Fig. 1. Conceptual schematic of the rapid adiabatic coupler (RAC). (a) 2×2 RAC with the adiabatic mode evolution of TM-polarized input light. Wg1 and Wg2 denote the top and bottom waveguides, respectively. The width of the Wg1 (Wg2) increases (decreases) gradually. The widths of the output waveguides are identical. (b), (c) Cross-sectional schematic of RACs. Height of the ridge waveguide, gap between the top of the waveguides, and sidewall angle are 600 nm, 550 nm, and 67°, respectively. (b) Cross-section at the start point of adiabatic tapering region. The widths of the top and bottom waveguides, denoted by W1 and W2, are 500 and 800 nm, respectively. (c) Cross-section at the last point of the adiabatic tapering region. The widths of the output waveguides (W3 and W4) are identical to 650 nm. (d) Change of the effective refractive index as a function of the gradually controlled Wg1 (red solid line) and Wg2 (black solid line) widths. (e) Mode evolutions of the excited modes at Wg1 and Wg2 in accordance with the waveguide width.

Fig. 2. Design of TFLN-based 2×2 RAC. (a) RAC propagates with tilting angles θr(z′). (b) Four slanted boundary walls of the TFLN waveguides where electrical fields are calculated. The sidewalls are indexed by p=1−4. (c) Coupling coefficient along the tapering width of bottom waveguides from 0.8 to 0.65 μm. The vertical axis in the 2D mapping image of calculated C12 is the tilting angle (θr). (d) Tilted angle (θr) of RAC varying with the different bottom waveguide widths from 0.8 to 0.65 μm.

Fig. 3. Numerical investigations on TFLN RAC. (a) Calculated transmission spectra for the RAC with the different gaps: 550 nm (black), 600 nm (red), and 650 nm (blue) between the two adiabatic-tapered waveguides in region 2. (b) Calculated transmission for the optimized RAC as a function of tapering length in region 2. (c) Calculated transmission loss of the 150 μm RACs. (d) Transmission spectra of the RAC device (solid line) and the DC (dashed line). The gray-shadowed region shows the bandwidth of DC within the splitting ratio of 55%:45% in the wavelength range from 1530 to 1570 nm.

Fig. 4. Measurement of the RAC devices. (a) Top view of array of unbalanced MZIs. (b) Two identical RACs are in an unbalanced MZI. (c), (d) Transmission measurement of unbalanced MZI composed of two identical RACs. (e), (f) Transmission measurement of a single RAC device. Wg1 (Wg2) is the input waveguide for (c) and (e) [(d) and (f)]. In (c)–(f), black and red colors represent Wg3 and Wg4 output ports, respectively.

Fig. 5. On-chip HOM interference. (a) Schematic of experiment setup for on-chip HOM effect. (b) Measured single-photon and coincidence counts as a function of delay between two photons.

Fig. 6. Fabrication procedures of the TFLN RACs.

Fig. 7. Schematic of SPDC and measurement setup for observing HOM interference on TFLN RAC.

Fig. 8. HOM interference using a fiber beam splitter.

Fig. 9. Manipulation of a bending curvature along the propagation direction for optimal RAC designs. (a) Calculated transmission spectra of the conventional adiabatic coupler. (b) Calculated transmission spectra for the conventional adiabatic coupler as a function of tapering length without the rotation of the waveguides. (c) Calculated transmission spectra of the adiabatic coupler with the opposite bending orientation. (d) Calculated transmission spectra of the adiabatic coupler as a function of tapering length with the opposite bending orientation.

Fig. 10. Optimal design and measurement of the 50 μm long RAC. (a) Coupling coefficient along the tapered width of the bottom waveguides from 0.8 to 0.65 μm. The vertical axis in the 2D mapping image of calculated coupling coefficient (C12) is the tilting angle (θr). (b) Tilted angle (θr) of 50 μm long RAC varying with the different bottom waveguide widths from 0.8 to 0.65 μm. (c), (d) Transmission measurement of 50 μm long RAC device. Wg1, Wg2 are the input waveguides for measuring the transmission of the RAC device.

Fig. 11. HOM interference of the 50 μm long RAC.

Fig. 12. Analysis and comparison of directional couplers (DCs) compared to RACs. (a) Calculated transmission for the DCs with different gaps: 550 nm (black), 600 nm (red), and 650 nm (blue) between the two waveguides. (b) Transmission spectra of DC (dashed line) and RAC (solid line) in the wavelength range from 1530 to 1570 nm.