We describe Shil'nikov chaos in the antiphase dynamics of a multimode
laser with intracavity second-harmonic generation. A theoretical model
of a laser operating with a sparse-mode spectrum has been studied usi
ng multimode rate equations, which include the effects of spatial grat
ings and birefringence of the intracavity optical elements. We use the
methods of dynamical systems theory to prove the existence of Shil'ni
kov behavior. Experimental observations of Shil'nikov chaos were carri
ed out with a miniature lithium-neodymium-tetraphosphate (LNP) laser w
ith an intracavity KTP doubler. Numerical modeling is in good agreemen
t with experimental results.