Lithium niobate~(LN) is a birefringent material, where the strong birefringence thermo-optic effect is promising for the generation of quantum photon source with widely tunable wavelength. Here, we demonstrate birefringent phase-matching in a 20-mm-long waveguide fabricated on 5~
μm-thick x-cut lithium niobate on insulator. The waveguide is deviated from the optical axis of LN by an angle of 53.5
∘, enabling the phase matching between telecom and visible wavelengths. The phase-matching wavelength of this device can be thermally tuned with rate of 0.617~nm/K. We demonstrate the type-1 spontaneous parametric down-conversion to generate photon pairs with brightness of 2.2~MHz/mW and coincidence-to-accidental ratio up to
2.8×105. Furthermore, the heralded single photon is obtained from the photon pair with efficiency of 13.8\% and count rate up to 37.8~kHz.
The generation of pure single-photon states and their characterization are fundamental in quantum information processing applications like quantum computing. In this work, we design integrated optical directional couplers on a silicon nitride platform for heralded single-photon characterization. We assume the generation of such photons in silicon nitride waveguides through the spontaneous four-wave mixing process. We show that manipulating the waveguide geometry and dielectric contrast makes it possible to obtain nearly wavelength-independent directional coupler designs that perform as 50:50 beamsplitters over a broad bandwidth around the central design wavelength. Assuming two independent but identical heralded single-photon sources, we compare the visibility obtained by simulating the Hong-Ou-Mandel interference for three different 50:50 beamsplitters: an ideal one (perfectly wavelength-independent), an engineered one (nearly wavelength-independent), and an unengineered one (significantly wavelength-dependent). The purity obtained with the engineered beamsplitter closely matches the purity obtained with the ideal one, for which the interference visibility is a direct measure of the quantum state purity. This finding implies that the proposed engineered beamsplitter is suitable for characterizing heralded single-photon states, provided its bandwidth is 23 nm.