Orange no-entry signs posted by the U.S. military in English and Spanish dot the New Mexico desert, where a border wall cuts past onion fields and parched ranches with tufts of tall grass growing amidst wiry brush and yucca trees.

Annexed militarized zones on public land will soon cover nearly one-third of the U.S. border with Mexico, empowering soldiers to arrest people who cross the border illegally and facilitating new criminal trespassing charges.