Asymptotic dominance by subdominant exponentials

A prevalent though unexpected asymptotic phenomenon occurs near anti–Stokes lines, on which two exponentials contributing to a function have the same absolute value: the subdominant exponential contribution can be larger than that from the dominant exponential. The phenomenon arises because the factors multiplying the two exponentials have different asymptotic forms. The boundary of the region of dominance by the subdominant exponential (DSE) is a line, for which an explicit general form is given; this shows that the region of DSE is asymptotically infinitely wide. The DSE line contains the zeros of the function, resulting from complete destructive interference between the two exponential contributions. Several examples are given; two have a physical origin in diffraction physics, and illustrate the fact that DSE can explain observed optical phenomena.