We study via Carleman estimates the sharpest possible exponential decay for {it waveguide} solutions to the Laplace equation $$(partial^2_t+triangle)u=Vu+Wcdot(partial_t, abla)u,$$ and find a necessary quantitative condition on the exponential decay in the spatial-variable of nonzero waveguides solutions which depends on the size of $V$ and $W$ at infinity.
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