed by Perturbative equation while the temporal shift under the influence of Third Order Dispersion and Intra-pulse Raman scattering is noted by Moment equation. By combining the Perturbative and Moment equations, the temporal shift under the combined effects is noted analytically. Also the similar effect is noted numerically by using the Split-Step Fourier transform (SSFT) to support analytics. The temporal shift at the interaction point (where two in-phase soliton interacts) using analytical and numerical method is characterized by the ‘Spacing between the solitons’ in terms of picoseconds. It could be realized by both analytical and numerical methods that the Intra-pulse Raman scattering is more dominant over third order dispersion in shifting the soliton pulses temporally with respect to distance. Apart from analytical and numerical approached, the shift of soliton pulses under the combined effect is realized in telecommunication system and the performance is noted using the Q-value and Time domain analyzer view.

Ultrashort high-amplitude dissipative solitons in the presence of higher-order effects

In this work, the propagation of high-amplitude solitons of the cubic-quintic complex Ginzburg–Landau equation in the presence of higher-order effects, namely, the intra-pulse Raman scattering (IRS) and the third-order dispersion (TOD), has been studied. Starting from a singularity found by Akhmediev and co-workers, high-amplitude pulses are predicted using a perturbation approach and numerically obtained. We have found that this singularity is no longer present if the intra-pulse Raman scattering effect is considered and zero velocity pulses may be achieved in the presence of both IRS and TOD. The predictions from perturbation theory are numerically confirmed to a certain extent.

Experimental and theoretical study of red-shifted solitonic resonant radiation in photonic crystal fibers and generation of radiation seeded Raman soliton

Redshifted solitonic resonant radiation (RR) is a fascinating phase-matching phenomenon that occurs when an optical pulse, launched in the normal dispersion regime of photonic crystal fiber, radiates across the zero-dispersion point. The formation of such phase-matched radiation is independent of the generation of any optical soliton and mainly governed by the leading edge of an input pump which forms a shock front. The radiation is generated at the anomalous dispersion regime and found to be confined both in the time and frequency domain. We experimentally investigate the formation of such radiation in fabricated photonic crystal fiber for two different pulse width regimes (femtosecond and picosecond) with detailed theoretical analyses. Theoretically predicted results corroborate well with experimental results and confirm the existence of such unique radiation which is robust in nature. Further, we extend the study to long-length fiber and investigate the interplay between redshifted solitonic RR and intrapulse Raman scattering (IPRS). The consequence of the formation of such solitonic RR in an anomalous dispersion domain is found to be very interesting where it seeds a series of Raman solitons and behaves like a secondary source. These Raman solitons are now continuously redshifted and open up the possibility of wideband supercontinuum generation even in normal dispersion pumping. We fabricate a suitable photonic crystal fiber and experimentally demonstrate the RR-seeded IPRS process.

Self-frequency shift and nonlinear interaction of equilibrium and pulsating solutions in the presence of linear and nonlinear gain, spectral filtering, and intrapulse Raman scattering

In this work we study numerically the self-frequency shift of the equilibrium and pulsating solutions in the presence of linear and nonlinear gain, spectral filtering, and intrapulse Raman scattering (IRS). It has been established that the stationary value of the central frequency of solutions, which appears as a result of the collective action of these physical effects, is a linearly increasing function of the Raman parameter γ for the solution of Tsoy and Akhmediev (Phys Lett A 343:17–422, 2005), Tsoy et al. (Phys Rev E 73:036621, 2006), and the quadratic function of γ for the parameters used in Uzunov et al. (Phys Rev E 90:042906, 2014). We have found a complete suppression of the self-frequency shift of the equilibrium and pulsating solutions in the presence of linear and nonlinear gain, spectral filtering, and IRS below and at the point of the Poincare–Andronov–Hopf bifurcation (PAHB) (Uzunov et al. in Phys Rev E 90:042906, 2014). We have numerically observed stable pairs and sequences of equidistant equilibrium solutions and pulsating solutions propagating in the presence of linear and nonlinear gain, spectral filtering, and IRS below and at the point of the PAHB. The pairs and equidistant sequences of pulsating solutions at the point of bifurcation require larger initial separation and exist at smaller distances of propagation than the pairs and equidistant sequences of the equilibrium solutions below the point of bifurcation.

Influence of higher-order effects on pulsating solutions, stationary solutions and moving fronts in the presence of linear and nonlinear gain/loss and spectral filtering

We have studied the impact of the higher-order effects: intrapulse Raman scattering (IRS), third-order of dispersion (TOD) and self-steepening (SS) on pulsating solutions, moving fronts and stationary solutions of the complex cubic–quintic Ginzburg–Landau equation (CCQGLE) found in Tsoy and Akhmediev (2005) as well as on the solutions presented in Uzunov et al. (2014). The applied basic equation generalizes the CCQGLE with the IRS, TOD and SS effects. A finite-dimensional dynamical system has been derived using the method of moments. Applying the derived dynamical system alongside with the numerical solution of the generalized CCQGLE performed by means of the fourth-order Runge–Kutta interaction picture method we have found that the influence of IRS and SS is stronger than the impact of TOD for the solutions of Tsoy and Akhmediev (2005). Perturbed pulsating solutions, moving fronts and stationary solutions in the presence of IRS, SS and TOD have been numerically observed. They exist up to some critical values of the parameters of perturbations. For the values of parameters larger than the critical ones the pulsating solutions are transformed into stable stationary solutions or unstable solutions. New localized fluctuating and stationary solutions have been obtained for fairly large values of parameters of IRS and TOD, respectively. The transformation of the stable stationary solution of Uzunov et al. (2014) under the influence of SS into pulsating solution has been numerically observed.

Localized Pulsating Solutions of the Generalized Complex Cubic-Quintic Ginzburg-Landau Equation

We study the dynamics of the localized pulsating solutions of generalized complex cubic-quintic Ginzburg-Landau equation (CCQGLE) in the presence of intrapulse Raman scattering (IRS). We present an approach for identification of periodic attractors of the generalized CCQGLE. Using ansatz of the travelling wave and fixing some relations between the material parameters, we derive the strongly nonlinear Lienard-Van der Pol equation for the amplitude of the nonlinear wave. Next, we apply the Melnikov method to this equation to analyze the possibility of existence of limit cycles. For a set of fixed parameters we show the existence of limit cycle that arises around a closed phase trajectory of the unperturbed system and prove its stability. We apply the Melnikov method also to the equation of Duffing-Van der Pol oscillator used for the investigation of the influence of the IRS on the bandwidth limited amplification. We prove the existence and stability of a limit cycle that arises in a neighborhood of a homoclinic trajectory of the corresponding unperturbed system. The condition of existence of the limit cycle derived here coincides with the relation between the critical value of velocity and the amplitude of the solitary wave solution (Uzunov, 2011).