We propose a vectorial basis-function expansion formulation for analyzing modal characteristics of the complex 2-D dielectric waveguides. To reduce costs and to shorten the product development cycle of integrated dielectric waveguides, it is crucial to be able to accurately compute the propagation constants ( ) as well as the electromagnetic field profiles of these complex optical devices so that the devices will perform as intended. Although waveguide propagation constants can be very accurately computed, accurate 2-D vector field solutions are harder to compute especially when there are degenerate modes with similar . We first derive the coupled differential equations of the two transverse magnetic field components which satisfy the continuous boundary conditions across all material interfaces. Then we investigate and verify the accuracy of this method on 1-D rectangular waveguide so that we can apply the technique to those more complex 2-D waveguides. And the one dimension case has exact solution, so we can compare with our bases expansion method to verify the accuracy. By means of linear combination of simple 2-D orthogonal bases, we expand the mode of rectangular dielectric waveguide. Through rigorous mathematical closed-form integration, we obtain the equivalent matrix whose eigenvalues and associated eigenvectors become the mode propagation constants and mode field distribution functions of the underlying 2-D dielectric waveguide. We can reduce the size of the problem by choosing appropriate boundary conditions via particular mode polarization desired. We examined optical fiber modes both the step-index profile and the graded-index profile to confirm the accuracy and feasibility of our method. We get at least five significant digits of propagation constant and detailed field description of the rectangular dielectric waveguide. Finally to do the rectangular-like case, even if the ridged ARROWs wavegude we can accurately get the fields. We believe that it is an effective method for modal analysis of 2-D complex dielectric-waveguides.

Univ., Diss.--Mainz, 2003.

Th. 3e cycle--Linguist.--Caen, 1988.

Since 1970, there have been many analytic theories studying waveguide modes in optical fibers. As the years progressed, the structure of optical fiber and its characteristics have undergone many changes. In recent years, the methods of analysis have also evolved into a more numerical style, such as the finite element and finite difference approach. In this thesis, we propose a semi-analytic, coupled Ez and Hz method for solving a multiple layered piecewise constant cylindrical dielectric waveguides. In our mathematical model, we are able to handle any arbitrary layered structure, in particular, the step-index fiber, W-type fiber, and dielectric tubes. Within each layer, we express the azimuthal field components in terms of Bessel functions whose coefficients are determined by two pairs of Ez and Hz components that define the layer. By equating the transverse fields (above) on either side of each layer interface the coupled field equations are derived. The field components are either real, or purely imaginary, this allows us to formulate our matrix in real arithmetic. Further simplification is possible by using the Wronskians of the Bessel functions. The resulting matrices are both real and symmetric, which is consistent with the reciprocity principle. Compared to the traditional formulation from the early 1970s, we have reduced the variables by half and extended the formulation to include any arbitrary number of layers. Numerous numerical results are presented in this thesis for all three types of fiber previously mentioned. Both lower-order modes as well as higher-order modes including TE, TM, HE, and EH modes are presented and discussed. Our formulations are compared to that of textbook formulas for the simple two-layered step index fiber, and are found to be identical.

Heinrich-Heine-Universiẗat, Magisterarbeit--Düsseldorf, 2003.

Zugl.: Düsseldorf, Univ., Magisterarbeit, 2003

Univ., Diss.--Ginevra, 2000.

Diss.--Erlangen-Nürnberg--Philosophische Fakultät, 1984. / Bibliogr. p. 271-280. Index.

Th.--Ecole du Louvre, 1951.

Thesis--Freiburg im Breisgau. / In Periodical Room.