Effects of dark soliton on self-deflection of bright soliton in a separate bright-dark soliton pair

Abstract

Based on the theory of one-dimensional separate soliton pairs formed in a serial photorefractive crystal circuit, the effects of the dark soliton on the self-deflection of the bright one in one separate bright-dark soliton pair are investigated by taking the diffusion term into account. The numerical results obtained by solving the nonlinear propagation equation show that the bright soliton moves on a parabolic trajectory in the crystal and its spatial shift changes with the input intensity of the dark soliton. These effects are further studied using perturbation analysis and the characteristics of the spatial shift of the bright soliton varying with the input maximum intensity of the dark soltion are analysed. The position of the bright soliton at the output surface of the crystal can be determined accurately according to the formula obtained from perturbation method.     

Cubic-quintic saturable nonlinearity effects on a light pulse strongly distorted by the fourth-order dispersion

Abstract

We analyze a useful process able to safeguard the fundamental soliton light pulse stability in a strongly perturbed environment by the fourth-order dispersion (FOD). This optical pulse propagation is described by the nonlinear Schrödinger equation (NLSE) with cubic–quintic saturable nonlinearities. Some pulse parameters, called collective variables (CVs) such as amplitude, temporal position, width, chirp, frequency shift and constant phase are obtained analytically. Numerical evolution of CVs and their stability are studied under a typical example to verify our analysis.     

Optical Double-resonance Spectra with Time-dependent Pulses

Abstract

The optical double-resonance spectrum for a three-level atom interacting with two monochromatic laser pulses with arbitrary temporal profiles is calculated by use of Light's perturbation theory. Unlike some earlier work, the theory is not restricted to exact resonance of the pump laser, or to pulse areas which are exact multiples of 2π. A variety of pulse profiles are investigated, and the spectra are found to depend strongly on the detuning of the pump laser.     

Optical solitons in some SIT type equations

Abstract

In this paper, we consider the SIT type equations with group velocity dispersion, Kerr nonlinearity, higher order dispersion, self-steepening and pumping effects and analyse the dynamics of ultra short pulse propagation in nonlinear resonant fibre. The nature of the pulse propagation is governed by the nonlinear Schrödinger-Maxwell Bloch (NLS-MB) type equations. Considering the isospectral and non-isospectral eigen value parameter, we generate the soliton solutions through the Bäcklund transformation method.     

Dispersion effects on the interaction of Airy beams and dark solitons

We simulate and analyse an Airy pulse coupled with a dark soliton in a single-mode fibre by solving the non-linear Schrödinger equation (NLSE). Simulations show that the group velocity parameter β₂₂ has a huge impact on the interaction between the Airy pulse and the dark soliton. At some values of β₂₂, a bright soliton arises from the Airy pulse. The intensity of the bright soliton reaches a maximum when β₂₂ takes a certain value. Meanwhile, the transmission distance and the primary energy of the Airy pulse are affected by the different values of β₂₂. However, when the Airy pulse propagates in a linear medium, varying the value of β₂₂ has only a slight impact on the interaction, and no bright soliton detaches from the Airy pulse. In brief, the dispersion effect has a large impact on the interaction of Airy pulses and dark solitons in a non-linear medium; however, dispersion has a lesser impact on interactions in a linear medium.     

Dynamics of subpicosecond dispersion-managed soliton in a fibre: a perturbative analysis

A model is studied which describes the propagation of a subpicosecond optical pulse in dispersion-managed fibre links. In the limit of weak chromatic dispersion management, the model equation is reduced to a perturbed modified NLS equation having a nonlinearity dispersion term. By means of the Riemann–Hilbert problem, a perturbation theory for the soliton of the modified NLS equation is developed. It is shown in the adiabatic approximation that there exists a unique possibility to suppress a perturbation-induced shift of the soliton centre at the cost of proper matching of the soliton width and nonlinearity dispersion parameter. In the next-order approximation, the spectral density of the radiation power emitted by a soliton is calculated.     

Spectral Filtering Effect of Fused Fibre Couplers in Femtosecond Fibre Soliton Lasers

Abstract

A fused fibre coupler has been used as a spectral filter in a femtosecond fibre soliton laser to eliminate the spectral sideband structure associated with periodic amplification of solitons in the regime where the characteristic soliton period of the generated pulses approaches that of the overall fibre laser loop length.     

Supercontinuum and rogue soliton generation by induced modulational instability in photonic crystal fibre

Abstract

We present an approach that enables active control of supercontinuum (SC) and rogue soliton (RS) generation through the modulation of a 500 fs input pulse by numerical simulations. The induced modulational instability contributes to the initial comb-like SC generation, which is fundamentally different from SC initiated by high-order soliton fission. The output spectrum shows great dependence on modulation frequencies and depths. It is interesting that we can manipulate the RS generation by adjusting the modulation parameters. And we also demonstrate the conditions which can be beneficial to RS generation: (i) very weak or large values of modulation depth; (ii) seeding in the vicinity of the peak of the modulational instability gain spectrum. Although RS degrades the smoothness of the SC, it is of great significance in the generation of tailored SC.     

Two-photon absorption of ultrashort electromagnetic pulses by negative halogen ions

Abstract

Within the framework of the perturbation theory, two-photon absorption of ultrashort electromagnetic pulses of a corrected Gaussian shape by negative halogen ions during the action of a pulse is calculated and analysed. Photoabsorption with excitation of an electron to a state with a specified energy is also considered. Particular attention is given to the dependence of the probability of these processes on the pulse duration. The features of two-photon absorption that are characteristic of sufficiently short pulses and do not take place in the monochromatic limit are revealed.     

MEH-PPV organic material as saturable absorber for Q-switching and mode-locking applications

ABSTRACT

Q-switched and mode-locked pulse generation in Erbium-doped fiber lasers (EDFLs) are demonstrated using Poly [2-methoxy-5-(2-ethylhexyloxy)-1,4-phenylenevinylene] (MEH-PPV) organic semiconductor material as a saturable absorber (SA) for the first time. The MEH-PPV was prepared in the form of a thin film having a modulation depth of 12% and saturation intensity of 40?MW/cm². The SA was placed in a laser cavity to produce a stable Q-switched operating at 1564.0?nm. The maximum repetition rate of 78.62?kHz, minimum pulse width of 3.54?µs and maximum pulse energy of 59.45?nJ were attained at 125.2?mW pump power. On the other hand, by incorporating an additional 100?m long single mode fiber, the mode locked EDFL self-started as the pump power was raised above 125.2?mW. The soliton pulse was obtained due to the enhancement of the nonlinearity in the cavity. The mode-locked laser operated at 1568.5?nm with a fixed repetition rate of 1.859?MHz and pulse width of 2.97?ps.     

Ti: Sapphire Pumped Femtosecond Optical Parametric Oscillator Exhibiting Soliton Formation

Abstract

The configuration and operation of a singly resonant Ti: sapphire pumped optical parametric oscillator (OPO) based on KTP is discussed. Cavity arrangements with and without dispersion compensation are described and the generation of sub-40 fs transform-limited pulses is highlighted. Evidence for soliton pulse formation in the OPO is presented and good quantitative agreement with existing theory is implied. Results of amplitude and phase noise measurements of the OPO are given and compared with those of the pump laser. Generation of pulses at several visible wavelengths by non-phase-matched processes is also briefly discussed.     

Generation of soliton and bound soliton pulses in mode-locked erbium-doped fiber laser using graphene film as saturable absorber

We report an observation of soliton and bound-state soliton in passive mode-locked fibre laser employing graphene film as a passive saturable absorber (SA). The SA was fabricated from the graphene flakes, which were obtained from electrochemical exfoliation process. The graphene flakes was mixed with polyethylene oxide solution to form a polymer composite, which was then dried at room temperature to produce a film. The film was then integrated in a laser cavity by attaching it to the end of a fibre ferrule with the aid of index matching gel. The fibre laser generated soliton pulses with a 20.7 MHz repetition rate, 0.88 ps pulse width, 0.0158 mW average output power, 0.175 pJ pulse energy and 18.72 W peak power at the wavelength of 1564 nm. A bound soliton with pulse duration of ~1.04 ps was also obtained at the pump power of 110.85 mW by carefully adjusting the polarization of the oscillating laser. The formation of bound soliton is due to the direct pulse to pulse interaction. The results show that the proposed graphene-based SA offers a simple and cost efficient approach of generating soliton and bound soliton in mode-locked EDFL set-up.     

Influence of nonlinear coupling of pulses on spatio-temporal compression

Abstract

Properties of a novel configuration of an optical (spatio-temporal) pulse compressor, that is based on a Kerr-type planar waveguide into which two pulses are simultaneously launched, are studied. It is assumed that the pulse which is the subject of the compression propagates in the anomalous dispersion regime, while the auxiliary pulse is in normal dispersion. The best parameters of the proposed compressor are obtained when duration of the auxiliary pulse is so large that this dispersion can be neglected, while energy of the second pulse is above the threshold of first-order soliton generation. It is observed that in such a configuration the compression occurs simultaneously with the generation of a soliton-like solution. It is argued that the proposed configuration with two simultaneously propagating pulses has advantages over the configuration with a single pulse, namely the maximal compression factor and the optimal length of the compressor is, respectively, more than 3 times larger and, at least, 10 times greater than the corresponding values of the compressor with a single pulse. It is also demonstrated that such a compressor can be considered as a universal device, since its operation depends only slightly on the initial parameters of the pulse subject to the compression.     

Bloch Wave Analysis of Dispersion and Pulse Propagation in Pure Distributed Feedback Structures

Abstract

The excitation and behaviour of monochromatic and pulsed optical Bloch waves in pure distributed feed-back structures are discussed and analysed. The Bloch wave approach, based on a detailed knowledge of the natural optical modes of the periodic structure, is complementary to the more commonly used coupled-wave approach. The inter-relationship between dispersion, field micro-structure and group velocity is discussed, and the effects of group-velocity and higher-order dispersion on pulse propagation treated. Questions about the usefulness of DFB structures for dispersion correction and soliton formation are addressed.     

Realization of wavelength conversion with hyperbolic secant femtosecond pulse in normal dispersion regime

Realization of wavelength conversion based on second-order femtosecond dark solitons with hyperbolic secant pulse is presented. This is achieved by introducing localized dispersion perturbation along the optical fiber. We demonstrate that an initial 30 fs second-order pulse decays to similar sub-pulses by applying perturbation using a step increment of β₂ from 6.3 to 15.75 ps² km^?1. This shows that the realization of a 1 × 2 channel wavelength converter for femtosecond pulses is possible. Recent research shows the possibility of realizing wavelength conversion generated from picosecond solitons neglecting nonlinear effects. However, employing the same method for femtosecond pulses fails due to the manifestation of nonlinear effects. In this paper, pulse deformation under different levels of perturbation was tested, and appropriate perturbation leading to similar sub-pulses is achieved.     

Dynamics near a minimal-mass soliton for a Korteweg–de Vries equation

We study soliton solutions to a generalized Korteweg–de Vries (KdV) equation with a saturated nonlinearity, following the line of inquiry of Marzuola, Raynor and Simpson for the nonlinear Schrödinger equation (NLS). KdV with such a nonlinearity is known to possess a minimal-mass soliton. We consider a small perturbation of a minimal-mass soliton and numerically shadow a system of ordinary differential equation (ODEs), which models the behaviour of the perturbation for short times. This connects nicely to analytic works of Comech, Cuccagna and Pelinovsky as well as of Grimshaw and Pelinovsky. These ODEs form a simple dynamical system with a single unstable hyperbolic fixed point with two possible dynamical outcomes. A particular feature of the dynamics is that they are non-oscillatory. This distinguishes the KdV problem from the analogous NLS one.     

Two-dimensional solitons in a Kerr cavity

Abstract

We study the existence and nature of soliton-like localized states in a passive cavity containing a Kerr medium driven by a plane-wave input field. As the background intensity is increased, these structures are always created in pairs, for topological reasons. The smaller ‘soliton’ is always unstable, while in two transverse dimensions the larger ‘soliton’ usually collapses to a singularity or decays.     

Mixed-type solitons for the coupled higher-order nonlinear Schrödinger equations in multi-mode and birefringent fibers

Abstract

In this paper, coupled higher-order nonlinear Schrödinger equations are studied for the ultrashort pulse propagation in such optical media as the multi-mode fibers and birefringent fibers. Through the Hirota method and symbolic computation, analytic mixed-type one- and two-soliton solutions are derived, and three sets of conditions for the non-singular solutions are given as well. Via the one-soliton solutions obtained, critical condition for the black and gray solitons is obtained analytically. Asymptotic analysis is carried out on the two-soliton solutions to derive the condition for the inelastic interaction. Evolution of the bound vector solitons, elastic and inelastic interactions between the two vector solitons are also investigated graphically. Moreover, after the inelastic interaction, the two bright solitons are observed to disappear, while the two dark ones form the new bound soliton.     

Information storage and retrieval by stopping pulses of light1

Abstract

Despite the importance of quantum interference and coherent population trapping to the theory of electromagnetically induced transparency (EIT), it is shown that the recent experiments which slow down and even stop a light pulse in a dielectric really rely on a linear, refractive index type theory. From this point of view and in considerable contrast, the experiment on degenerate self-induced transparency (SIT) done 27 years ago which slowed down an optical pulse (in principle to zero velocity) was based on an intrinsically nonlinear (soliton type) theory. In quantum mechanical terms both theories are developed at the level of expectation values only and at this level the two different theories come together in terms of the storage and retrieval of information. In the Appendix we analyse the nature of this information in terms of the quantum equations governing linear EIT and nonlinear SIT.     

Robustness of a biomolecular oscillator to pulse perturbations

Biomolecular oscillators can function robustly in the presence of environmental perturbations, which can either be static or dynamic. While the effect of different circuit parameters and mechanisms on the robustness to steady perturbations has been investigated, the scenario for dynamic perturbations is relatively unclear. To address this, the authors use a benchmark three protein oscillator design – the repressilator – and investigate its robustness to pulse perturbations, computationally as well as use analytical tools of Floquet theory. They found that the metric provided by direct computations of the time it takes for the oscillator to settle after pulse perturbation is applied, correlates well with the metric provided by Floquet theory. They investigated the parametric dependence of the Floquet metric, finding that the parameters that increase the effective delay enhance robustness to pulse perturbation. They found that the structural changes such as increasing the number of proteins in a ring oscillator as well as adding positive feedback, both of which increase effective delay, facilitates such robustness. These results highlight such design principles, especially the role of delay, for designing an oscillator that is robust to pulse perturbation.Inspec keywords: proteins, oscillators, biomolecular electronics, biotechnologyOther keywords: biomolecular oscillator, environmental perturbations, circuit parameters, steady perturbations, dynamic perturbations, benchmark three protein oscillator design, Floquet theory, pulse perturbation, Floquet metric, ring oscillator, effective delay, repressilator, analytical tools, parametric dependence, positive feedback