Pulse propagation in a nonlinear dielectric slab waveguide

The evolution of an optical pulse in a single-mode, step index dielectric slab waveguide which is characterized by an intensity dependent dielectric function in the core and cladding regions is treated by means of differential equation techniques. A cubic order non-linearity is considered. The electromagnetic field distribution in the slab waveguide region satisfies a non-linear wave equation. This field can be represented in terms of even TE guided modes with a slowly varying envelope amplitude function.Then using the well known approximation, based on the slowly varying character of the amplitude function, a non linear partial differential equation is obtained for the amplitude function. As the coefficients of this equation depend on the distance across the transverse direction X, an averaging technique over x is applied to reduce the nonlinear partial differential equation into a form that is easily transformed to the so-called non-linear Scroedinger differential equation.This equation is then attacked by means of the well known Inverse Scattering method in the case of reflection less potentials. The single and double soliton solutions are obtained explicitly for a single-mode slab waveguide. Finally numerical results are presented in the time domain.     

Pulse propagation in one-dimensional nonlinear chains

Summary Several numerical computations are carried out to investigate the effects of the propagation of pulses (solitons and quasi-solitons) in one-dimensional nonlinear chains. Numerical results concerning the Toda lattice and a Coulomb-like lattice are discussed and compared. We consider lattices both with and without defects.

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Riassunto Si studiano gli effetti della propagazione di solitoni e di quasi solitoni in reticoli non lineari unidimensionali usando procedure di calcolo numerico. Si considerano il reticolo di Toda ed un reticolo di tipo Coulomb sia in presenza che in assenza di difetti.

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Резюме Используя процедуру численных вычислеий, исследуются эффекты распространения импульсов (солитонов или квази-солитонов) в одномерных нелинейных цепях. Обсуждаются и сравниваются численные редультаты, относящиеся к решетке тода и решетке кулоновского типа. Мы рассматриваем решетки с и вез дефектов.

     

Pulse propagation through multimode fibres

To evaluate their communication potential, measurements have been made on multimode glass fibres. Detector limited pulses of 180 psec risetime from a Ga-As laser were transmitted through various lengths of fibre. After a 120 m length the risetime was still not greater than 450 psec. Measurements with a mode locked He-Ne laser, done on shorter lengths of fibre, agreed with the above results.     

Cascadable all-optical inverter based on a nonlinear vertical-cavity semiconductor optical amplifier

We report, for the first time to our knowledge, the operation of a cascadable, low-optical-switching-power(~10 microW) small-area (~100 microm(2)) high-speed (80 ps fall time) all-optical inverter. This inverter employs cross-gain modulation, polarization gain anisotropy, and highly nonlinear gain characteristics of an electrically pumped vertical-cavity semiconductor optical amplifier (VCSOA). The measured transfer characteristics of such an optical inverter resemble those of standard electronic metal-oxide semiconductor field-effect transistor-based inverters exhibiting high noise margin and high extinction ratio (~9.3 dB), making VCSOAs an ideal building block for all-optical logic and memory.     

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.     

All-optical sampling exploiting nonlinear polarization rotation in a single semiconductor optical amplifier

An all-optical sampling scheme using a single semiconductor optical amplifier is proposed for analog signal processing. The analog optical signal is sampled by the probe pulse train through the nonlinear polarization rotation arising in the semiconductor optical amplifier. Conversion efficiency and total harmonic distortion are presented to evaluate the sampling linearity. In the experiment, 40 GSa/s all-optical sampling for 2.5 GHz analog optical signal is successfully demonstrated with commercially available fiber-pigtailed components. The results show that the fundamental conversion efficiency and the total harmonic distortion are 1.35 and 2.01% at the operating power of 5 mW, respectively. The proposed all-optical sampling requires only one semiconductor optical amplifier and has low power consumption, which is simple and has potential for photonic integration.     

Intraband effects on ultrafast pulse propagation in semiconductor optical amplifier

High bit-rate (>10 Gb/s) signals are composed of very short pulses and propagation of such pulses through a semiconductor optical amplifier (SOA) requires consideration of intraband phenomena. Due to the intraband effects, the propagating pulse sees a fast recovering nonlinear gain which introduces less distortion in the pulse shape and spectrum of the output pulse but introduces a positive chirping at the trailing edge of the pulse.     

Some observations on uncertainty propagation through a simple nonlinear system

This paper discusses a number of issues relating to the analysis of uncertain systems or data in the context of (low-frequency) structural dynamics. In order to illustrate potential problems in applying ‘classical’ uncertainty analysis methods to nonlinear systems, a simple nonlinear system is simulated and the breakdown of two standard approaches is demonstrated on data from the system. By relaxing the requirements of the analysis, it is shown that an alternative uncertainty theory gives useful qualitative information about the system. This motivates a discussion of how uncertainty frameworks should be chosen to suit the problem in hand and leads to a clustering of uncertainty problems in structural dynamics into three types: quantification, fusion and propagation.     

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     

Pulse propagation in a nonlinear system on the basis of coupled magnonic crystals

A structure on the basis of coupled magnonic crystals has been considered, for which a nonlinear model in the form of a system of nonlinear Schrödinger equations has been developed. By numerical simulation, the possibility of nonlinear branching of the signal has been shown, in which, depending on the input amplitude, pulses exit through different ports of the coupled structure. The results of this work can be used for developing magnonic crystal devices for functional processing of microwave signals.     

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.     

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.     

Nonstationary nonlinear phenomena in optical slab-waveguides. II. Pulse shaping by a nonlinear overlay

Pulse shaping of TE-polarized slab-guided Gaussian pulses, in resonance with two-level systems which form a nonlinear overlay, is considered. Pulse shortening for various incident pulse energies and different propagation length is investigated in detail numerically.     

Theory of pulse propagation and four-wave mixing in a quantum dot semiconductor optical amplifier

A theory, combining the relations of pulse traveling into quantum dot (QD) semiconductor optical amplifier (SOA) with the four-wave mixing (FWM) theory in these SOAs, is developed. Carrier density pulsation (CDP), carrier heating (CH), and spectral hole burning (SHB) contributions on FWM efficiency are discussed. Effect of QD ground state and wetting layer are included. An additional parameter appears in the gain integral relation of QD SOAs. An equation formulating pulses in the QD SOAs is introduced. We have found that FWM in QD SOAs is detuning and is pulse width dependent. For short pulses, CH is dominant at high detunings (10–100 GHz) while at higher detunings (>100 GHz) the SHB is the dominant one. Undesired paunch behavior is shown in QD SOAs then, CDP must be reduced.     

On the velocity of propagation of a signal in nonlinear optical media

The maximum velocity of propagation of a signal, which is defined as the velocity of propagation of the wave front, is considered for electromagnetic waves in nonlinear media. It is shown that the magnitude of velocity is determined to a considerable extent on the form of the constitutive equation defining the relation between the polarization of the medium with the radiation field strength. In the noninertial nonlinearity model, this velocity may be smaller (in media with self-focusing nonlinearity) or larger (defocusing nonlinearity) than the velocity of light in vacuum. For real nonlinear media, for which the inertia of their response is taken into account, the wave front velocity coincides with the velocity of light in vacuum.     

Passively mode-locked fiber laser based on nonlinear optical loop mirror with semiconductor optical amplifier

We propose a novel passively mode-locked fiber laser based on nonlinear optical loop mirror with semiconductor optical amplifier (SOA). Its operation principle is based on the creation of a polarization asymmetry between the counter propagating beams, through the use of a SOA and a polarization controller in the loop. Stable pulse train with duration of 2 ns (FWHM) and repetition rate of 257.7 MHz has been experimentally obtained. Theoretical simulation results in well agreement with the experimental results are also presented.     

Spectral broadening of femtosecond pulses in an nonlinear optical fiber amplifier

A promising method for the generation of a supercontinuum with a high spectral power density based on the spectral broadening of ultrashort pulses in a fiber amplifier is considered. The advantage of the method, as compared to the conventional way of the supercontinuum generation in a microstructure fiber, is a lower pulse spectral broadening rate, which allows one to achieve higher SC spectral power densities. The initial stage of the supercontinuum generation in an ytterbium fiber amplifier (a fiber core diameter of 7 μm) with side pumping from an array of laser diodes with a total power of 8 W at a wavelength of 976 nm is experimentally studied. Yb:KYW laser pulses with a duration of 250 fs, a central wavelength of 1046 nm, and an average power of 150 mW have been supplied to the input of the amplifier. In this case spectrally broadened radiation with an average spectral power density of higher than 65 mW/nm and a spectrum width of 50 nm has been obtained.     

Pattern stabilization through parameter alternation in a nonlinear optical system

We report the first experimental realization of pattern formation in a spatially extended nonlinear system when the system is alternated between two states, neither of which exhibits patterning. Dynamical equations modeling the system are used for both numerical simulations and a weakly nonlinear analysis of the patterned states. The simulations show excellent agreement with the experiment. The nonlinear analysis provides an explanation of the patterning under alternation and accurately predicts both the observed dependence of the patterning on the frequency of alternation and the measured spatial frequencies of the patterns.