Abstract

The early time dependence of the refractive-index variation leading to thermal blooming is known to develop rather slowly as O(t³) in very general conditions for a beam l(r) turned on at time t =0. This dependence may be established¹ by showing that the third derivative with respect to time is the first nonvanishing term in the Taylor expansion of the refractive-index change (proportional to the density change) in the medium about t= 0. However, the third derivative is proportional to the Laplacian of the beam intensity profile. This paper examines the interesting case in which the intensity distribution l(r) is discontinuous or has a discontinuous spatial derivative at a point leading to an infinite Laplacian. We show that in these circumstances, the early time development is O(t) at a point of discontinuity in the intensity and O(t²) at a point of discontinuity in its spatial derivative. These more rapid variations propagate to nearby points (where the Laplacian may be well behaved) at the speed of sound in the medium. When they arrive at such a nearby point, the initial t³ dependence at that point is augmented by more rapidly varying refractive-index contributions, O(t) or O(t²) or both as appropriate.

© 1987 Optical Society of America