Structures for a photodetector and methods of forming a structure for a photodetector. The structure includes a semiconductor layer having a p-n junction and a deep trench isolation region extending through the semiconductor layer. The deep trench isolation region includes first layers and second layers that alternate with the first layers to define a Bragg mirror. The first layers contain a first material having a first refractive index, and the second layers contain a second material having a second refractive index that is greater than the first refractive index.