Kerr Dispersion Research Articles

Dispersive wave propagation of the nonlinear Sasa-Satsuma dynamical system with computational and analytical soliton solutions

The Sasa-Satsuma equation on a continuous background describes a nonlinear fiber system with higher-order effects including the third-order dispersion and Kerr dispersion. The Sasa-Satsuma equations describe the simultaneous propagation of two ultrashort pulses in the birefringent or two-mode fiber with the third-order dispersion, self-steepening, and stimulated Raman in scattering effects, and govern the propagation of ultra-fast pulses in optical fiber transmission systems. We consider the Sasa-Satsuma equation, which is one of the integrable extensions of the nonlinear Schrödinger equations. We find the functional integral and the Lagrangian of this model. We derived the computational and analytical soliton solutions of the nonlinear Sasa-Satsuma dynamical system. We discuss the stability analysis for our solutions.

Propagation of chirped periodic and localized waves with higher-order effects through optical fibers

We study the propagation properties of nonlinear periodic waves in an optical fiber medium exhibiting Kerr dispersion and quintic nonlinearity. The quintic derivative nonlinear Schrödinger equation is applied to model the evolution of femtosecond light waves in such system. Unlike periodic structures in Kerr media, the novel waves possess a nonlinear chirp which varies with their intensity. In addition to the linear part, the pulse chirp also includes two intensity dependent chirping terms. The conditions on fiber parameters for the existence of the newly found periodic waves are presented. A wide variety of solitary pulse shapes including the bright, dark, kink, anti-kink, and gray solitary waves are obtained in the long-wave limit. Our results show that Kerr dispersion plays a crucial role in introducing a nonlinear chirp for the periodic and solitary waves. Finally, the stability of these nonlinearly chirped solutions is numerically studied under the finite perturbations.

Dynamics of optical solitons incorporating Kerr dispersion and self-frequency shift

This paper deals with the dynamics of optical solitons in nonlinear Schrödinger equation (NLSE) with cubic-quintic law nonlinearity in the presence of self-frequency shift and self-steepening. This type of equation describes the ultralarge capacity transmission and traveling of laser light pulses in optical fibers. Two robust analytical approaches are employed to determine contemporary solutions. Some new explicit rational, periodic and combo periodic soliton solutions are extracted using the extended trial equation method. The Riccati–Bernoulli sub-ODE method provided us with singular and dark soliton solutions. The constraints found are necessary for the existence of solitons.

Gray and black optical solitons with quintic nonlinearity

A higher-order nonlinear Schrödinger equation with the third-order dispersion, the cubic–quintic nonlinearities, derivative non-Kerr nonlinear terms, Kerr dispersion, and stimulated inelastic scattering is considered. The model can be used to describe the subpicosecond or femtosecond optical pulse propagation in highly nonlinear optical fibers. We find the exact gray solitary wave solution (i.e., a dark localized structure with nonzero minimum in intensity) on a continuous-wave background for the equation by adopting an appropriate ansatz solution. The propagation characteristics of such solitary pulses are determined in the presence of all higher-order effects. We also find black solitary wave solutions for the higher-order evolution equation under specific conditions for its coefficients. The parametric conditions on fiber parameters for the existence of both types are given.

Kerr nonlinearity enhancement by double tunnelling from quantum dot nanostructure

A model of the dynamical equations of the density matrix describes double tunnelling between double quantum dot (QD) system states, this is to study Kerr nonlinearity in QD structure. Inhomogeneity in the QD system is included which is not included in earlier studies of Kerr nonlinearity in QDs. Possibilities of subluminal and superluminal light propagation and switching between them are examined. Double tunnelling is shown to obtain giant Kerr dispersion compared with single tunnelling. High conduction- and low valence-band tunnelling components are required to obtain high Kerr dispersion. Working with one tunnel component reduced Kerr dispersion and switching between subluminal and superluminal can be obtained and the EIT window can be removed.

Kerr dispersion in a Y-configuration quantum dot system

We introduce a Y-configuration model for a double quantum dot (QD) system, which is modeled for Kerr nonlinearity using the density matrix theory. Inhomogeneity in QDs is included in the calculations of the real part (Kerr) and the imaginary part (absorption) of the density matrix, which has not been covered before in Kerr calculations. Five configurations are studied: Y, ladder, Λ, staircase, and weak probe. Frequency detunings, controlling fields, and phases are used to study the structures. Our system shows high controllability as well as a giant Kerr dispersion, propagation without distortion, wide electromagnetic induced transparency, and switching between subluminal to superluminal propagation by tuning its fields.

Kerr effect in Y-configuration double-quantum-dot system

We have introduced a Y-configuration model from the double-quantum-dot (QD) system to study third-order Kerr nonlinearity based on the density-matrix method. Inhomogeneity in QDs has been included in the calculations of the real (Kerr) and imaginary (absorption) parts of the density matrix, which has not been covered in the earlier Kerr calculations. Our system exhibits high controllability with a single parameter. Giant Kerr dispersion, propagation without distortion, wide electromagnetic-induced transparency, and switching between subluminal to superluminal propagation are obtained by tuning its fields. Controlling and cycling fields can also control the system in addition to the pump field.

Kerr effect in quantum dot structure

A three-level ladder QD system is used to study Kerr effect in QD structures. Inhomogenous broadening is included where it is shown to be critical in calculating Kerr effect in QDs. Signal detuning is shown to control Kerr dispersion.

Rational W-shaped solitons on a continuous-wave background in the Sasa-Satsuma equation.

We investigate the solution in rational form for the Sasa-Satsuma equation on a continuous background which describes a nonlinear fiber system with higher-order effects including the third-order dispersion, Kerr dispersion, and stimulated inelastic scattering. The W-shaped soliton in the system is obtained analytically. It is found that the height of hump for the soliton increases with decreasing the background frequency in certain parameter regime. The maximum height of the soliton can be three times the background's height and the corresponding profile is identical with the one for the well-known eye-shaped rogue wave with maximum peak. The numerical simulations indicate that the W-shaped soliton is stable with small perturbations. Particularly, we show that the W-shaped soliton corresponds to a stable supercontinuum pulse by performing exact spectrum analysis.

Linear and nonlinear behaviors of light in a silicon ring resonator

We have investigated the nonlinear switching characteristics of an optical device using a double-coupler silicon ring resonator in the presence of the linear losses, the Kerr nonlinearity, two-photon absorption, free-carrier-induced absorption and dispersion, and thermo-optic, in which the general features of the nonlinear switching of the throughput and drop port signals are similar to a single-couple ring resonator and nonlinear Fabry–Perot resonator results, respectively. The interesting results of the double-coupler silicon ring resonator are the low switching power conditions and the linear amplification gain, in which the various applications can provide by controlling the input–output characteristic of silicon-based resonators, for instance, by controlling the coupling ratio, free-carrier lifetime, and input wavelength, which can provide the multiple applications for optical switches, logic gates, and memories. © 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:997–1000, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.25948

Nonlinear switching in silicon-based ring resonators

In this paper, we analyzed and investigated the nonlinear switching characteristics of an optical device using a double-coupler silicon ring resonator in the presence of the linear losses, the Kerr nonlinearity, two-photon absorption, thermo-optic effects, free-carrier-induced absorption, and dispersion. Results obtained have shown that the general features of the nonlinear switching of the throughput and drop port signals are similar to a single-couple ring and nonlinear Fabry-Perot resonators, respectively. The interesting results of the double-coupler silicon ring resonator are the low switching power conditions and the linear amplification gain. The various applications can be provided by controlling the input-output of silicon-based resonators, for instance, by controlling the coupling ratio, free-carrier lifetime, and input wavelength, in which the multiple applications for optical switches, logic gates, and memories can be provided.

A compact split step Padé scheme for higher-order nonlinear Schrödinger equation (HNLS) with power law nonlinearity and fourth order dispersion

In this paper we propose a compact split step Padé scheme (CSSPS) to solve the scalar higher-order nonlinear Schrödinger equation (HNLS) with higher-order linear and nonlinear effects such as the third and fourth order dispersion effects, Kerr dispersion, stimulated Raman scattering and power law nonlinearity. The stability of this method has been proved. It has been shown as well that the CSSPS method gives the same results as classical numerical methods like the split step Fourier method and Crank–Nicholson (CN) method but it presents many advantages over theme. It is more efficient. This proposed scheme is well suited to higher-order dispersion effects and readily generalized for nonlinear and dispersion managed fibers. We tested this scheme for the case of the quintic nonlinearity and confirmed that this effect has no significant role on the propagation of single solitons.

Propagation of ultrashort optical pulses for nonconservative systems with higher order effect

The complex Ginzburg–Landau equation with three higher order terms (third-order dispersion, Kerr dispersion and self-frequency shift), which can describe the propagation of an ultrashort (subpicosecond or femtosecond) optical pulse in optical fibre systems is studied. Stable propagation of a soliton-like bright pulse is obtained numerically not only in negative and zero group velocity dispersion domains but also in the positive group velocity dispersion domain. The main features of these optical pulses and the parameter regions where they exist are presented. In addition, it is found that in the positive group velocity dispersion domain, a bright pulse would change into a dark pulse under some special parameter conditions.

Quantum Theory of Femtosecond Soliton Propagation in Single-Mode Optical Fibers**The project partially supported by Natural Science Foundation of Hubei Province of China under Grant No. 0212012007

In this paper we have derived the generalized QNLS equation with considering the third-order dispersion and Kerr dispersion, which can be applicable to the femtosecond regime and is suitable for discussing the quantum properties of femtosecond solitons in single-mode optical fibers, as compared with its classical counterpart. This quantum operator equation can be solved by many methods such as the linearized perturbations and phase-space methods. Moreover, owing to the fact that this quantum equation is rather similar to its classical counterpart, all these methods can be facilitated to a great extent by citing correctly the classical results obtained before.

Simultaneous propagation of N dark solitons in optical fibres with higher order linear and nonlinear effects

We consider the simultaneous propagation of N fields in the normal dispersion regime of an optical fibre with higher order dispersion, stimulated Raman scattering and Kerr dispersion. The linear eigenvalue problem associated with the integrable form of the system equation is presented. Using the Hirota bilinear method, exact dark soliton solutions are explicitly derived.

Soliton-based ultra-high speed optical communications

Multi-terabit/s, ultra-high speed optical transmissions over several thousands kilometers on fibers are becoming a reality. Most use RZ (Return to Zero) format in dispersion-managed fibers. This format is the only stable waveform in the presence of fiber Kerr nonlinearity and dispersion in all optical transmission lines with loss compensated by periodic amplifications. The nonlinear Schrodinger equation assisted by the split step numerical solutions is commonly used as the master equation to describe the information transfer in optical fibers. All these facts are the outcome of research on optical solitons in fibers in spite of the fact that the commonly used RZ format is not always called a soliton format. The overview presented here attempts to incorporate the role of soliton-based communications research in present day ultra-high speed communications.

ALL-OPTICAL POWER LIMITING

We derived a numerical technique for the propagation of the electromagnetic field in a five-level reverse saturable absorber including the nonlinear Kerr effect and dispersion. The numerical method combines the split step beam propagation method and the Crank–Nicholson method. Using our numerical technique we observed new behavior, not previously observed nor predicted to our knowledge, including the temporal splitting caused by the dynamics of the carrier densities in a reverse saturable absorber and the enhancement of absorption due to the Kerr nonlinearity. Our numerical calculation enables the prediction of nonlinear absorption using material parameters such as the absorption cross-sections and decay rates. We can also investigate the interplay between the optical pulse properties such as the temporal pulse width, spatial radius, incident energy and the carrier dynamics and nonlinear absorption of the reverse saturable absorber.

Complete integrability ofN-coupled higher-order nonlinear Schrödinger equations in nonlinear optics

The coupled higher-order nonlinear Schrodinger equations are generalized to an N-coupled system which governs the propagation of N fields in a fibre with all the higher-order effects like third-order dispersion, Kerr dispersion and stimulated Raman scattering. The explicit Lax pair is constructed and the soliton solutions are obtained using the Darboux-Backlund transformation. Finally, the Hirota bilinear form for the N-coupled system equations is also presented.

Optical Solitons inN-Coupled Higher Order Nonlinear Schrödinger Equations

We consider the coupled higher order nonlinear Schr\"odinger (CHNLS) equations which govern the propagation of the fields in a birefringent fiber with all higher order effects like the third order dispersion, Kerr dispersion, and stimulated Raman scattering. We generalize the $2\ifmmode\times\else\texttimes\fi{}2$ Ablowitz-Kaup-Newell-Segur method to the $5\ifmmode\times\else\texttimes\fi{}5$ eigenvalue problem and construct the Lax pair. The exact soliton solutions are explicitly obtained using the Darboux-B\"acklund transformation. A similar case of study is extended to three coupled HNLS equations and hence generalized to $N$-coupled equations.

Optical Solitons in Presence of Kerr Dispersion and Self-Frequency Shift [Phys. Rev. Lett. 76, 3955 (1996)

Optical Solitons in Presence of Kerr Dispersion and Self-Frequency Shift [Phys. Rev. Lett. 76, 3955 (1996)