Abstract
The wave dislocations (phase singularities, optical vortices) in a light field represented by a complex scalar can react together; for example, a pair of opposite sign can merge and annihilate one another. This is analogous to the annihilation of two critical points in the fold catastrophe. The analogy with catastrophe theory goes further, with each mth-order polynomial solution of the Helmholtz equation corresponding to a cuspoid catastrophe of order m+1; nevertheless, there are very significant differences from catastrophe theory. The paper examines the pair creation and triplication reactions that are organized by the polynomial solutions up to m = 6.
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