Polarizers are universal components deployed in diverse application fields including imaging, display, microscopy, interferometry, ellipsometry, and instrumentation. Here, we demonstrate design and fabrication of a new class of polarizers that are extremely compact and efficient. Based on an elemental low-loss single-resonant grating, we develop multilayer modules providing ultrahigh extinction ratio polarizers. The elemental polarizer contains a subwavelength periodic pattern of crystalline silicon on a quartz substrate. A stack of two dual-grating modules exhibits a measured extinction ratio (ER) of ∼100,000 in a sparse 2-mm-thick device across a bandwidth of ∼50 nm in the telecommunications spectral region. Theoretical computations indicate that extreme values of extinction are possible. Further development of the basic concepts explored herein may lead to a new class of practical polarizers with excellent attributes.