A proposal for the bottom mirrors of resonant-cavity-enhanced GaAs homojunction far-infrared (FIR) detectors has been suggested and optimized based on undoped/doped GaAs layers with the Fresnel matrix method. With this kind of bottom mirror, the calculated absorption probability in the detector cavity increases two times over that in the normal detector structure. Comparing optical measurements have been carried out on n-GaAs homojunction FIR detector structures with and without the bottom mirrors, as well as a single optimized bottom mirror structure (without the detector cavity structure). The experimental FIR reflection and transmission results demonstrate well the theoretical design.