Families of cosmic inflation models predict a primordial gravitational-wave background that imprints B-mode polarization pattern in the Cosmic Microwave Background (CMB). High sensitivity instruments with wide frequency coverage and well-controlled systematic errors are needed to constrain the faint B-mode amplitude. We have developed antenna-coupled Transition Edge Sensor (TES) arrays for high-sensitivity polarized CMB observations over a wide range of millimeter-wave bands. BICEP Array, the latest phase of the BICEP/Keck experiment series, is a multi-receiver experiment designed to search for inflationary B-mode polarization to a precision $\sigma$(r) between 0.002 and 0.004 after 3 full years of observations, depending on foreground complexity and the degree of lensing removal. We describe the electromagnetic design and measured performance of BICEP Array low-frequency 40-GHz detector, their packaging in focal plane modules, and optical characterization including efficiency and beam matching between polarization pairs. We summarize the design and simulated optical performance, including an approach to improve the optical efficiency due to mismatch losses. We report the measured beam maps for a new broad-band corrugation design to minimize beam differential ellipticity between polarization pairs caused by interactions with the module housing frame, which helps minimize polarized beam mismatch that converts CMB temperature to polarization ($T\to P$) anisotropy in CMB maps.