We report on polymer nanocomposite films with spectrum down-converting properties that can be transferred using pulsed laser deposition (PLD) on silicon avalanche photodiodes (APD) for responsive and fast UV sensing. The proposed spectrum down-convertors use two types of nanoparticles (NPs) embedded in a colorless polyimide matrix: semiconductor CdSe/ZnS core-shell quantum dots (QDs) and the QDs made of rare-earth (RE) doped lead halide perovskites CsPbX3 (X stands for Br and Cl). These NPs have efficient down-conversion of UV radiation into visible and near-infrared (NIR) light matching spectral responsivity of Si APD with the photoluminescence quantum yield (PLQY) from 50 to 190%. Once an APD detects visible/NIR signal, it responds with an electronic gain >106 and a response time of ∼10 ns thus making rapid and strong UV sensing possible. Both types of NPs have strong absorption of UV and additionally protect the APD from degradation caused by UV radiation. CdSe/ZnS core-shell QDs convert UV spectrum in visible with a red peak at 631 nm using the down-shifting mechanism. The perovskite QDs doped with the ion of Yb3+ emitted in NIR with a peak at 980 nm due to the mechanism of down-conversion or quantum cutting. Both types of NPs were embedded in a polymer matrix and PLD deposited on a transparent substrate. We describe the results of characterization of the down-convertors using dynamic light scattering, X-ray diffraction, optical photoluminescence spectroscopy, and the photo-voltaic characteristics of silicon photodetectors integrated with the down-convertors.