The third-order nonlinear intersubband optical absorption coefficient
within the conduction band of semiconductor superlattices with complex
bases have been calculated using the density matrix formalism includi
ng intrasubband and intersubband relaxation. The subband dipole moment
s z(ij)(k) and z(ii)(k) are first studied in superlattices with comple
x bases including a general coupled-well basis and a general step-well
basis. The results show that z(ij)(k) and z(ii)(k) are complicated fu
nctions of and strongly depends on the well parameters. The intersubba
nd transition optical absorption coefficient alpha(omega, I) is furthe
r studied. The numerical illustrations are also given.