Conventional couplers including the $2\times 2$ directional coupler and the self-imaging multimode interference coupler always produce a $90°$ coupling phase to yield complementary power transfer functions when the relative phase of the two input fields changes. For applications in coupled-cavity lasers, a $2\times 2$ half-wave optical coupler with a $180°$ coupling phase is required in order to produce synchronous output power for achieving high single-mode selectivity. We present the designs and optimization of $2\times 2$ half-wave couplers, including a three-waveguide directional coupler and a nonimaging multimode interference coupler.