The nonlinear wave interaction in a periodic structure formed by alternatin
g semiconductor and insulator layers has been studied. The translation symm
etry of the structure is shown to be the reason for a number of peculiariti
es of the nonlinear interaction. Conditions of the resonance interaction be
tween the first and second harmonics are analyzed. The excitation of the se
cond harmonic via the interaction of the first spatial harmonics propagatin
g in the opposite directions is considered for the first time. An explanati
on is given for the significant enhancement of the wave interaction near th
e passband edge. (C) 2001 MAIK "Nauka/Interperiodica".