On the basis of a non-local theory, the linear intersubband optical response in quantum wells embedded in an asymmetric microcavity is investigated. Starting from the Maxwell-Lorentz equations, the field in the quantum-well microcavity is derived, and the expression for the optical absorption is given. Detailed numerical simulations show that modifying the field modes via changing the number of distributed Bragg reflecting layers in front of the cavity can lead to significant change of the absorption spectrum: Rabi splitting of the absorption, more peaks appearing in the spectrum, even formation of an absorption bandgap, and the centre and width of the bandgap can be modified by changing the corresponding wavelength of the distributed Bragg reflecting layers.