Efficient high-quality photon pair generation in modal phase-matched thin-film lithium niobate micro-ring resonators

2.1 Photon pair generations based on modal phase matching

We employ Z-cut TFLN to ensure efficient nonlinear conversion, where light propagates along the circumference of the MRR and the crystal’s optical axis is oriented perpendicular to the light propagation direction. This alignment ensures the preservation of Type I collinear phase matching. In contrast, using X-cut TFLN – with a horizontal optical axis – introduces a continuously changing angle between the propagation direction and the optical axis, thereby hindering efficient nonlinear processes [39].

To achieve efficient nonlinear processes in the MRR, both phase matching and resonance conditions must be simultaneously met. The required phase matching condition must satisfy Δk = k _p − k _s − k _i = 0, where k _p , k _s , and k _i are the propagation constants of the pump, signal, and idler light, respectively. Here, we choose the TM20 mode for the pump light and TE00 mode for the signal and idler light to achieve modal phase matching. Simultaneously, we require that the MRR free spectral range (FSR) is not too large to ensure all interacting beams can resonate. Therefore, we choose a minimal micro-ring radius of 150 μm, corresponding to an FSR of 1.1 nm. Under these conditions, along with temperature control and previse wavelength selection, the pump, signal, and idler can simultaneously achieve resonance with ease. To ensure properly control, we calculate the waveguide mode dispersion of the MRR.

Figure 1(c) shows the MRR waveguide cross section. We choose a TFLN layer thickness of 300 nm, etching depth of 200 nm, and the waveguide sidewall inclination angle of 70°. Here, we consider the change in the effective refractive index caused by waveguide bending. The variation of the effective refractive index of TM20 mode at 775 nm and TE00 mode at 1,550 nm are shown in Figure 2(a). Here, we vary the top width of the 150-μm-radius MRR waveguide. From Figure 2(a), it can be seen that the TM20 mode at 775 nm and the TE00 mode at 1,550 nm satisfy modal phase matching when the top width is 1.21 μm. Figure 2(b) shows that for a top width of 1.21 μm, the pump wavelength satisfying phase matching also increases with increase of the MRR radius. However, only a 0.1 nm change in the required pump wavelength for phase matching is observed when varying the radius from 150 μm to 400 μm.

Figure 2:

Numerical calculations for modal phase-matching conditions and mode conversion. (a) The effective refractive index of 775 nm TM20 and 1,550 nm TE00 as a function of waveguide top width at R = 150 μm. (b) Pump wavelength required for phase matching as a function of different MRR radii for a waveguide top width of w = 1.21 μm. (c) Effective refractive index of two modes at 775 nm with varying waveguide top width of the mode converter. (d) The coupling efficiency versus input pump wavelength. The inset in (d) shows the modal field distribution of the mode converter at 775 nm.

2.2 Mode converter design

We designed and integrated a mode converter at the front end of the micro-ring structure to achieve modal phase matching in the MRR system, such that the pump light operates in the TM20 mode and the input straight waveguide supports the fundamental mode, TM00 (see Figure 1(a)). As shown in Figure 2(c), the effective refractive indices of the TM00 and TM20 modes of 775 nm pump light were calculated under different waveguide widths. Effective energy exchange can be achieved between these two modes when their effective refractive indices in each waveguide are equal. As a result, we chose top widths of 0.84 μm and 3 μm, for the mode converter input and output waveguide, respectively, as depicted by the red lines of Figure 2(c). The coupling gap between these waveguides was set to be 0.2 μm, making an overall compact structure. To achieve complete mode conversion, a coupling length of 600 μm is required. Using a coupling length of 600 μm, we calculated the coupling efficiency of different pump wavelengths using FDTD, plotted in Figure 2(d), resulting in a maximum coupling efficiency of 98 % within the range of 700–850 nm. The field distribution at optimal energy transfer is shown in the insert in Figure 2(d).

3.1 Sample preparation and characterization

The fabricated sample consists of commercial Z-cut silicon-based TFLN (NANOLN Inc.), with a 525-μm-thick silicon bottom layer, a 2.025-μm-thick silicon dioxide middle layer, and a 300-nm-thick TFLN layer on top. The sample fabrication process primarily involves electron beam lithography and ion beam etching, thereby avoiding the complexity associated with periodically poled waveguides. From here, MRRs with different coupling gaps and radii were prepared. One sample set varied the coupling gap from 0.3 μm to 0.5 μm in 0.05 μm increments while holding a constant radius of 150 μm. The other sample set held a constant coupling gap of 0.3 μm while varying the radius from 150 μm to 300 μm with 50 μm increments. After etching, a polish of 150 μm was applied to both ends of the chip to reduce end face roughness. Figure 3 shows the detailed analysis of the fabricated samples.

Figure 3:

Sample characterization. (a) Microscopic image of the MRRs. (b) SEM image of the mode converter. (c) SEM image of the waveguide. (d) Transmission spectrum of TFLN MRR for a radius of 150 μm and coupling gap of 0.45 μm, showing FSR of 1.1 nm for the MRR. (e) Transmittance spectrum around the resonant wavelength of the MRR in blue and the corresponding fitted curve in red indicating the intrinsic versus measured Q-factor.

The MRR microscopy image is shown in Figure 3(a), and SEM images of the coupler and waveguide are shown in Figure 3(b) and (c). The measured transmission spectrum of the sample without a mode converter with 150 μm radius and 0.45 μm coupling gap is shown in Figure 3(d). Under these conditions, we observed critical coupling and measured the FSR to be 1.1 nm, consistent with our theoretical calculation. We found that the propagation loss is approximately 1.36 dB/cm at 1,550 nm. The intrinsic quality factor can reach 2.97 × 10⁵ and the measured loaded quality factor to be 1.28 × 10⁵, as shown in Figure 3(e).

3.2 Second-harmonic generation

The experimental setup for SHG is shown in Figure 4(a). A continuously tunable laser (Santec TSL-570) is amplified by an erbium-doped fiber amplifier, directed through a polarization controller, and coupled into a waveguide using a fiber with a diameter of 3.2 μm. The output power and spectrum of the SHG signal is captured by a power meter and spectrometer. Note that the fundamental light is coupled directly, while the SHG signal is coupled with the mode converter for output, as depicted in Figure 4(a).

Figure 4:

Measurement results of SHG for the MRR (R = 150 μm, d = 0.45 μm) with a mode converter. (a) Schematic diagram of experimental setup for SHG. A tunable CW laser centered at 1,550 nm is sent through an amplifier and polarization controller. The input fundamental light is coupled in the sample, and the output SHG light is sent through a 50/50 beam splitter to measure both the transmission spectrum and the output power. (b) Measured transmission spectrum of the fundamental light signal through the sample, and (c) the corresponding SHG signal. (d) The SHG signal intensity for a fundamental wavelength of 1,571.05 nm, corresponding to the fundamental and SHG signal’s resonance and phase-matched conditions. The insets in (d) show the fundamental and SHG signal in the MRR captured by CCD cameras. (e) The SHG power as a function of the square of the fundamental light power, confirming the quadratic dependence (slope = 0.027 ± 0.0016 mW⁻¹).

Figure 4(b) shows the transmission spectrum of the fundamental light from 1,560 to 1,580 nm for the critically coupled MRR, with a radius and coupling gap of 150 μm and 0.45 μm, respectively. The discrepancy between the transmission spectra presented here and those measured previously arises from the mode converter. The fundamental wavelength that satisfies the resonance condition of the MRR corresponds to the valley position on the transmission spectrum. Figure 4(c) shows the SHG signal measured in the range of 1,560–1,580 nm. It can be seen that in Figure 4(b) and (c), the SHG signal remains weak regardless of the resonant fundamental signal, as depicted by dashed lines outside the shaded regions. Only when fundamental signal and SHG signal are resonant and phase matched, we achieve efficient SHG, as depicted by the shaded area in Figure 4(b) and (c). Careful tuning of the temperature allows for precise control of the optimal conditions. Figure 4(d) shows the second harmonic spectrum, with a maximum signal at λ _SHG = 785.525 nm, corresponding to a fundamental wavelength of λ _FF = 1,571.05 nm. The SHG and fundamental signals are measured using CCD cameras, as shown by the two inserts in Figure 4(d), indicating that both signals are resonant. Moreover, the CCD measurement shows that SHG is indeed generated in the MRR, rather than the straight waveguide. Finally, the power dependence of the SHG signal is measured by varying the input power of the fundamental plotted in Figure 4(e), following the expected quadratic dependence of the input fundamental power.

3.3 Photon pair generation

The schematic diagram of the experimental setup for photon pair generation and detection is shown in Figure 5(a). A near-visible wavelength tunable laser (SL-N-780-L-CW semiconductor laser) is passed through a polarization controller and then coupled through a 775 nm lens fiber into the tapered waveguide. The light is converted to a TM20 mode by the mode converter and then coupled into an MRR through the straight waveguide. Photon pairs are then generated from the MRR and coupled through a tapered waveguide to an output fiber with a diameter of 3.2 μm. After filtering the input pump light, the generated photon pairs are sent down two paths via a 50:50 beam splitter. The polarization of the light in each path is first controlled and then subsequently detected on a superconducting nanowire single photon detector (SNSPD, detection efficiency ∼60 %). The coincidence counts between the photon pairs are measured using a time-dependent single photon counter (TCSPC) (PicoQuant PicoHarp 300). The chip-to-fiber coupling losses are 10.7 dB around 780 nm and 6.2 dB around 1,570 nm. The losses in each path from the output fiber to the detector are 7.47 dB and 6.68 dB at 1,570 nm, respectively.

Figure 5:

Photon pair generation, detection, and measurement. (a) Schematic diagram of experimental setup for measuring photon pairs. A tunable pump laser at 775 nm is sent through a polarization controller and then coupled into the sample. The fundamental light is then filtered at the output such that only the generated signal is detected. The generated photon pairs are sent through a 50/50 beam splitter, subsequently sent through polarization controllers. Finally, single photon counts and coincidence counts are measured using a time-dependent single-photon counter. (b) The pump wavelength for max coincidence count at different coupling gaps. The red line at λ = 785.21 nm corresponds to near-degenerate photons generated by SPDC. (c) Coincidence counts for different coupling gaps for a 150 μm radius MRR. (d) Resonant pump wavelength for an MRR with a coupling gap of 0.3 μm for different radii.

The photon pair generation was analyzed for various MRRs with different coupling gaps and radii. Firstly, the coupling gap directly affects the pump light coupling efficiency into the MRR and the output signal coupling efficiency, thereby affecting the overall nonlinear conversion efficiency. As previously stated, optimal SHG efficiency occurs at a radius of 150 μm with a coupling gap of 0.45 μm. Therefore, one can expect similar peak in efficiency for photon pair generation under these conditions. Consequently, the average measured pump light wavelength for near-degenerate SPDC occurs at 785.21 nm, as shown in Figure 5(b). Note that, the change of gap width does not affect the phase-matching condition, but as the coupling gap gradually increases, the coincidence count increases up to a maximum at a gap of 0.45 μm, and hereby after decreases, as shown in Figure 5(c). Figure 5(d) shows monotonic increase of the measured pump light wavelength for near-degenerate SPDC with respect to the MRR radius. The experimentally measured results are consistent with theory. Slight only differences can be attributed to minor fabrication errors affecting the resonance characteristics of the MRR.

Figure 6 shows a more detailed analysis of the photon pair generation. The spectral dependence of the pump light on pair generation is plotted in Figure 6(a) for an MRR with a 150 μm radius and a 0.45 μm coupling gap. Maximum coincidence counts were found to be at a pump wavelength of 785.44 nm. Note that the pump wavelength of the SPDC process only differs by approximately 0.1 nm from that of the SHG process. This discrepancy arises primarily from the inherent measurement uncertainty associated with the wavelength meter employed in the SPDC experiment. These results reveal a wavelength consistency between the two processes.

Figure 6:

Characterization of the quality of the generated photon pairs for an MRR of 150 μm radius and a 0.45 μm coupling gap. (a) Measured coincidence counts highlight the SPDC spectrum as a function of pump wavelength, indicating maximum coincidence for an input pump wavelength of 785.44 nm, consistent with the conditions for SHG. (b) Measured PGR in red, with corresponding fit curve in black, and CAR in blue for different input pump powers. The brightness, B, is found to be B = 40.2 MHz/mW.

Figure 6(b) details about the measured rates and overall statistics of the source. Single photon and coincidence counts are measured as a function of input pump power and used to determine the on-chip photon pair generation rate (PGR) per unit of time, defined as:

where N 1 2 is the single-photon detection count rate in each path and N ₁₂ is the two-photon coincidence count rate. The brightness of a photon source quantified by its PGR serves as a metric for evaluating performance as a quantum light source. Hence, the PGR at different pump powers is plotted in red, with the corresponding fit shown in black in Figure 6(b). When the pump light power is 12.3 μW, the coincidence count rate is found to be 167 Hz, and singles are found to exceed 14 KHz, the dark count is 1.5 KHz, resulting in a PGR up to 0.49 MHz. The slope of the fitting indicates the two-photon source brightness of 40.2 MHz/mW.

The coincidence-to-accidental ratio (CAR) plotted in blue in Figure 6(b) provides relevant information about the quality and is defined as:

where N _CC is the number of total coincidence counts and N _AC is the number of accidental coincidence counts. The maximum CAR was found to be 1786 at an input pump power of 6.14 μW. The CAR shows monotonic decrease with input pump power but remains above 1,200 over a relatively wider range of input powers up to 12.3 μW. These results demonstrate the high quality of the generated photons from our source. Furthermore, we present a comparative assessment of MRRs fabricated from different materials for photon-pair generation using modal phase matching and continuous-wave pumping as shown in Table 1. Table 1 clearly indicates that the TFLN MRR developed in this work achieves exceptional brightness and CAR metrics, establishing their advantages as high-performance photon pair sources. Future improvements targeting the mode converter efficiency and quality of the chip facet coupling are expected to further elevate photon pair spectral brightness within the TFLN MRR.