  We investigate the effect of an inhomogeneous exchange field on the proximity
effect in superconductor-ferromagnet hybrid structures within the
quasi-classical theory of superconductivity. As an example we study the
proximity effect in a superconductor-ferromagnet bilayer with an in-plane
spiral magnetic order in the ferromagnet. This model simulates a multiple
magnetic domain structure where the domain walls of the N\'{e}el type are of
equal size as the domains. Triplet correlations are induced in the bilayer by
the superconducting proximity effect, which are sensitive to the local
quantization axis of the exchange field in the ferromagnet. The coexistence of
singlet and triplet pair correlations in the bilayer results into a sensitivity
of the superconducting transition temperature on the spatial variation of the
exchange field in the ferromagnetic layer. We show that the inhomogeneity tends
to suppress the oscillating behavior of the pair amplitudes in the ferromagnet.
As a result, the superconducting critical temperature is found to be strongly
dependent on the spiral wavevector. We study the spin-dependent local density
of states and the effect of an induction of a spin magnetization in the
superconductor.
