  Bound states in the continuum (BICs) have been extensively studied in various
systems since its first proposal in quantum mechanics. Photonic BICs can enable
optical mode confinement and provide field enhancement for nonlinear optics,
but they have rarely been explored in nonlinear integrated photonic waveguides.
Applying BICs in photonic integrated circuits enables low-loss light guidance
and routing in low-refractive-index waveguides on high-refractive-index
substrates, which is suitable for integrated photonics with nonlinear
materials. Here, we report experimental demonstration of second-harmonic
generation from telecom to near-visible wavelengths on an etchless lithium
niobate platform by using a photonic BIC for the second-harmonic mode. The
devices feature second-harmonic conversion efficiency of 0.175%W-1cm-2 and
excellent thermal stability with a wavelength shift of only 1.7 nm from
25{\deg}C to 100{\deg}C. Our results represent a new paradigm of nonlinear
integrated photonics on a cost-effective and convenient platform, which can
enable a broad range of on-chip applications such as optical parametric
generation, signal processing, and quantum photonics.
