In this paper we show theoretically that cascaded surface solitons can exis
t on the surface of a medium with the bulk inversion symmetry center. Altho
ugh in the bulk of such media the second order nonlinearity vanishes, chi((
2)))= 0, the optical quadratic nonlinearity appears due to the contribution
of spatial derivatives of the fields to the nonlinear response, This nonli
nearity is localized at the surface and leads to the cascaded chi((2))) sur
face solitons. (C) 1999 Published by Elsevier Science B.V. All rights reser
ved.