Light Pulses In Optical Fibers Research Articles

Exactly Solvable Model for Nonlinear Pulse Propagation in Optical Fibers

The nonlinear Schrödinger (NLS) equation is a fundamental model for the nonlinear propagation of light pulses in optical fibers. We consider an integrable generalization of the NLS equation, which was first derived by means of bi‐Hamiltonian methods in [1]. The purpose of the present paper is threefold: (a) We show how this generalized NLS equation arises as a model for nonlinear pulse propagation in monomode optical fibers when certain higher‐order nonlinear effects are taken into account; (b) We show that the equation is equivalent, up to a simple change of variables, to the first negative member of the integrable hierarchy associated with the derivative NLS equation; (c) We analyze traveling‐wave solutions.

Bäcklund transformation in bilinear form for a higher-order nonlinear Schrödinger equation

Bäcklund transformation in bilinear form is presented for a higher-order nonlinear Schrödinger equation, which describes the propagation of ultrashort light pulses in optical fibers. With symbolic computation and starting from the Bäcklund transformation, the analytical soliton solution is obtained from a trivial solution and the inverse scattering transform scheme is also derived. Furthermore, the N -soliton solution in double Wronskian form is given, and the value of the arbitrary constant appearing in the Bäcklund transformation is determined for a transformation between the ( N − 1 ) and N -soliton solutions. The results obtained from the Bäcklund transformation might be valuable in optical communications.

EXACT SOLITON SOLUTIONS FOR THE HIGHER-ORDER NONLINEAR SCHRÖDINGER EQUATION

Based on the complex envelope ansatz method, the projective Riccati equation method and q-deformed hyperbolic functions, a method is developed for constructing a series of exact analytical solutions for higher-order nonlinear Schrödinger (HNLS) equation, which describes propagation of femtosecond light pulse in optical fiber under certain parametric conditions. With the help of symbolic computation, six families of new solitary wave solutions are obtained. The solitary wave solutions obtained by Li et al.18 are special cases of our solutions. The novel soliton solutions can describe W-shaped, bright and dark soliton properties in the same expression and their amplitude may approach nonzero when the time variable approaches infinity. Furthermore, the soliton propagation and solitons interaction scenario are discussed and simulated by computer.

Nonlinear Control of the Propagation of Optical Pulses in Doped Optical Fibers

Results of study of nonlinear processes occurring during the propagation of light pulses in optical fibers doped with atoms of rare-earth elements under conditions of atomic coherence and interference are presented. For a three-level Λ scheme of interaction, the linear (χ(1)) and nonlinear (χ(3)) susceptibilities of such a medium are calculated. It is shown that the coefficients of Kerr nonlinearity and nonlinear absorption can reach extremely large values and can be negative. The competition between linear and nonlinear processes in the Λ scheme allows one to obtain compensation regimes when the coefficients of dispersion or absorption of the optical fiber material vanish. The efficient control of the optical properties of such a system over wide limits proves to be possible owing to variations in the parameters of light pulses at the input of the medium. The necessary conditions for realizing regimes with “slow” light, as well as for self-compression of a probing pulse on ultimately small spatial scales in a doped optical fiber, were obtained.

Painlevé Analysis of a Higher-Order Nonlinear Schrödinger Equation

The Painleve test for integrability is applied to the Kodama-Hasegawa higher-order nonlinear Schrodinger equation which describes ultra-short light pulses in optical fibers. Only the four known integrable cases of this equation pass the test if the standard Painleve property is required. However, there is another case of this equation with the weak Painleve property and softer constraints on parameters. The integrability of this new case remains unkhown, and its possible kind is discussed.

Solitons Made Simple

Y.R. Shen Solitons are solitary waves, sometimes seen in water canals or as light pulses in optical fibers, that propagate for long distances without changing shape. This phenomenon is the result of a delicate balancing act between the tendency for waves to disperse and the nonlinear properties of the propagation medium. As a result of this interaction, the mathematical description of solitons can be highly complex. In his Perspective, Shen discusses a report in the same issue by Snyder and Mitchell that shows a much simpler way to mathematically approach solitons.

Time-resolved measurement of dynamic frequency chirp due to electrostriction mechanism in optical fibers

The electrostrictional excitation of acoustic waves by light pulses in optical fibers results in a timing jitter in soliton transmissions which, in turn, imposes a limitation on the transmission rate in long-distance communication systems. In this letter, we report for the first time an experimental investigation of this electrostriction effect by time-domain resolution dynamic frequency shift measurement in a copropagating probe and pulse signal arrangement. The experimental results show a very good agreement with the theoretical model reported by Dianov.

Envelope soliton propagation in media with temporally modulated dispersion.

The problem of soliton propagation in media with time dependent second-order dispersion is considered. We present analytical and numerical results for the variation of the soliton parameters and characteristics of the emitted radiation by the soliton, for the cases of a periodic or random modulation of the dispersion. In the case of a periodically modulated dispersion it is shown that resonant emission of linear waves is possible. The law of radiative decay of the soliton is found in both cases. Applications to the propagation of light pulses in optical fibers with variable dispersion are discussed.

Influence of noise on the propagation of light pulses in optical fibers

The method of path integration is used to solve the problem of the influence of weak noise on nonlinear propagation of an ultrashort light pulse in an optical fiber. A calculation is made of the correlation function and pulse intensity. It is shown that the coherent properties of a pulse deteriorate in a nonlinear medium. Noise also increases the pulse duration by an amount depending on the interaction length. It follows that steady-state propagation of pulses cannot be expected in the presence of noise.