A 3-dB optical coupler (power splitter) based on a Y-junction waveguide with a channel profile of proton-exchanged lithium niobate has been modeled. Finite difference beam propagation method has been used to investigate light wave propagation in axially varying waveguides. It is found that the structure splits the input power equally at the Y-junction with an efficiency of 99% and an average excess loss ⩽0.04 dB. The novelty of the coupling structure proposed is its capability to function as a wavelength-independent 3-dB coupler while maintaining very low-power imbalance for widespread optical communication wavelengths of 1.3 and 1.55 µm.