Optical isolators are $n\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}p\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}l$ devices, transmitting forward-propagating light while blocking backward propagation. They are as important in optical and microwave applications as diodes are in electrical circuits. Common problems with free-space isolators are an inherently small aperture and the failure to block backward propagation at oblique incidence. This paper presents a thin free-space isolator offering virtually unlimited aperture and broadband rejection of light incident from behind, regardless of the exact direction. The key design elements are verified at microwave frequencies, and the same physical idea can also be applied up to the midinfrared.