Alignment of Gaussian beams

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 theta(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) < or = 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.