For optical parametric amplifiers in proton-exchange waveguide devices reported to date, both the signal and the idler photons are in the ${\mathrm{TM}}_{00}$ mode, causing difficulty in distinguishing signal from idler. We report a two-mode optical parametric amplifier. The key components, asymmetric Y junctions, successfully launch the pump wave in a pure ${\mathrm{TM}}_{10}$ mode and separate the signal and the idler in the ${\mathrm{TM}}_{10}$ and ${\mathrm{TM}}_{00}$ modes with a power ratio of as much as 27.5 dB. With high parametric gain, optical parametric generation with a threshold of $300\mathrm{pJ}∕\text{pulse}$ was demonstrated for 1.8 ps long pump pulses near 780 nm. These periodically poled lithium niobate waveguides are efficient integrable photon sources.