Second-order Group Velocity Dispersion Research Articles

Optical nondegenerate solitons in a birefringent fiber with a 35 degree elliptical angle.

In this paper, we investigate the optical nondegenerate solitons in a birefringent fiber with a 35 degree elliptical angle. We derive the nondegenerate bright one- and two-soliton solutions by solving the coupled Schrödinger equation. The formation of nondegenerate solitons is related to the wave numbers of the solitons, and we further demonstrate that it is caused by the incoherent addition of different components. We note that the interaction between two degenerate solitons or a nondegenerate soliton and a degenerate soliton is usually inelastic. This is led to the incoherent interaction between solitons of different components and the coherent interaction between solitons of the same component. Through the asymptotic analysis, we find that the two degenerate solitons are elastic interactions under certain conditions, and analyzed the influence of the Kerr nonlinear intensity coefficient γ and the second-order group velocity dispersion β2 in this system on solitons: the velocity and amplitude of the solitons are proportional to |β2|, while the amplitude of the solitons is inversely proportional to γ. Two nondegenerate solitons are elastic interactions, but the phase of the soliton can be adjusted to make it inelastic. Furthermore, regardless of the situation mentioned above, total intensities of the solitons before the interaction are equal to that after the soliton interaction.

Various exact optical soliton solutions for time fractional Schrodinger equation with second-order spatiotemporal and group velocity dispersion coefficients

Various exact optical soliton solutions for time fractional Schrodinger equation with second-order spatiotemporal and group velocity dispersion coefficients

On-demand harnessing of photonic soliton molecules

Soliton molecules (SMs) are fundamentally important modes in nonlinear optical systems. It is a challenge to experimentally produce SMs with the required temporal separation (TS) in mode-locked fiber lasers. Here, we propose and realize an experimental scenario for harnessing SM dynamics in a laser setup. In particular, we tailor SMs in a mode-locked laser controlled by second-order group-velocity dispersion and dispersion losses: the real part of dispersion maintains the balance between the dispersion and nonlinearity, while the dispersion loss determines the balance of gain and losses. The experimental results demonstrate that the dispersion loss makes it possible to select desired values of the TS in bound pairs of SMs in the system. Tunability of a SM’s central wavelength and the corresponding hysteresis are addressed too. The demonstrated regime allows us to create multiple SMs with preselected values of the TS and central wavelength, which shows the potential of our setup for the design of optical data-processing schemes.

The distinctive feature of long time adiabatic modulation in the context of cnoidal wave and Akhmediev breaser interaction

For a nonintegrable system of two coupled nonlinear Schrödinger equations the adiabatic approximation is extended for long time interaction. The method enables analytical description of the modulation of a cnoidal wave by Akhmediev breather in an isotropic nonlinear gyrotropic medium with Kerr nonlinearity and second-order group-velocity dispersion. The conditions which must be fulfilled for stable propagation of the obtained solution with amplitude and frequency modulation are determined.

Spectral representation of adiabatic interaction of cnoidal waves in an isotropic gyrotropic nonlinear medium

We analyse the evolution of the spectra of an approximate solution of the adiabatic interaction problem of two waves with orthogonal circular polarisations in an isotropic gyrotropic nonlinear medium with the second-order group velocity dispersion. It is shown that a gradual ‘chaotisation’ of the approximate solution for the amplitude of a rapidly changing wave is associated with its non-equidistant frequency spectrum.

Adiabatic interaction between a dark soliton and a cnoidal wave with orthogonal circular polarizations in an isotropic gyrotropic nonlinear medium

An analytical solution to the one-dimensional (plane waves) nonintegrable problem of interaction (collision) of a dark soliton with a cnoidal wave (control and information signals with orthogonal circular polarizations) in an isotropic gyrotropic medium with Kerr nonlinearity and second-order groupvelocity dispersion is obtained in the adiabatic approximation. The asymptotic behavior of the obtained solution is considered. It is shown that the role of the control signal is reduced to strong amplitude and frequency modulation, which is localized only in the region of variation in the control signal intensity.

Consistent dynamics of the components of an elliptically polarised wave with zero mean amplitudes in a nonlinear isotropic gyrotropic medium in the adiabatic approximation

The adiabatic approximation is used to obtain an analytical solution to a nonintegrable problem of propagation of a plane elliptically polarised light wave with zero mean amplitudes of orthogonal circularly polarised field components through an isotropic gyrotropic medium with local and nonlocal components of Kerr nonlinearity and second-order group velocity dispersion. We describe the aperiodic evolution of bound (attributable to the medium nonlinearity) paired states, which are responsible for the propagation of two orthogonal polarisation components – cnoidal waves with significantly different periods.

Adiabatic modulation of a cnoidal wave by a breather with orthogonal circular polarization in an isotropic gyrotropic nonlinear medium.

An approximate analytical solution of the non-integrable problem of steady-state adiabatic interaction of a cnoidal wave with a breather is obtained. The solving algorithm is described by the example of one-dimensional problem of steady-state interaction of a plane cnoidal wave with circular polarization (the "information" signal) with orthogonally polarized rational soliton (the "control" signal) in an isotropic nonlinear gyrotropic medium with Kerr nonlinearity and second-order group-velocity dispersion. It is shown that such the interaction results in a strong amplitude and frequency modulation of the information signal and this modulation is localized in the region where intensity of the control signal changes.

Adiabatic interaction of a cnoidal wave and a soliton with orthogonal circular polarizations in an isotropic gyrotropic nonlinear medium

In the adiabatic approximation, an approximate analytical solution for a nonintegrable problem of interaction (collision) of a soliton with a cnoidal wave is obtained. An algorithm for solving is described by the example of a one-dimensional problem of interaction of a plane cnoidal wave with circular polarization (an ‘information’ signal) with an orthogonally polarized bright soliton (a ‘control’ signal) in an isotropic gyrotropic nonlinear medium with Kerr nonlinearity and second-order group-velocity dispersion. It is shown that, in addition to the amplitude modulation, localized within the soliton width (change of the ‘instantaneous’ amplitude of the cnoidal wave), a no less important consequence of the interaction is the drastic frequency modulation, localized in the same region (change of the ‘instantaneous’ frequency of the cnoidal wave).

All-optical soliton switching for the asymmetric fiber couplers

Coupled nonlinear Schrodinger (CNLS) equations for the fiber couplers with asymmetric self-phase modulation (SPM) and cross-phase modulation (XPM) are studied. With symbolic computation, one- and two-soliton solutions are obtained for the constant- and variable-coefficient CNLS equations. Switching dynamics of the solitons is discussed, and effects of the second-order group-velocity dispersion β 2, SPM coefficient σ 1, XPM coefficient σ 2 and Kerr nonlinear intensity γ on the all-optical switching properties are studied, while other coefficients in those equations are seen not to affect the all-optical switching properties. For the constant-coefficient CNLS equations, we find that |β 2| is proportional to the optical switching speed, and the optical extinction ratios increase with the decrease of σ 1/σ 2 and increase of |β 2| and γ. A numerical simulation by the split-step Fourier and Runge-Kutta methods is presented on the constant-coefficient CNLS equations to analyse the stability of the one- and two-solitons with the random initial perturbations. For the variable-coefficient CNLS equations, effects of σ 1/σ 2, β 2(z) = a 2 e bz and γ(z) = a 3 e bz on the optical switching are analyzed (where a 2, a 3 and b are all constants, and z gives the direction of propagation in the fiber couplers): optical switching speed increases with the increase of |a 2| and decrease of |b|, and optical extinction ratios increase with the increase of |a 2| and decrease of σ 1/σ 2 and |a 3|.

GVD effect and nonlinear pulse propagation in 40Gbit/s optical fiber communication systems

In this paper, group velocity dispersion (GVD) and second-order GVD effects are shortly discussed and then the limitations on the bit rate induced by dispersion or second-order GVD are estimated. For relative higher pulse energy and shorter pulse width in 40Gbit/s systems, self-phase modulation(SPM) is significant. The combined effect of GVD and SPM on the propagation pulses are analyzed through Nonlinear Schrödinger Equation(NLSE).

On the third harmonic generation in a medium with negative pump wave refraction

The propagation of the pump and its third harmonic pulses in a cubically nonlinear medium is considered theoretically, provided that the linear properties of the medium are characterized by a negative refractive index at the pump frequency and a positive refractive index at the harmonic frequency. For low-intensity interacting waves, the pump and third harmonic pulses propagate in opposite directions, but sufficiently intense pulses can produce a simulton—a solitary two-frequency wave that propagates in a certain direction as a single whole. The system of equations is investigated numerically for a model that, apart from the harmonic generation, includes the second-order group velocity dispersion and the nonlinear self- and cross-phase modulations of the interacting waves. The separation of the pump and harmonic pulses due to the difference in the directions of their group velocities and peculiarities of the Manley-Rowe relation for parametric processes in metamedia are discussed.

Spatiotemporal solitons in birefringent media near the zero-dispersion point

We present a new species of spatiotemporal solitons (STSs, alias light bullets) that may be formed through the interaction of two waves with different polarizations in a birefringent Kerr medium near the point at which the second-order group-velocity dispersion (GVD) vanishes in the presence of a uniform cw background in one component. The analysis is based on an asymptotic reduction of the two cross-phase, modulation-coupled (2+1)-dimensional nonlinear Schrodinger equations, incorporating the third-order GVD to the Davey-Stewartson (DS) systems of type I or II for the self-defocusing and focusing Kerr nonlinearity, respectively. The STSs are then predicted following the pattern of the dromion solutions of the DS-I system and lump solitons of the DS-II system. Strictly speaking, the solitons are unstable, but they are shown to be stable objects on experimentally relevant scales of the propagation distance.

Time-Frequency (Wigner) Analysis of Linear and Nonlinear Pulse Propagation in Optical Fibers

Time-frequency analysis, and, in particular, Wigner analysis, is applied to the study of picosecond pulse propagation through optical fibers in both the linear and nonlinear regimes. The effects of first- and second-order group velocity dispersion (GVD) and self-phase modulation (SPM) are first analyzed separately. The phenomena resulting from the interplay between GVD and SPM in fibers (e.g., soliton formation or optical wave breaking) are also investigated in detail. Wigner analysis is demonstrated to be an extremely powerful tool for investigating pulse propagation dynamics in nonlinear dispersive systems (e.g., optical fibers), providing a clearer and deeper insight into the physical phenomena that determine the behavior of these systems.

Periodic pulse sequences in nonlinear optical fibres with the third-order group-velocity dispersion

A new class of stationary periodic solutions of the nonlinear wave Schrödinger equation is studied taking the third-order group-velocity dispersion into account and their main properties and regions of existence are analysed. It is shown that a periodic sequence of pulses with a high contrast and a high repetition rate can be formed near the zero second-order group-velocity dispersion point.

High bit-rate OTDM transmission over standard fiber using mid-span spectral inversion and its limitations

An accurate modeling of very high bit-rate transmission systems over standard-fiber using mid-span spectral inversion (MSSI) is reported. As for the pulsewidth, comparison of simulations with experimental data in an 80-Gb/s transmission system over 106 km shows that second-order group velocity dispersion (GVD) is the limiting factor in this transmission scheme. Additionally, it is shown that even though first-order GVD can be compensated easily second-order GVD, is still remaining. It is pointed out that the performance of the system is very sensitive to the length of the different fiber spans.

Transmission of 2-ps optical pulses at 1550 nm over 40-km standard fiber using midspan optical phase conjugation in semiconductor optical amplifiers

We demonstrate transmission of 2-ps optical pulses at 1550 nm over 40 km of standard fiber by employing midspan optical phase conjugation in semiconductor optical amplifiers (SOAs). The second-order group-velocity dispersion of the fiber is completely compensated and the third-order dispersion becomes a major transmission limitation. This experiment shows that the midspan optical phase conjugation system using SOAs is applicable to ultrahigh bit rates greater than 100 Gb/s.

Effect of higher-order group-velocity dispersion on ultrashort pulses propagating in optical fibers

The effects of higher-order group-velocity dispersion (GVD) on spectral development and temporal shaping of ultrashort pulses propagating in normal dispersion domain of fibers are investigated by using an improved split-step Fourier method. It is verified that the second-order GVD contributes to asymmetry in the pulse power spectrum and temporal shaping. This asymmetry depends on the fiber length, the pulse duration, the pulse intensity, and the parameters of the second-order GVD. The effect of the higher-order GVD on the first-order soliton of an ultrashort pulse propagation in anomalous dispersion fibers is also calculated. Our results agree well with experiments and results obtained by solving the generalized nonlinear Schrödinger equation.

Analysis of a passively mode-locked self-starting all-fiber soliton laser

Modeling results are presented for a passively mode-locked figure-eight laser (F8L) supporting a linear polarization state. Starting from amplified spontaneous emission, the model produces soliton, chirped, red-shifted, ultra-short pulses. The self-starting conditions of the laser are investigated, and the erbium-doped fiber amplifier gain threshold to passively mode-lock the laser is determined as a function of the center coupler splitting ratio (C/sub r/). The influence of C/sub r/, as well as the effects of the cavity length (L/sub c/), first- and second-order group velocity dispersion to the F8L operating, parameters, and output pulse characteristics such as width, peak power, chirp, self-frequency shift and envelope distortion, are studied. >

Broadband dispersion compensation by using the higher-order spatial mode in a two-mode fiber

A fiber-optic technique for compensating both first- and second-order group-velocity dispersion in single-mode fiber spans is demonstrated by using the large waveguide dispersion that occurs for the higher-order (LP11) spatial mode in a two-mode fiber near cutoff. Complete restoration of 7-ps pulses that had been dispersed by a factor of 10 in 5 km of single-mode fiber is demonstrated over a 20-nm-wavelength window. First-order dispersion as large as −228 ps/(nm km) is observed for the LP11 mode at 1560 nm in the two-mode fiber.