  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 ($T \rightarrow P$) anisotropy in CMB maps.
