Effects of fourth-order fiber dispersion on ultrashort parabolic optical pulses in the normal dispersion regime

We propose a new method for the generation of both triangular-shaped optical pulses and flat-top, coherent supercontinuum spectra using the effect of fourth-order dispersion on parabolic pulses in a passive, normally dispersive highly nonlinear fiber. The pulse reshaping process is described qualitatively and is compared to numerical simulations.

Effects of fourth-order fiber dispersion on ultrashort parabolic optical pulses in the normal dispersion regime

We propose a new method for the generation of both triangular-shaped optical pulses and flat-top, coherent supercontinuum spectra using the effect of fourth-order dispersion on parabolic pulses in a passive, normally dispersive highly nonlinear fiber. The pulse reshaping process is described qualitatively and is compared to numerical simulations.

Identification of nonlinear systems by correlation using pseudorandom signals

This thesis is concerned with the measurement of the characteristics of nonlinear systems by crosscorrelation, using pseudorandom input signals based on m sequences. The systems are characterised by Volterra series, and analytical expressions relating the rth order Volterra kernel to r-dimensional crosscorrelation measurements are derived. It is shown that the two-dimensional crosscorrelation measurements are related to the corresponding second order kernel values by a set of equations which may be structured into a number of independent subsets. The m sequence properties determine how the maximum order of the subsets for off-diagonal values is related to the upper bound of the arguments for nonzero kernel values. The upper bound of the arguments is used as a performance index, and the performance of antisymmetric pseudorandom binary, ternary and quinary signals is investigated. The performance indices obtained above are small in relation to the periods of the corresponding signals. To achieve higher performance with ternary signals, a method is proposed for combining the estimates of the second order kernel values so that the effects of some of the undesirable nonzero values in the fourth order autocorrelation function of the input signal are removed. The identification of the dynamics of two-input, single-output systems with multiplicative nonlinearity is investigated. It is shown that the characteristics of such a system may be determined by crosscorrelation experiments using phase-shifted versions of a common signal as inputs. The effects of nonlinearities on the estimates of system weighting functions obtained by crosscorrelation are also investigated. Results obtained by correlation testing of an industrial process are presented, and the differences between theoretical and experimental results discussed for this case;

Line-by-line fiber Bragg grating made by femtosecond laser

In this letter, we report on the inscription of a fourth-order fiber Bragg grating made line-by-line in the optical fiber using a femtosecond laser. Strong Bragg resonance (~17 dB) and low insertion loss (~0.5 dB) were obtained with only 2000 periods. Measured refractive index change of these inscribed lines reaches up to 7 × 10-3. The grating was fully characterized and the low insertion loss together with low polarization-dependent loss were realized compared to gratings made by the point-by-point method. The high temperature annealing experiment shows the grating can survive up to at least 800°C.

Quasi-separation of the biharmonic partial differential equation

In this paper, we consider analytical and numerical solutions to the Dirichlet boundary-value problem for the biharmonic partial differential equation on a disc of finite radius in the plane. The physical interpretation of these solutions is that of the harmonic oscillations of a thin, clamped plate. For the linear, fourth-order, biharmonic partial differential equation in the plane, it is well known that the solution method of separation in polar coordinates is not possible, in general. However, in this paper, for circular domains in the plane, it is shown that a method, here called quasi-separation of variables, does lead to solutions of the partial differential equation. These solutions are products of solutions of two ordinary linear differential equations: a fourth-order radial equation and a second-order angular differential equation. To be expected, without complete separation of the polar variables, there is some restriction on the range of these solutions in comparison with the corresponding separated solutions of the second-order harmonic differential equation in the plane. Notwithstanding these restrictions, the quasi-separation method leads to solutions of the Dirichlet boundary-value problem on a disc with centre at the origin, with boundary conditions determined by the solution and its inward drawn normal taking the value 0 on the edge of the disc. One significant feature for these biharmonic boundary-value problems, in general, follows from the form of the biharmonic differential expression when represented in polar coordinates. In this form, the differential expression has a singularity at the origin, in the radial variable. This singularity translates to a singularity at the origin of the fourth-order radial separated equation; this singularity necessitates the application of a third boundary condition in order to determine a self-adjoint solution to the Dirichlet boundary-value problem. The penultimate section of the paper reports on numerical solutions to the Dirichlet boundary-value problem; these results are also presented graphically. Two specific cases are studied in detail and numerical values of the eigenvalues are compared with the results obtained in earlier studies.

Thin film bearings with phase change of lubricant

The possible evaporation of lubricant in fluid film bearings has been investigated theoretically and by experiment using a radial flow hydrostatic bearing supplied with liquid refrigerant R114. Good correlation between measured and theoretical values was obtained using a bespoke computational fluid dynamic model in which the flow was assumed to be laminar and adiabatic. The effects of viscous dissipation and vapour generation within the fluid film are fully accounted for by applying a fourth order Runge-Kutta routine to satisfy the radial and filmwise transverse constraints of momentum, energy and mass conservation. The results indicate that the radial velocity profile remains parabolic while the flow remains in the liquid phase and that the radial rate of enthalpy generation is then constant across the film at a given radius. The results also show that evaporation will commence at a radial location determined by geometry and flow conditions and in fluid layers adjacent to the solid boundaries. Evaporation is shown to progress in the radial direction and the load carrying capacity of such a bearing is reduced significantly. Expressions for the viscosity of the liquid/vapour mixture found in the literature survey have not been tested against experimental data. A new formulation is proposed in which the suitable choice of a characteristic constant yields close representation to any of these expressions. Operating constraints imposed by the design of the experimental apparatus limited the extent of the surface over which evaporation could be obtained, and prevented clear identification of the most suitable relationship for the viscosity of the liquid/vapour mixture. The theoretical model was extended to examine the development of two phase flow in a rotating shaft face seal of uniform thickness. Previous theoretical analyses have been based on the assumption that the radial velocity profile of the flow is always parabolic, and that the tangential component of velocity varies linearly from the value at the rotating surface, to zero at the stationary surface. The computational fluid dynamic analysis shows that viscous shear and dissipation in the fluid adjacent to the rotating surface leads to developing evaporation with a consequent reduction in tangential shear forces. The tangential velocity profile is predicted to decay rapidly through the film, exhibiting a profile entirely different to that assumed by previous investigators. Progressive evaporation takes place close to the moving wall and does not occur completely at a single radial location, as has been claimed in earlier work.

New developments in the study of optical parabolic pulses in normally dispersive fibers

We report two recent studies dealing with the evolution of parabolic pulses in normally dispersive fibres. On the one hand, the nonlinear reshaping from a Gaussian intensity profile towards the asymptotic parabolic shape is experimentally investigated in a Raman amplifier. On the other hand, the significant impact of the fourth order dispersion on a passive propagation is theoretically discussed: we numerically demonstrate flat-top, coherent supercontinuum generation in an all-normal dispersion-flattened photonic crystal fiber. This shape is associated to a strong reshaping of the temporal profile what becomes triangular.

New developments in the study of optical parabolic pulses in normally dispersive fibers

We report two recent studies dealing with the evolution of parabolic pulses in normally dispersive fibres. On the one hand, the nonlinear reshaping from a Gaussian intensity profile towards the asymptotic parabolic shape is experimentally investigated in a Raman amplifier. On the other hand, the significant impact of the fourth order dispersion on a passive propagation is theoretically discussed: we numerically demonstrate flat-top, coherent supercontinuum generation in an all-normal dispersion-flattened photonic crystal fiber. This shape is associated to a strong reshaping of the temporal profile what becomes triangular.

Two Bayesian treatments of the n-tuple recognition method

Two probabilistic interpretations of the n-tuple recognition method are put forward in order to allow this technique to be analysed with the same Bayesian methods used in connection with other neural network models. Elementary demonstrations are then given of the use of maximum likelihood and maximum entropy methods for tuning the model parameters and assisting their interpretation. One of the models can be used to illustrate the significance of overlapping n-tuple samples with respect to correlations in the patterns.