Group Velocity Dispersion Coefficient Research Articles

Bright, dark and other optical solitons with second order spatiotemporal dispersion

In this article, the single (bright, dark, singular) and combined (bright-dark, dark-singular) optical solitons have been extracted using extended fan sub-equation method. The corresponding integrability criteria, also known as constraint conditions, naturally emerge during the analysis of this model which is considered with the coefficients of group velocity dispersion and second order spatiotemporal dispersion.

Soliton interactions for a generalized variable-coefficient coupled higher-order nonlinear Schrödinger system in an inhomogeneous optical fiber

Studied in this paper are the interactions between bright–dark solitons for a generalized variable-coefficient coupled higher-order nonlinear Schrödinger system, which can be used to describe the simultaneous propagation of two ultrashort pulses in an inhomogeneous optical fiber. Under certain constraints, we obtain the analytic bright–dark one- and two-soliton solutions through the Hirota method and symbolic computation. With the help of this analytic treatment, properties of the single solitons, including the amplitudes, velocities, widths and central positions, are studied. Considering the amplification/absorption, group velocity and third-order dispersion effects, we study the interactions between two solitons with periodical variations of amplitudes and velocities. We find that the amplitudes of the two solitons depend solely on the amplification/absorption coefficient, while the velocities of the two solitons are related to the group velocity and third-order dispersion coefficients. Switches from the periodical interactions to head-on interactions and parallel propagation are presented.

Dynamics of optical solitons in dual-core fibers via two integration schemes

This article studies the dynamics of optical solitons in dual-core fibers with group velocity mismatch, group velocity dispersion and linear coupling coefficient under Kerr law nonlinearity via two integration schemes, namely, Q-function scheme and trial solution approach. The Q-function scheme extracts dark and singular 1-soliton solutions, along with the corresponding existence restriction. This scheme, however, fails to retrieve bright 1-soliton solution. Moreover, the trial solution approach extracts bright, dark and singular 1-soliton solutions. The constraint conditions, for the existence of the soliton solutions, are also listed. Additionally, a couple of other solutions known as singular periodic solutions, fall out as a by-product of this scheme. The obtained results have potential applications in the study of solitons based optical communication.

Entanglement, uncertainty and dispersion: a simple experimental demonstration of non-classical correlations

We perform an experiment to verify the presence of entanglement in photon pairs. By sending down-converted light through dispersive media with opposite group velocity dispersion coefficients, we overcome the minimum broadening of temporal correlation for classical light. Entanglement is proved via an inequality derived directly from Heisenberg’s uncertainty principle. We present a criterion to select a suitable down-conversion source. Moreover, we introduce a new method to analyze the temporal correlations between the entangled photons.

Formation of solitons in a waveguide at second harmonic generation

Second harmonic generation in a quadratic nonlinear waveguide is analyzed analytically and numerically. Formation of spatio-temporal solitons is demonstrated. They can form both positive and negative coefficients of group velocity dispersion due to the waveguide geometry. Analytical results are confirmed by computer simulations.

Dynamics of Peregrine combs and Peregrine walls in an inhomogeneous Hirota and Maxwell-Bloch system

Under investigation in this paper is an inhomogeneous Hirota-Maxwell-Bloch (IHMB) system which can describe the propagation of optical solitons in an erbium-doped optical fiber. The breather multiple births (BMBs) are derived with periodically varying group velocity dispersion (GVD) coefficients. Under large periodic modulations in the GVD coefficient of IHMB system, the Peregrine comb (PC) solution is produced, which can be viewed as the limiting case of the BMBs. When the amplitude of the modulation satisfies a special condition, the Peregrine wall (PW) that can be regarded as an intermediate state between rogue wave and PC is obtained. The effects of the third-order dispersion on the spatiotemporal characteristics of PCs and PWs are studied. Our results may be useful for the experimental control and manipulation of the formation of generalized Peregrine rogue waves in inhomogeneous erbium-doped optical fiber.

Nonautonomous solitons, breathers and rogue waves for the cubic-quintic nonlinear Schrödinger equation in an inhomogeneous optical fibre

Under investigation in this paper is a cubic-quintic nonlinear Schrödinger equation which can describe the propagation of ultrashort pulses in an inhomogeneous optical fibre. Lax pair and conservation laws are constructed from which the integrability of the equation can be verified. Through a gauge transformation, spectral problem for the equation is converted to an Ablowitz–Kaup–Newell–Segur spectral problem. Nonautonomous solitons and breathers are derived based on the Darboux transformation (DT), while nonautonomous rogue waves are obtained via the generalized DT. Influence of the group-velocity dispersion, gain-or-loss coefficient and group-velocity coefficient on the propagation and interaction of the nonautonomous solitons, breathers and rogue waves is also discussed. The gain-or-loss coefficient influences the amplitude of nonautonomous soliton. The characteristic line and velocity for the nonautonomous soliton are dependent on the group-velocity dispersion and group-velocity coefficient, but independent of the gain-or-loss coefficient. For the second-order nonautonomous soliton, if the two spectral parameters have the same real part, the bound-state structure can be formed, and the intensity becomes amplified in the attractive procedure. There exist two types of the nonautonomous breathers. Quasi-periods for the nonautonomous breathers are given, and effects of those coefficients on the quasi-periods are also discussed: The group-velocity dispersion can influence the trajectories of the nonautonomous breathers and rogue waves, while the gain-or-loss coefficient affects the backgrounds for the nonautonomous breathers and rogue waves

Breather transition dynamics, Peregrine combs and walls, and modulation instability in a variable-coefficient nonlinear Schrödinger equation with higher-order effects.

We study a variable-coefficient nonlinear Schrödinger (vc-NLS) equation with higher-order effects. We show that the breather solution can be converted into four types of nonlinear waves on constant backgrounds including the multipeak solitons, antidark soliton, periodic wave, and W-shaped soliton. In particular, the transition condition requiring the group velocity dispersion (GVD) and third-order dispersion (TOD) to scale linearly is obtained analytically. We display several kinds of elastic interactions between the transformed nonlinear waves. We discuss the dispersion management of the multipeak soliton, which indicates that the GVD coefficient controls the number of peaks of the wave while the TOD coefficient has compression effect. The gain or loss has influence on the amplitudes of the multipeak soliton. We further derive the breather multiple births and Peregrine combs by using multiple compression points of Akhmediev breathers and Peregrine rogue waves in optical fiber systems with periodic GVD modulation. In particular, we demonstrate that the Peregrine comb can be converted into a Peregrine wall by the proper choice of the amplitude of the periodic GVD modulation. The Peregrine wall can be seen as an intermediate state between rogue waves and W-shaped solitons. We finally find that the modulational stability regions with zero growth rate coincide with the transition condition using rogue wave eigenvalues. Our results could be useful for the experimental control and manipulation of the formation of generalized Peregrine rogue waves in diverse physical systems modeled by vc-NLS equation with higher-order effects.

V-shaped dark solitons in inhomogeneous optical fibers

Soliton control offers novel conceptual opportunities for all-optical shaping, switching and routing of optical signals encoded in soliton formats. In this paper, V-shaped dark solitons propagation in inhomogeneous optical fibers are investigated to carry out soliton control. Analytic dark soliton solutions for the variable coefficient nonlinear Schrödinger equation are obtained with the Hirota method. The group velocity dispersion coefficient of inhomogeneous optical fibers is chosen to be the tanh function, and the influences of corresponding parameters are analyzed. Results might be of potential applications in the design of all optical switches and pulse signal converters in ultra-fast optics.

Nonautonomous soliton, controllable interaction and numerical simulation for generalized coupled cubic–quintic nonlinear Schrödinger equations

The study of soliton interactions is a significance for improving pulse qualities in nonlinear optics. In this paper, a generalized coupled cubic–quintic nonlinear Schrodinger (GCCQNLS) equation with the group-velocity dispersion, fiber gain-or-loss and nonlinearity coefficient functions is studied, which describes the evolution of a slowly varying wave packet envelope in the inhomogeneous optical fiber. In particular, based on the similarity transformation, we report several families of nonautonomous wave solutions of the GCCQNLS equation. It is reported that there are possibilities to manipulate the interactions of nonautonomous wave solution through manipulating nonlinear and gain/loss functions. Interactions between the different-type bright two solitons have been asymptotically analyzed and presented. And, the two parabolic-type bright solitons propagating with the opposite directions both change their directions after the interaction. Interactions between the linear-, parabolic- and periodic-type bright two solitons are elastic. At last, the numerical simulations on the evolution and collision of two soliton solutions are performed to verify the prediction of the analytical formulations. We present the general approach can provide many possibilities to manipulate soliton waves experimentally and consider the potential applications for the optical self-routing, non-Kerr media and Bose–Einstein condensates (BEC).

Conservation laws, bilinear Bäcklund transformations and solitons for a nonautonomous nonlinear Schrödinger equation with external potentials

Under investigation in this paper is a nonautonomous nonlinear Schrödinger equation with external potentials, which can govern the dynamics of nonautonomous solitons in the nonlinear optical medium non-uniformly distributed in both the transverse and longitudinal directions. Based on the Lax pair, we present an infinite sequence of the conservation laws. Bilinear forms, bilinear Bäcklund transformations, one-, two- and N-soliton solutions under a known variable-coefficient constraint are generated via the Hirota method. With G(t)=0 and R(t)B(t) being a constant, amplitude of the soliton remains unvarying during the propagation, where t is the scaled time, G(t) is the gain/loss coefficient, B(t), the group velocity dispersion coefficient, and R(t), the nonlinearity coefficient. If we set G(t) ≠ 0 or R(t)B(t) as a variable, the amplitude becomes varying. Due to the different choices of the linear oscillator potential coefficient α(t), periodic-, parabolic-, S- and V-type solitons are observed. Meanwhile, we find that α(t) has no influence on the soliton amplitude. Interaction between the two amplitude-unvarying solitons and that between the two amplitude-varying ones are displayed, respectively. The velocity of a moving soliton always keeps varying.

Group velocity dispersion of CdSSe/ZnS core–shell colloidal quantum dots measured with white light interferometry

We measure the group velocity dispersion coefficient of CdSSe/ZnS core–shell colloidal quantum dots in liquid suspension in the ∼700–900nm wavelength range using a white-light Michelson interferometer. Two different sizes of dots are investigated. In both cases, the group velocity dispersion coefficient decreases with increasing wavelength above the absorption edge in the dots. For quantum dots in which the linear absorption spectrum shows clear peaks, the absorption characteristics of the dots can be used to accurately model the wavelength-dependence of the group velocity dispersion coefficient.

Controllable Nonautonomous Rogue Waves in the Modified Nonlinear Schrödinger Equation with Distributed Coefficients in Inhomogeneous Fibers

Abstract Under investigation in this paper is an inhomogeneous modified nonlinear Schrödinger (MNLS) equation describing the ultrashort pulse dynamics with the distributed dispersion, self-phase modulation, self-steepening, and linear gain/loss. Nonautonomous rogue waves for the inhomogeneous MNLS equation are constructed via the modified Darboux transformation with the inhomogeneous parameters. The dynamical behaviours and main characteristics of the nonautonomous rogue waves in inhomogeneous fibers are discussed by analysing certain physical quantities. The inhomogeneous effects on the evolution of rogue waves are considered by virtue of the presented rational solutions with distributed coefficients. It is found that the group velocity dispersion (GVD) and linear gain/loss coefficients have effects on the trajectories and amplitudes of the rogue waves, respectively. Additionally, an intriguing composite rogue wave of the inhomogeneous MNLS equation is revealed, owing to the proper choice of the GVD coefficient. Our results could be useful for controlling the rogue waves in the dispersion-managed fiber system.

Analytic study on the generalized ( $$3+1$$ 3 + 1 )-dimensional nonlinear Schrödinger equation with variable coefficients in the inhomogeneous optical fiber

Studied in this paper is a (\(3\,+ 1\))-dimensional nonlinear Schrodinger equation with the group velocity dispersion, fiber gain-or-loss and nonlinearity coefficient functions, which describes the evolution of a slowly varying wave packet envelope in the inhomogeneous optical fiber. With the Hirota method and symbolic computation, the bilinear form and dark multi-soliton solutions under certain variable-coefficient constraint are derived. Interactions between the different-type dark two solitons have been asymptotically analyzed and presented. Both velocities and amplitudes of the two linear-type dark solitons do not change before and after the interaction. The two parabolic-type dark solitons propagating with the opposite directions both change their directions after the interaction. Interaction between the two periodic-type dark solitons is also presented. Interactions between the linear-, parabolic- and periodic-type dark two solitons are elastic.

Strong group-velocity dispersion compensation with phase-engineered sheet metamaterials

Resonant metamaterials usually exhibit substantial dispersion, which is considered a shortcoming for many applications. Here we take advantage of the ability to tailor the dispersive response of a metamaterial introducing a new method of group-velocity dispersion compensation in telecommunication systems. The method consists of stacking a number of highly dispersive sheet metamaterials and is capable of compensating the dispersion of optical fibers with either negative or positive group-velocity dispersion coefficients. We demonstrate that the phase-engineered metamaterial can provide strong group-velocity dispersion management without being adversely affected by large transmission loss, while at the same time offering high customizability and small footprint.

A study on an actively mode-locked picosecond pulsed ytterbium-doped fibre laser with dispersion controlled by a photonic crystal fibre

We report on the generation of picosecond pulses in a modulator-based actively mode-locked ring cavity ytterbium-doped fibre laser by means of numerical simulation. A photonic crystal fibre (PCF) with large anomalous group velocity dispersion (GVD) and small nonlinearity can compensate the large normal GVD in the cavity accumulated by the ytterbium-doped fibre and the single mode fibre. Numerical models of the laser are established and solved by a simulation program. We study the laser behaviour and simulate the forming of the mode-locked pulses. The laser can easily produce stable pulses with 11.5 ps pulse width, 0.73 nJ pulse energy and 2.67 GHz repetition rate at 1 μm, which indicates that this laser can perfectly meet the demands of smaller pulse width and higher pulse energy as a seed laser. More numerical simulations are performed to test several key parameters, such as the small signal gain, the mode-locking order and the GVD coefficient of the PCF. The results show how these parameters affect the output pulses and help us to optimize the laser performance. The numerical simulation plays a guiding role in optimal design for later experiments.

Vector modulational instability induced by parametric resonance in periodically tapered highly birefringent optical fibers

We study the modulational instability induced by periodic variations of group-velocity dispersion and nonlinear coefficients in a highly birefringent fiber. We observe, for each resonance order, the presence of two pairs of genuine vector type sidebands, which are spectrally unbalanced between the polarization components for nonzero group-index mismatch, and one pair of balanced sidebands emerging and dominating at increasing group-index mismatch. As the conventional modulational instability manifests itself, it is partially suppressed by the proximity of these new unstable regions.

Dispersion compensation in Fourier domain optical coherence tomography using the fractional Fourier transform

We address numerical dispersion compensation based on the use of the fractional Fourier transform (FrFT). The FrFT provides a new fundamental perspective on the nature and role of group-velocity dispersion in Fourier domain OCT. The dispersion induced by a 26 mm long water cell was compensated for a spectral bandwidth of 110 nm, allowing the theoretical axial resolution in air of 3.6 μm to be recovered from the dispersion degraded point spread function. Additionally, we present a new approach for depth dependent dispersion compensation based on numerical simulations. Finally, we show how the optimized fractional Fourier transform order parameter can be used to extract the group velocity dispersion coefficient of a material.

Mid-infrared to telecom-band supercontinuum generation in highly nonlinear silicon-on-insulator wire waveguides

We demonstrate the generation of a supercontinuum in a 2 cm long silicon wire by pumping the wire with mid-infrared picosecond pulses in the anomalous dispersion regime. The supercontinuum extends from 1535 nm up to 2525 nm for a coupled peak power of 12.7 W. It is shown that the supercontinuum originates primarily from the amplification of background noise. A detailed analysis of the spectral components which are generated through phase-matched processes is applied to extract the group velocity dispersion and fourth-order dispersion coefficient of the silicon wire waveguide.

Group velocity dispersion of dyes in solution measured with white-light interferometry

The group velocity dispersion (GVD) coefficient of four different dyes in solution is measured as a function of wavelength and concentration using a white-light Michelson interferometer. We find that the wavelength dependence of the GVD can be considerably different at wavelengths above and below the absorption resonance in a dye. Above the absorption resonance, the dye molecules can make a strong, wavelength-dependent contribution to the GVD of the solution. Below the absorption resonance, the dye molecules tend to contribute negligibly to the GVD of the solution. We find that the contribution of the dye molecules to the GVD can be modeled quite accurately using a simple Lorentz model with parameters set using the measured linear absorption properties of the dye.