Algebraic and geometric space-time analogies in nonlinear optical pulse propagation

We extend recently developed algebraic space-time analogies for the dispersive and nonlinear propagation of optical breathers. Geometrical arguments can explain the similarity of evolutionary behavior between spatial and temporal phenomena even when strict algebraic translation of solutions may not be possible. This explanation offers a new set of tools for understanding and predicting the evolutionary structure of self-consistent Gaussian breathers in nonlinear optical fibers.     

An improved nonlinear optical pulse propagation equation

A new equation for self-focusing of extremely focused short-duration intense pulses is derived using a method that treats diffraction and dispersion to all orders with nonlinearity present, and self-consistently determines the nonlinear derivative terms present in the propagation equation. It generalizes both the previous formulation of linear optical pulse propagation to the nonlinear regime, and the cw nonlinear regime propagation to the pulsed regime by including temporal characteristics of the pulse. We apply the new equation and propagate a tightly focused picosecond pulse in silica and explicitly show the effects of spatial-derivative nonlinear coupling terms.     

Chirped optical pulse propagation in saturating nonlinear media

Using a variational method, we have investigated the propagation characteristics of a chirped optical pulse in anomalously dispersive media possessing saturating nonlinearity. For the special case of uniform loss less media, the dynamics of the temporal width of the pulse is shown to be equivalent to an oscillator of unit mass which is executing its motion under some effective potential well. The potential is examined and four different types of behavior of the pulse width are noticed. The role of saturation parameter and the initial chirp in determining the propagation characteristics have been examined. It is found that, both high value of chirp and saturation are detrimental to stable pulse propagation. Particularly, the effect of chirp becomes severe with the increase in the value of saturation. We have shown that incorporation of saturation in the nonlinearity leads to the existence of bistable soliton. For the case of a lossy medium, net broadening of width takes place over many cycles of oscillation. The net broadening decreases with the increase in the value of saturation.     

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.     

Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures

The linear and nonlinear characteristics of optical slow-wave structures made of direct coupled Fabry–Pérot and Ring Resonators are discussed. The main properties of an infinitely long slow-wave structure are derived analytically with an approach based on the Bloch theory. The spectral behaviour is periodical and closed form expressions for the bandwidth, the group velocity, the dispersion and the linear and nonlinear induced phase shift are derived. For structures of finite length the results still hold providing that proper input/output matching sections are added. In slow-wave structures most of the propagation parameters are enhanced by a factor S called the slowing ratio. In particular nonlinearities result strongly enhanced by the resonant propagation, so that slow-wave structures are likely to become a key point for all-optical processing devices. A numerical simulator has been implemented and several numerical examples of propagation are discussed. It is also shown as soliton propagation is supported by slow-wave structures, demonstrating the flexibility and potentiality of these structures in the field of the all-optical processing.     

The period map for pulse propagation in nonlinear optical DM fibers

We have derived a simple recursion formula for the amplitude and chirp of the optical pulse propagating over a Dispersion Managed fiber with zero mean dispersion. We neglect dissipation and assume that the dispersion is constant along the adjacent legs of the waveguide, thus providing the applicability of the integrable nonlinear Schrödinger models within each leg. Choosing the legs long enough to ensure the formation of a self-similar profile, we apply the well-known asymptotic formulas for the nonsoliton initial pulses. Matching them through the interfaces of the legs, we get recursion formulas for the pulse amplitude and chirp. Our analytical results are justified by numerical simulations.     

Spectral interference measurement of nonlinear pulse propagation dynamics in optical fibers

Ultrafast pulse shaping and ultrafast pulse spectral phase-retrieval techniques are used in the spectral interference measurement of nonlinear pulse propagation dynamics in dispersion-shifted optical fiber. Nonlinear responses in both amplitude profile and phase profile of the pulses at zero-dispersion wavelength as well as at nonzero-dispersion wavelength are directly measured. A numerical simulation that uses a third-oder-dispersion-included nonlinear Schr?dinger equation gives excellent agreement with the experimental data.     

Study of ultra-fast optical pulse propagation in a nonlinear directional coupler

We showed that the application of a soliton in a nonlinear coupler does not show a better switching performance than a Gaussian pulse, unlike what the existing theory expected. Like the Gaussian pulse, a soliton could also suffer distortion, broadening, or narrowing in a nonlinear directional coupler. In addition, by using a new normalized format the linearly coupled nonlinear Schrödinger equations were investigated. For the first time, we found that both the coupling behavior and the switching performance of pulses in a nonlinear coupler depend on the product of the coupling coefficient and the dispersion length. We also showed that for a given nonlinear coupler with a Gaussian-like or soliton-like pulse input, switching performance and whether a pulse breaks up or not mainly depend on the input pulse width, not the pulse shape. PACS 42.65.Tg; 42.65.Wi; 42.81.Qb     

Generalized nonlinear coupled mode equations for ultrashort pulse propagation in optical fibers

A generalized model to describe the ultrashort pulse propagation in optical fibers with arbitrary modes present by taking advantage of the coupled mode approach is proposed. First the generalized nonlinear coupled mode equations in the frequency domain are derived exactly. Then the simplified forms for the weakly guiding optical fibers are obtained both in the frequency domain and in the time domain. Finally we discuss the particular forms in two special cases, i.e., ideal single-mode fibers and birefringent single-mode fibers.     

Polariton effect in nonlinear pulse propagation

The joint influence of the polariton effect and Kerr-like nonlinearity on the propagation of optical pulses is studied. The existence of different families of envelope solitary wave solutions in the vicinity of the polariton gap is shown. The properties of solutions depend strongly on the carrier wave frequency. In particular, solitary waves inside and outside the polariton gap exhibit different velocity and amplitude dependences on their duration.     

Modulational instability and space-time dynamics in nonlinear parabolic-index optical fibers

Beam propagation in multimode graded-index parabolic optical fibers in the presence of group-velocity dispersion and Kerr nonlinearity is theoretically investigated. It is shown that a modulational instability arising from the periodic spatial focusing of the beam takes place regardless of the sign of fiber dispersion, leading to a highly nonlinear space-time dynamics and the generation of ultrashort optical pulses.     

Analysis of femtosecond optical pulse propagation in one-dimensional nonlinear photonic crystals using finite-difference time-domain method

In this paper, we have used the finite-difference time-domain (FDTD) method to analyze the optical pulse propagation in a nonlinear, one-dimensional photonic crystal (1DPC). Hyperbolic secant pulses with various carrier wavelengths are utilized in this study. In a nonlinear regime, a 1DPC introduces a photonic band-gap whose central wavelength and width depend on the input pulse intensity. In the present work, three different cases are considered. These correspond to the carrier wavelengths of the incident pulses being out of, near to, and partially in the band-gap. For each case, the effect of nonlinearity on pulse propagation is investigated. Also, we have analyzed the two-frequency regime, in which each of the two pulses has a different carrier frequency (wavelength). This kind of study can be done directly with FDTD without any further computational burden but it is somewhat complicated using nonlinear coupled-mode equations (NLCME) and nonlinear Schrödinger equation (NLSE), which require separate treatments for each carrier wavelength.     

Chirped nonlinear pulse propagation in a dispersion-compensated system

We study nonlinear pulse propagation in an optical transmission system with dispersion compensation. A chirped nonlinear pulse can propagate in such a system, but eventually it decays into dispersive waves in a way similar to the tunneling effect in quantum mechanics. The pulse consists of a quadratic potential that is due to chirp in addition to the usual self-trapping potential and is responsible for the power enhancement and the decay.     

Linear approximation in pulse propagation problems in nonlinear media

It seems obvious that the manifestation of nonlinear effects (such as shock wave and soliton formation) is possible only at comparatively high levels of nonlinearity. Nevertheless, there are well-known examples where a disturbance which is as small as one pleases ceases in time to be linear, and must be described in nonlinear terms. This, e.g., is the situation for the well-known Korteweg-de Vries (KdV) equations, which for an impulsive initial condition of definite sign has an asymptotic solution described by a set of solitons and by a rapidly oscillating wave packet. There will in fact always be at least one soliton asymptotically, no matter how small the initial pulse amplitude [1]. Another example is shock wave (triangular pulse) attenuation at large distances (or times) within the framework of the Burgers equation; the wave remains a shock wave even though its amplitude decreases to zero [1]. It is thus necessary to indicate a criterion which might be used to establish the nature of the asymptotic solution. The aim of the present note is the definition of such a criterion; that is, a relation between nonlinearity and dispersion (dissipation) in which nonlinear effects are manifested only above some threshold level.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 21, No. 11, pp. 1706–1708, November, 1978.     

Three-dimensional optical storage inside transparent materials: errata

In our recent Letter1 a line of text was dropped in printing. On p. 2024 the beginning of the paragraph above Fig. 3 should read as follows: "Surprisingly, the 0.5-muJ pulse energy used in these microexplosions...".     

A variational approach of nonlinear dissipative pulse propagation

A variational technique to deal with nonlinear dissipative pulse propagation is established. By means of a generalization of the Kantorovitch method, suitable for non-conservative systems, we are able to cope with an extended nonlinear Schr?dinger equation (NLSE) which describes pulse propagation under the influence of nonlinear loss and/or gain, in particular, in the presence of two-photon absorption (TPA). Based on the characteristics of the exact solution of the NLSE in the absence of TPA, we investigate the effects of frequency dispersion of the nonlinear susceptibility associated to the two-photon resonance, obtaining the necessary conditions for a solitary wave solution, even in the presence of a self-steepening term. Received: 4 August 1997 / Received in final form: 25 November 1997 / Accepted: 14 January 1998     

Nonparaxial equation for linear and nonlinear optical propagation

The formalism of coupled-mode theory, specialized to the continuum of radiation modes, allows us to extend the standard parabolic wave equation to include nonparaxial terms and vectorial effects, and, in particular, to generalize the nonlinear Schr?dinger equation that describes propagation in the presence of an intensity-dependent refractive index.