Alignment of Gaussian beams

Abstract

The design of a coupling between a semiconductor laser and a single-mode fiber, or between any two optical or acoustical elements that support Gaussian modes, is presented as a trade-off among coupling efficiency T_a, offset misalignment tolerance d_e, and angular misalignment tolerance θ_e. We show that these three parameters are subject to a trade-off limitation which takes the form $0<T_a^{1/2}{\theta }_e{d}_e\le \mathrm{\lambda }/\pi$, and we show how to design a coupling so that the upper bound on the alignment product $T_a^{1/2}{\theta }_e{d}_e$ is achieved.

© 1984 Optical Society of America

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