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|Type of Document
||Vectorial expansion of complex dielectric waveguide modes with bi-orthonormal guiding mode bases|
|Date of Defense
||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.
||Tzyy-sheng Horng - chair|
Hidenori Taga - co-chair
Nai-hsiang Sun - co-chair
Hung-wen Chang - advisor
indicate accessible in a year|
|Date of Submission