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In this paper, a graphical method to solve the eigenvalue equations of the thin—filmoptical waveguideis proposed. This method can be applied to the thin-film optical waveguide of arbitrary parameters. The eigenvalue equation of the TE mode of one dimensional waveguide as Eq.(2) stands; it is a transcendental equation, for its solution, the author introduces two dimensionless parameters: ξ and η, the Eq. (2) is then transformed into a system of Eq. (7a) and (7b). The former, as shown by fig. 3, is a set of straight...

In this paper, a graphical method to solve the eigenvalue equations of the thin—filmoptical waveguideis proposed。 This method can be applied to the thin-film optical waveguide of arbitrary parameters。 The eigenvalue equation of the TE mode of one dimensional waveguide as Eq。explicit solution(2) stands; it is a transcendental equation, for its solution, the author introduces two dimensionless parameters: ξ and η, the Eq。 (2) is then transformed into a system of Eq。 (7a) and (7b)。 The former, as shown by fig。 3, is a set of straight lines and the latter is a family of curves, as shown by fig。

2。 The point of intersection of straight and the curved lines gives the solution of the eigenvalue equation。 To the designers of integrated optical circuits, it is important to know the dispersive character of the waveguide。 Hence the solution between the effective index of refraction and the dimensionless parameter ξ of the waveguide is derived from the Eq。 (3b)。 This relationship is represented by a circle in the Cartesian coordinates。 Through the geometrical relation furnished by this circle, it is very easy to describe the charateristic curves of dispersion of the waveguide。

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