Mathematical Analysis of the Guided Modes of Integrated Optical Guides

The paper considers a class of smoothly irregular integrated optical multilayer waveguides, whose properties determine the characteristic features of guided propagation of monochromatic polarized light. An asymptotic approach to the description of such electromagnetic radiation is proposed, in which the solutions of Maxwells equations are expressed in terms of the solutions of a system of four ordinary differential equations and two algebraic equations for six components of the electromagnetic field in the zero approximation. The gradient of the phase front of the adiabatic guided mode satisfies the eikonal equation with respect to the effective refractive index of the waveguide for the given mode.The multilayer structure of waveguides allows one more stage of reducing the model to a homogeneous system of linear algebraic equations, the nontrivial solvability condition of which specifies the relationship between the gradient of the radiation phase front and the gradients of interfaces between thin homogeneous layers.In the final part of the work, eigenvalue and eigenvector problems (differential and algebraic), describing adiabatic guided modes are formulated. The formulation of the problem of describing the single-mode propagation of adiabatic guided modes is also given, emphasizing the adiabatic nature of the described approximate solution of Maxwells equations.

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Guided modes of integrated optical guides. A mathematical study

IMA Journal of Applied Mathematics ◽

10.1093/imamat/60.3.225 ◽

1998 ◽

Vol 60 (3) ◽

pp. 225-261 ◽

Cited By ~ 9

Author(s):

A. Bonnet

Keyword(s):

Mathematical Study ◽

Guided Modes ◽

Integrated Optical

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Density waves in disk galaxies

Symposium - International Astronomical Union ◽

10.1017/s0074180900101135 ◽

1967 ◽

Vol 31 ◽

pp. 313-317 ◽

Cited By ~ 8

Author(s):

C. C. Lin ◽

F. H. Shu

Keyword(s):

Mathematical Analysis ◽

Spiral Structure ◽

Stellar System ◽

Collective Modes ◽

Disk Galaxies ◽

Spiral Pattern ◽

Density Waves ◽

The Galaxy ◽

Detailed Mathematical Analysis

Density waves in the nature of those proposed by B. Lindblad are described by detailed mathematical analysis of collective modes in a disk-like stellar system. The treatment is centered around a hypothesis of quasi-stationary spiral structure. We examine (a) the mechanism for the maintenance of this spiral pattern, and (b) its consequences on the observable features of the galaxy.

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Computing cell tractions from particle displacements on silicone rubber substrata

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100168542 ◽

1994 ◽

Vol 52 ◽

pp. 162-163

Author(s):

Tim Oliver ◽

Akira Ishihara ◽

Ken Jacobsen ◽

Micah Dembo

Keyword(s):

Plane Stress ◽

Linear Elasticity ◽

Silicone Rubber ◽

Mathematical Analysis ◽

Elastic Recovery ◽

Video Images ◽

Cell Traction Forces ◽

Latex Beads ◽

Cell Traction ◽

Better Than

In order to better understand the distribution of cell traction forces generated by rapidly locomoting cells, we have applied a mathematical analysis to our modified silicone rubber traction assay, based on the plane stress Green’s function of linear elasticity. To achieve this, we made crosslinked silicone rubber films into which we incorporated many more latex beads than previously possible (Figs. 1 and 6), using a modified airbrush. These films could be deformed by fish keratocytes, were virtually drift-free, and showed better than a 90% elastic recovery to micromanipulation (data not shown). Video images of cells locomoting on these films were recorded. From a pair of images representing the undisturbed and stressed states of the film, we recorded the cell’s outline and the associated displacements of bead centroids using Image-1 (Fig. 1). Next, using our own software, a mesh of quadrilaterals was plotted (Fig. 2) to represent the cell outline and to superimpose on the outline a traction density distribution. The net displacement of each bead in the film was calculated from centroid data and displayed with the mesh outline (Fig. 3).

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