Arbitrary Coupling Coefficient Research Articles

Doubly resonant sum-frequency generation from molecules with general harmonic potential surfaces

A many-body approach is used to analyse the doubly resonant infrared-visible sum-frequency generation from molecules with general harmonic potential surfaces. This multi-mode model includes arbitrary linear and quadratic electron-phonon coupling coefficients, and is valid at any temperature. Numerical simulations have been performed on a simple two-mode model with equilibrium position displacements, frequency shifts and Duschinsky rotation under electronic excitation. Our study leads us to propose these types of experiments to discriminate between the effects of linear and quadratic electron-phonon coupling terms.

Explicit evaluation of coupling coefficients for the most degenerate representations of SO(n)

Explicit results for particular coupling coefficients for the most degenerate representations of SO(n) are given. The isoscalar factors which allow a recursive calculation of arbitrary coupling coefficients from those of SO(3) are derived. 6j- and 9j-symbols for most degenerate representations are also briefly discussed.

Effect of crystallinity and swelling on the permeability and selectivity of polymer membranes

The conventional equations describing mass transport through membranes predict proportionality between flux and driving force. Experimental results inconsistent with this prediction are usually attributed to a concentration dependency of the diffusion coefficients of the species involved. It has now been found that, in addition to this effect, simplifications in the models and the neglect of crystallinity and swelling of the membrane material contribute in no small way to the noted deviations. On the basis of the well-known “solution-diffusion” theory a new permeation rate equation has been derived, which accounts for the various shortcomings mentioned and which is capable of predicting the large effects of crystallinity and swelling of the membrane material on permeability. This equation also expresses the mutual effects of permeants on their separation without the introduction of an arbitrary coupling coefficient, which is required in the conventional equations. A simplified procedure is proposed for calculating membrane separation of multicomponent mixtures, which is based on the assumption of an exponential concentration gradient inside the membrane in accordance with reported experimental observations. The exponential form, which differs for each composition and set of conditions, can be calculated from the boundary conditions of the membrane.

Numerical Solution of the Coupled-Power Equation in Step-Index Optical Fibers

By use of the finite-difference method of numerical analysis, a simple numerical solution is obtained for the coupled-power equation in optical fibers. For a specified arbitrary coupling coefficient and launching condition, the solution yields all the quantities of interest in the interior of the fiber: power distribution, attenuation, and far-field radiation pattern as functions of length. Results for buffered and cabled Corning fibers are reported. Attention is mainly focused on the influence of the microbends on the optical losses.

A theoretical analysis of mode-mixing in optical waveguides with nearest-neighbour mode coupling

Properties of the solutions of the coupled equations describing the flow of average mode power in optical waveguides are investigated. All of the important properties and their theoretical foundations are first reviewed for systems with arbitrary coupling and loss coefficients. It is then shown that, for the special class of systems with nearest-neighbour coupling, the solutions are expressible in terms of orthogonal polynomials. In particular, for systems obeying a quasi-uniform loss model and having coupling coefficients with simple dependence on mode number (uniform or linear), the solutions are associated with the classical polynomials. As illustrations of this analysis, the characteristics of optical power flow in three such systems are studied in detail. These include a slab-waveguide with uniform coupling, the corresponding cylindrical waveguide with uniform coupling, and a parabolic-index fibre with linear coupling dependence.

Transmission Distortion in Multimode Random Waveguides

We consider the coupled line equations for two-mode random media in which both modes travel in the same (forward) direction as a model for multimode millimeter waveguides and optical fibers, in which mode conversion at imperfections occurs primarily in the forward direction. Some exact general properties satisfied by the transfer function and the impulse response of such a system are given for an arbitrary coupling coefficient. A random stationary coupling coefficient with statistically independent successive values, and consequently a white spectrum (e.g., a white Gaussian or a Poisson noise), permits exact determination of transmission statistics; we obtain first- and second-order statistics in the time and frequency domains. No perturbation or other approximations are made in any of the above results, which are obtained directly from the coupled line equations. These results are used to study signal distortion in long guides. By straightforward extension of this work more complicated calculations can treat more forward modes, but not backward modes or nonwhite coupling coefficient spectra. In this paper the coupling coefficient is assumed frequency independent, and under certain conditions the signal distortion decreases as the mode conversion increases. In practical cases the coupling coefficients are frequency dependent and the above behavior is modified; the present work is extended to this important case in a companion paper.