Multilayer grid polarizers for millimeter waves produced with photolithographic technology have been simulated. Polarizers have spectral bands of enhanced performance where polarization extinction ratio in decibels grows in proportion to the number of layers. Full-wave modeling is compared with three asymptotic models for subwavelength gratings using adjusted grating parameters. Random variations of interlayer spacings reduce the enhancement of polarizing performance, yet the latter continues to grow in proportion to the number of layers. Broadband signal detection is also considered.