Future missions for astrophysical studies in the submillimeter region will need detectors with very high sensitivity and large fields of view. Bolometer arrays can fulfill these requirements over a very broad band. We describe a technique that enables bolometer arrays that use quarter-wave cavities to have a high spectral response over most of the submillimeter band. This technique is based on the addition on the front of the array of an antireflecting dielectric layer. The optimum parameters (layer thickness and distance to the array) are determined by a 2D analytic code. This general principle is applied to the case of Herschel PACS bolometers (optimized for the 60 to 210 μm band). As an example, we demonstrate experimentally that a PACS array covered by a 138 μm thick silicon layer can improve the spectral response by a factor of 1.7 in the 450 μm band.