Propagation Of Ultrashort Optical Pulses Research Articles

Bright and dark solitons and Bäcklund transformations for the coupled cubic-quintic nonlinear Schrödinger equations with variable coefficients in an optical fiber

Effects of the quintic nonlinearity for the ultrashort optical pulse propagation in a non-Kerr medium, or in the twin-core nonlinear optical fiber or waveguide, can be described by the coupled cubic-quintic nonlinear Schrödinger equations with variable coefficients. For such equations, a Lax pair and the infinitely-many conservation laws are constructed. Under certain variable-coefficient constraints, bilinear forms, bilinear Bäcklund transformations, bright/dark one-, two- and N-soliton solutions are derived via the Hirota method and symbolic computation. Those soliton solutions are merely related to the delayed nonlinear response effect, b(z). Graphical analyses on the soliton propagation and interaction suggest that b(z) can affect the bright/dark-soliton velocities but has no effect on their amplitudes. With the different choices of b(z), propagation of the linear-, periodic-, parabolic- and S-type bight and dark one solitons are seen, and different types of the interaction between the bright two solitons are displayed, such as the interactions between the bidirectional bright two ones, between the unidirectional bright two ones and between a moving bright one and a stationary one. Interactions between the linear-, S-, and parabolic-type dark two solitons are asymptotically analyzed and graphically illustrated as well, and those interactions are all elastic.

Noninstantaneous polarization dynamics in dielectric media

Third-order optical nonlinearities play a vital role for the generation and characterization of ultrashort optical pulses. One particular characterization method is frequency-resolved optical gating, which can be based on a large variety of third-order nonlinear effects. Any of these variants presupposes an instantaneous temporal response, as it is expected off resonance. In this paper we show that resonant excitation of the third harmonic gives rise to surprisingly large decay times, which are on the order of the duration of the shortest oscillator pulses generated to date. To this end, we measured interferometric third-harmonic frequency-resolved optical gating traces in TiO2 and SiO2, corroborating polarization decay times up to 6.5 fs in TiO2. This effect is among the fastest effects observed in ultrafast spectroscopy. Numerical solutions of the time-dependent Schrodinger equation are in excellent agreement with experimental observations. Our work (experiments and simulations) corroborates that a noninstantaneous polarization decay may appear in the presence of a 3-photon resonance. In turn, pulse generation and characterization in the ultraviolet may be severely affected by this previously unreported effect.

Dipole soliton solution for the homogeneous high-order nonlinear Schrödinger equation with cubic–quintic–septic non-Kerr terms

We consider a high-order nonlinear Schrödinger equation with third- and fourth-order dispersions, cubic–quintic–septic nonlinearities, self-steepening, and instantaneous Raman response. This equation models describes ultra-short optical pulse propagation in highly-nonlinear media. The ansatz solution of Choudhuri and Porsezian (in Ref. [16]) is adapted to investigate solutions composed of the product of bright and dark solitary waves. Parametric conditions for the existence of the derived soliton solutions are given and their stabilities are numerically discussed. These exact solutions provide insight into balance mechanisms between several high-order nonlinearities of different nature.

Integrability aspects and soliton solutions for the inhomogeneous reduced Maxwell–Bloch system in nonlinear optics with symbolic computation

In this paper, we investigate the inhomogeneous reduced Maxwell–Bloch system, which describes the propagation of the intense ultra-short optical pulses through an inhomogeneous two-level dielectric medium. Through symbolic computation, the integrability aspects including the Painlevé integrable condition, Lax pair and infinite conservation laws are derived. By virtue of the Darboux transformation method, one- and two-soliton solutions are generated on the nonvanishing background, including the bright solitons, dark solitons, periodic solutions and some two-soliton solutions. The asymptotic analysis method is performed to verify the elastic interaction between two solitons. Furthermore, by virtue of some figures, the dynamic properties of those solitons are discussed. The results may be useful in the study of the ultrashort pulses propagation in such situations as the model of the two-level dielectric media.

Dark–bright soliton interactions for the coupled cubic-quintic nonlinear Schrödinger equations in fiber optics

The coupled cubic-quintic nonlinear Schrödinger equations in fiber optics, which describe the effects of quintic nonlinearity on the ultrashort optical pulse propagation in non-Kerr media, are investigated. Using symbolic computation, we derive the dark–bright soliton solutions of such equations. By virtue of asymptotic analysis and graphical analysis, the overtaking and head-on elastic interactions of the two bright and dark solitons are presented. Mixed bound-state solitons also arise when all of the solitons propagate in parallel, displaying the beating effects due to the oscillatory terms, or displaying breather-like structures

Time-Domain BPM Technique for Modeling Ultra Short Pulse Propagation in Dispersive Optical Structures: Analysis and Assessment

In this work, the time-domain beam propagation method (TD-BPM) has been extended to model ultra-short optical pulse propagation in structures containing material dispersion. The method uses Pade approximant to solve the one-way non-paraxial wave equation. The TD-BPM is implemented and analyzed using several iterative numerical techniques to model the propagation of ultra-short pulses in optical waveguide structures containing Lorentz material dispersion. Systematic accuracy and efficiency assessment, compared to the FDTD, showed that the longitudinal and the temporal steps sizes can be a number of order of magnitude larger than the FDTD step sizes. It is concluded that the TD-BPM is suited for long dispersive dielectric structures interaction of short and ultra-short pulse propagation.

Conservation laws and Darboux transformation for the coupled cubic–quintic nonlinear Schrödinger equations with variable coefficients in nonlinear optics

In this paper, by Darboux transformation and symbolic computation we investigate the coupled cubic–quintic nonlinear Schrodinger equations with variable coefficients, which come from twin-core nonlinear optical fibers and waveguides, describing the effects of quintic nonlinearity on the ultrashort optical pulse propagation in the non-Kerr media. Lax pair of the equations is obtained, and the corresponding Darboux transformation is constructed. One-soliton solutions are derived; some physical quantities such as the amplitude, velocity, width, initial phases, and energy are, respectively, analyzed; and finally an infinite number of conservation laws are also derived. These results might be of some value for the ultrashort optical pulse propagation in the non-Kerr media.

Smooth and singular multisoliton solutions of a modified Camassa–Holm equation with cubic nonlinearity and linear dispersion

We develop a direct method for solving a modified Camassa–Holm equation with cubic nonlinearity and linear dispersion under the rapidly decreasing boundary condition. We obtain a compact parametric representation for the multisoliton solutions and investigate their properties. We show that the introduction of a linear dispersive term exhibits various new features in the structure of solutions. In particular, we find the smooth solitons whose characteristics are different from those of the Camassa–Holm equation, as well as the novel types of singular solitons. A remarkable feature of the soliton solutions is that the underlying structure of the associated tau-functions is the same as that of a model equation for shallow-water waves introduced by Ablowitz et al (1974 Stud. Appl. Math. 53 249–315). Finally, we demonstrate that the short-wave limit of the soliton solutions recovers the soliton solutions of the short pulse equation which describes the propagation of ultra-short optical pulses in nonlinear media.

Dynamics of ultra-short electromagnetic pulses in the system of chiral carbon nanotube waveguides in the presence of external alternating electric field

The paper addresses the propagation of ultra-short optical pulses in chiral carbon nanotubes in the presence of external alternating electric field. Following the assumption that the considered optical pulses are represented in the form of discrete solitons, we analyze the wave equation for the electromagnetic field and consider the dynamics of pulses in external field, their initial amplitudes and frequencies.

100 ps Optical pulse generator using laser diodes for visible light communication applications

ABSTRACTWe present a simple ultrashort optical pulse generator based on step recovery diode, short‐circuited transmission line and relaxation oscillation effect suppression with reduced dc bias. Experimental results achieved a 80‐ps optical pulse with 655 nm AlGaInP laser diode (LD) and a 200‐ps optical pulse with 420‐nm GaN‐based LD. © 2014 Wiley Periodicals, Inc. Microwave Opt Technol Lett 56:185–187, 2014

Ultrashort optical solitons in transparent nonlinear media with arbitrary dispersion

We consider the propagation of ultrashort optical pulses in nonlinear fibers and suggest a new theoretical framework for the description of pulse dynamics and exact characterization of solitary solutions. Our approach deals with a proper complex generalization of the nonlinear Maxwell equations and completely avoids the use of the slowly varying envelope approximation. The only essential restriction is that fiber dispersion does not favor both the so-called Cherenkov radiation, as well as the resonant generation of the third harmonics, as these effects destroy ultrashort solitons. Assuming that it is not the case, we derive a continuous family of solitary solutions connecting fundamental solitons to nearly single-cycle ultrashort ones for arbitrary anomalous dispersion and cubic nonlinearity.

Generalized Darboux transformation and rogue wave solutions for the higher-order dispersive nonlinear Schrödinger equation

In this paper, rogue wave solutions of the higher-order dispersive nonlinear Schrödinger equation are investigated, which describe the propagation of ultrashort optical pulse in optical fibers. The Nth-order rogue wave solutions with 2N + 1 free complex parameters are constructed via the generalized Darboux transformation method. As applications, rogue waves from the first to the fifth order are calculated according to different combinations of parameters. In particular, rogue waves dynamics and several new spatial–temporal structures are also discussed and exhibited to make a comparison with those of the nonlinear Schrödinger equation.

Chalcogenide glasses as a medium for controlling parameters of ultrashort IR pulses: II

The propagation of ultrashort optical pulses in planar chalcogenide glass waveguides with uniform or periodic claddings is considered. In comparison with silica waveguides a structure based on chalcogenide glass provides higher nonlinearity. This material has a high normal dispersion in the wavelength range of 1.5–3.5 μm. Periodic waveguide structures can be used to compensate for this dispersion. High-intensity laser pulses propagating in these structures undergo spectral broadening. The influence of the phase self-modulation of a pulse on its spectrum and width is analyzed using numerical simulations.

Multipole solitary wave solutions of the higher-order nonlinear Schrödinger equation with quintic non-Kerr terms

We consider a high-order nonlinear Schrödinger (HNLS) equation with third- and fourth-order dispersions, quintic non-Kerr terms, self steepening, and self-frequency-shift effects. The model applies to the description of ultrashort optical pulse propagation in highly nonlinear media. We propose a complex envelope function ansatz composed of single bright, single dark and the product of bright and dark solitary waves that allows us to obtain analytically different shapes of solitary wave solutions. Parametric conditions for the existence and uniqueness of such solitary waves are presented. The solutions comprise fundamental solitons, kink and anti-kink solitons, W-shaped, dipole, tripole, and fifth-order solitons. In addition, we found a new type of solitary wave solution that takes the shape of N, illustrating the potentially rich set of solitary wave solutions of the HNLS equation. Finally, the stability of the solutions is checked by direct numerical simulation.

Introduction to the OQE special issue on numerical simulation of optoelectronic devices NUSOD’12

This special issue ofOptical andQuantumElectronics contains a selection of papers that were presented at the 13th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD) in Vancouver, Canada, August 19–22 2013. NUSOD’13 was chaired by Lukas Chrostowski from the University of British Columbia, Canada and Joachim Piprek, NUSOD Institute, USA. The purpose of the NUSOD Conference is to provide a forum for scientists from research labs around the world to discuss the recent advances in the modelling of optoelectronic devices. This year the main topics included numerical modelling of light emitting diodes, photo-detectors, photonic crystal fibres, propagation of ultra-short optical pulses, photovoltaic and optical integrated devices. The papers collected in this special issue of Optical and Quantum Electronics provide a comprehensive representation of the topics discussed at the conference. The editorswish to thank all contributing authors for careful preparation of themanuscripts and the reviewers for their work and timely response. We now look forward to NUSOD’14 that will take place in Palma de Mallorca, Spain, September 1–4, 2014.

Optical rogue waves in the generalized inhomogeneous higher-order nonlinear Schrödinger equation with modulating coefficients

Higher-order dispersive and nonlinear effects (alias the perturbation terms) such as third-order dispersion, self-steepening, and the self-frequency shift play important roles in the study of ultra-short optical pulse propagation. We consider optical rogue wave solutions and interactions for the generalized higher-order nonlinear Schrödinger (NLS) equation with space- and time-modulated parameters. An appropriate transformation is presented to reduce the generalized higher-order NLS equation to an integrable Hirota equation with constant coefficients. This transformation allows us to relate a certain class of exact solutions of the generalized higher-order NLS equation to the variety of solutions of the integrable Hirota equation. In particular, we illustrate the approach in terms of the two lowest-order rational solutions of the Hirota equation as seeding functions, to generate rogue wave solutions localized in time that have complicated evolution in space, with or without the differential gain or loss term. We simply analyze the physical mechanisms of the obtained optical rogue waves on the basis of these constraints. Finally, the stability of the obtained rogue wave solutions is addressed numerically. The obtained rogue wave solutions may raise the possibility of related experiments and potential applications in nonlinear optics and other fields of nonlinear science, such as Bose–Einstein condensates and ocean waves.

Effect of the intrinsic nonlinearity on the propagation of ultrashort optical pulses in carbon nanotubes in dispersive nonmagnetic dielectric media

The Maxwell equations for the electromagnetic field that propagates in carbon nanotubes (CNTs) placed in dispersive nonmagnetic dielectric media are analyzed with allowance for the intrinsic nonlinearity of the medium. The dependences of the pulse on the initial pulse amplitude, dispersion constants, and nonlinearity are revealed.

Breathers and multi-soliton solutions for the higher-order generalized nonlinear Schrödinger equation

In this paper, the higher-order generalized nonlinear Schrödinger equation, which describes the propagation of ultrashort optical pulse in optical fibers, is analytically investigated. By virtue of the Darboux transformation constructed in this paper, some exact soliton solutions on the continuous wave (cw) background are generated. The following propagation characteristics of those solitons are mainly discussed: (1) Propagation of two types of breathers which delineate modulation instability and bright pulse propagation on a cw background respectively; (2) Two types propagation characteristics of two-solitons: elastic interactions and mutual attractions and repulsions bound solitons. Those results might be useful in the study of ultrashort optical solitons in optical fibers.

Symbolic computation on soliton dynamics and Bäcklund transformation for the generalized coupled nonlinear Schrödinger equations with cubic-quintic nonlinearity

In this paper, we study the generalized coupled nonlinear Schrödinger equations with the cubic-quintic nonlinearity and arbitrary coupling parameters which describe the effects of the quintic nonlinearity on the ultrashort optical soliton pulse propagation in the non-Kerr media. Dark–dark N- and bright–dark two-soliton solutions are derived with symbolic computation. The bilinear Bäcklund transformation and the corresponding one-soliton solution are also given. Interactions of the dark–dark solitons including the repulsive and coherent interactions are investigated analytically and graphically, which are different from those in previous studies. The relationship between the amplitude and the velocity of the dark soliton is studied, especially the soliton with the small amplitude catches up with the one with the large amplitude. Head-on and overtaking interactions of dark–dark solitons are presented. Interactions between a stationary dark soliton and another dark one are shown. The asymptotic analysis shows that the interaction of dark–dark two solitons is elastic. The periodic attraction and repulsion of the bright–dark two solitons in the bound state are also analyzed, which are in accordance with those in the bright–dark vector soliton studies but different from the asymmetric and symmetric stationary bound states of Manakov bright–dark solitons.

Spatio-temporal pulse propagation in nonlinear dispersive optical media

We discuss state-of-art approaches to modeling of propagation of ultrashort optical pulses in one and three spatial dimensions. We operate with the analytic signal formulation for the electric field rather than using the slowly varying envelope approximation, because the latter becomes questionable for few-cycle pulses. Suitable propagation models are naturally derived in terms of unidirectional approximation.