The performance of superconducting-nanowire single-photon detectors depends on the efficiency of light absorption in the ultrathin (3-8 nm) superconducting nanowire. In this work, we will discuss two approaches to boost light absorption: coupling the nanowire to the evanescent field propagating in a waveguide and enclosing the nanowire in an optical cavity. The latter method is the most widely used, but it is intrinsically very sensitive to the polarization of light. To overcome this issue, we propose some innovative cavity designs which make use of high-index (n >2) dielectrics. With this technique, highly-efficient polarization-insensitive devices can be easily implemented.