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The ABCD matrix in graded index tapers used for beam expansion and compression

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Abstract

A new form is proposed for the ABCD matrix in a graded index taper with a large variation in cross section such as might be used for single-mode beam expansion. Expressions are given for the loss of power from the fundamental mode and the coupling efficiency between fibers when two tapers are used in an expanded beam connector. Exact solutions are found for linear tapers and for a class of tapers with zero slope ends. The distinction between adiabatic and nonadiabatic tapers is made clear from the functional form of the matrix in the linear case. Comparisons are made with previously published results and the effect of taper shape on the coupling efficiency is discussed.

© 1989 Optical Society of America

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