Time domain simulation in photonics: A comparison of nonlinear dispersive polarisation models

The paper investigates and compares a range of different models currently used for modelling nonlinear optical phenomena. The models are implemented in the numerical time domain Transmission Line Modelling (TLM) method and include a Kerr model and different formulations of the Duffing model. The models are used to simulate an all-optical limiter for a CW input and results compared with ones available in the literature. This enables a comparison to be made between the different models, from which it is concluded that the Duffing model has some advantages, when modelling materials and phenomena involving more than one frequency, arising from its ability to describe dispersive effects. These conclusions are further supported by the simulation results obtained for a pulse input.     

Advection and dispersion in time and space

Previous work showed how moving particles that rest along their trajectory lead to time-nonlocal advection–dispersion equations. If the waiting times have infinite mean, the model equation contains a fractional time derivative of order between 0 and 1. In this article, we develop a new advection–dispersion equation with an additional fractional time derivative of order between 1 and 2. Solutions to the equation are obtained by subordination. The form of the time derivative is related to the probability distribution of particle waiting times and the subordinator is given as the first passage time density of the waiting time process which is computed explicitly.     

Effective and flexible analysis for propagation in time varying waveguides

The equivalence between the propagation of dispersive modal fields in two-dimensional waveguides, and plane waves in a one-dimensional plasma is presented. Exploitation of this equivalence allows a time domain variant of the effective index approach to be used to model dispersive waveguides problems very efficiently. A time domain integral equation is developed for this important practical case and the stability of a computer algorithm based upon it is improved by means of both a semi-implicit formulation and the use of a modified space–time mesh.     

Solvent detection using porous silicon optical waveguides

Since the first report on the use of porous silicon as an optical waveguide medium in 1995, significant development has been made towards the understanding and applicability of such material. Here, the introduction of solvents (acetone, methanol, and propan-2-ol) into the pores is shown to dramatically reduce the loss of the waveguides, in a reversible manner. Both the magnitude and duration of this effect are sensitive to the solvent introduced. In some waveguides, for example, the measured loss (at 0.633 μm) falls by as much as 34 dB cm⁻¹ on the introduction of acetone. Theoretical estimates of the effect of solvents on the interfacial scattering loss confirm this as the origin of the observed reductions. These results, combined with the fact that a substantial portion of the guided-mode field interacts with the solvent, indicate an enhanced sensitivity for sensor applications may be achievable.     

The very low-pressure dehydrogenation of cis-2-butene. The activation energy for 1,4-H2 elimination

Pyrolysis of cis-butene-2 under conditions of very low pressure (VLPP) has been studied in the range of 1100–1300°K. The principal products are butadiene and H₂, obtained in a unimolecular reaction. A competing reaction to form butene-l accounts for from 10% to 40% of the overall decomposition over the range. Using a «tight» model for the transition state and RRKM theory yields a high-pressure, unimolecular rate constant for the 1,4-H₂ elimination of where θ = 2.303RT in kcal/mol. There is some surface reaction of butadiene at these temperatures to yield H₂ + nonvolatile residue. Butene-l proceeds to decompose irreversibly to allyl + methyl radicals which have been observed directly. Comparison with related reactions leads to the conclusion that orbital symmetry-forbidden, 1,2-H₂ elimination from saturated organic compounds will have activation energies too high to observe.     

Excess enthalpies of binary mixtures of 2-ethyl-1-butanol with hexane isomers

Molar excess enthalpies, measured at 298.15 K in a flow microcalorimeter, are reported for binary mixtures of 2-ethyl-1-butanol with the five isomeric hexanes. The results are compared with previously published excess enthalpies for mixtures of 1-hexanol and 2-methyl-1-pentanol with the same hexane isomers.     

A procedure for obtaining quantum mechanical transformation of diagonalization from the classical

Using as an example two coupled harmonic oscillators, a transformation to normal coordinates is made using the classical-type simultaneous diagonalization of quadratic forms, and this is then used to develop a procedure for constructing the corresponding quantum mechanical transformation to normal coordinates. The total classical transformation is nonunitary, whereas the quantum mechanical is unitary as it has to be in order to satisfy Von Neumann's theorem. Since the classical transformation has definite steps and is a very straightforward procedure, this could be a very useful procedure for constructing the quantum mechanical transformation in many models, and/or an alternative method for many models.