An asymptotic study of the effective-index method for the analysis of rectangular-core dielectric waveguides is given. Two ways of applying the effective-index method, depending on how the effective index is calculated, are considered, and expressions for the errors in the calculation of the propagation constant are derived. These expressions show explicitly how the accuracy of the method varies with the normalized frequency, the mode orders, the dimensions of the waveguide, and the relative refractive indices of the core and the surrounding media. Many novel properties of the method are revealed by these expressions. For example, it can be shown that the effective-index method can underestimate the propagation constant for a strip waveguide.
© 1991 Optical Society of America
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