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Abstract
Second-order optical nonlinearity is widely used for both classical and quantum photonic applications. Due to material dispersion and phase matching requirements, the polarization of optical fields is pre-defined during the fabrication. Only one type of phase matching condition is normally satisfied, and this limits the device flexibility. Here, we demonstrate that phase matching for both type-I and type-II second-order optical nonlinearity can be realized simultaneously in the same waveguide fabricated from thin-film lithium niobate. This is achieved by engineering the geometry dispersion to compensate for the material dispersion and birefringence. The simultaneous realization of both phase matching conditions is verified by the polarization dependence of second-harmonic generation. Correlated photons are also generated through parametric down conversion from the same device. This work provides a novel approach to realize versatile photonic functions with flexible devices.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Second-order ($\chi ^{(2)}$) nonlinearity is a highly preferred property of optical materials. In the classical regime, $\chi ^{(2)}$ nonlinearity is used to generate optical fields at new frequencies. This can be achieved through frequency up-conversion with second harmonic generation and sum frequency generation [1,2], and frequency down-conversion with difference frequency generation and optical parametric oscillation [3,4]. Such approaches are especially valuable for frequency regimes where the choice of optical gain mediums is limited. In addition to classical applications, $\chi ^{(2)}$ nonlinearity also plays a critical role for quantum information science and technology [5–8]. Single photons and squeezed light generated with parametric down-conversion have been the driving force for numerous quantum technologies. Photonic entanglement in time [9,10], frequency [11,12], polarization [13,14], and path [15] have been realized based on parametric down-conversion. Quantum communications based on single photons have been demonstrated over long-distance commercial fiber networks [16–18], and quantum sensing has also been achieved to break the classical limit [6,7].
As non-centrosymmetric crystal structures are required, $\chi ^{(2)}$ optical processes are traditionally realized using bulk nonlinear crystals such as barium borate (BBO) [19,20], potassium titanyl phosphate (KTP) [11,21], lithium niobate [13,22], etc. Phase matching conditions are normally realized based on either angle tuning [23] or quasi-phase matching [24]. Depending on the polarizations of optical fields, phase matching conditions are classified into different types, where type-I (same polarization for signal and idler fields) and type-II (different polarizations for signal and idler fields) are two common choices. The angle tuning approach utilizes the birefringent property of nonlinear crystals to compensate the material chromatic dispersion. Therefore the polarizations of the optical fields and the orientation of the nonlinear crystal are fixed. With quasi-phase matching, the crystal axis is periodically poled to compensate the velocity mismatch among different optical fields. Due to the large material chromatic dispersion and strong birefringence, the poling pattern has to be designed in advance for different phase matching conditions. The simultaneous realization of different phase matching conditions is highly preferred for both classical and quantum applications [25–28]. It allows the continuous polarization tuning of the generated optical field [25], and the construction of all-optical nonlinear polarization switch [27]. For quantum applications, second-order nonlinearity is one of the most widely used methods to generate single photons. There are a variety of options for encoding qubits into photons. Depending on encoding methods, different phase matching conditions are preferred. Providing a single device that is capable of both type I and type II nonlinear interactions would allow one to easily switch between encoding methods.
With the recent development of nonlinear materials for integrated photonics, $\chi ^{(2)}$ optical processes have also been realized on chip. The small mode volume of on-chip devices significantly improves the efficiency of $\chi ^{(2)}$ nonlinearity. Second-harmonic generation [29,30], electro-optic phase modulation [31,32], quantum frequency conversion [33–35], and single-photon generation [36,37] have been realized with record-high efficiency. Among integrated photonic materials with non-zero $\chi ^{(2)}$ nonlinearity, lithium niobate is especially advantageous due to its large nonlinearity coefficient, broad transparency window [38], and fast modulation capabilities. Breakthroughs in lithium niobate nanofabrication have also yielded ring resonators with Q-factors of $10^7$ [39] and the ability to integrate single photon detectors on the LNOI platform [40].
Here, we present thin-film lithium niobate waveguides that can realize type-I and type-II $\chi ^{(2)}$ nonlinear optical processes at the same time. The geometry dispersion of the thin-film lithium niobate waveguide is precisely engineered to compensate the intrinsic birefringence and material dispersion of lithium niobate. We observe efficient second-harmonic generation with both phase matching conditions. We further demonstrate the generation of correlated photons from parametric down-conversion, and show that type-I phase matching condition has higher photon generation rate and larger bandwidth.
2. Device design
We use X-cut thin-film lithium niobate wafers with thickness of 450 nm (Fig. 1(a)). The $\chi ^{(2)}$ nonlinear optical processes are designed to involve two fundamental fields with wavelength around 1550 nm and one second-harmonic field with wavelength around 775 nm. The propagation direction is along the y axis of lithium niobate. Therefore, type-I phase matching condition requires that the two fundamental fields are transverse-electric (TE) modes, with electric components aligned with the z axis of lithium niobate. Type-II phase matching condition requires that the two fundamental fields are transverse-electric (TE) and transverse-magnetic (TM) modes, with electric components aligned with the z and x axis of lithium niobate. The nonlinear coefficients $d_{33}$ and $d_{31}$ are used for type-I and type-II phase matching conditions respectively. Ridge waveguide design is used with a slab thickness of 100 nm and waveguide sidewall angle of 65 degrees, as determined by fabrication processes. Modal dispersion is used to compensate for the material dispersion, which means that a higher-order mode for the second-harmonic field needs to be used. In order to maximize the field overlap, we use TM0 and TE0 for the fundamental fields and TE2 and TM2 modes for the second-harmonic fields (Fig. 2(a-d)).
Fig. 1. (a) Schematic of x-cut lithium niobate ridge waveguide cross section. (b) SEM image of the fabricated ridge waveguide.
Fig. 2. (a) Simulated power profile of TE0 mode at 1550 nm. (b) Simulated power profile of TM0 mode at 1550 nm. (c) Simulated power profile of TE2 mode at 775 nm. (d) Simulated power profile of TM2 mode at 775 nm. (e) Simulated effective indices as a function of waveguide width. (f) difference between type-I and type-II phase-matched wavelengths as a function of waveguide width.
The simulated refractive indices of the relevant modes with different waveguide widths is presented in Fig. 2(e). Type-I phase matching condition is fulfilled when $n_{\textrm {TE0,1550}}=n_{\textrm {TE2,775}}$, which is realized with a waveguide width around 545 nm. Type-II phase matching condition is fulfilled when $(n_{\textrm {TE0,1550}}+n_{\textrm {{TM0,1550}}})/2=n_{\textrm {TM2,775}}$, which is realized with a waveguide width around 570 nm. The calculated second-harmonic efficiencies are $17.67\%$W$^{-1}$cm$^{-2}$ and $3.325\%$W$^{-1}$cm$^{-2}$ for type-I and type-II phase matching conditions respectively [41]. The closeness of the phase-matched widths suggests the possibility of realizing type-I and type-II phase matching conditions with the same waveguide width at separate wavelengths. To verify this point, we track the phase-matched wavelengths for both type-I and type-II processes while changing waveguide width (Fig. 2(f)). The phase-matched wavelength refers to the fundamental wavelength at which the momentum mismatch $\Delta k$ for SHG is equal to zero. The difference between type-I and type-II phase-matched wavelengths changes monotonically with the waveguide width. This is due to the fact that the change of refractive index for TE and TM modes is different with the same change of waveguide width. Therefore, the material birefringence of lithium niobate can be compensated with geometry dispersion. For waveguide width around 550 nm, the difference between phase-matched wavelengths for type-I and type-II vanishes, and $\chi ^{(2)}$ nonlinear optical processes with both phase matching conditions can occur.
3. Device fabrication and experimental results
The waveguides are fabricated from thin-film lithium niobate wafers. The photonic circuit is patterned with 100-kV electron beam lithography using hydrogen silsesquioxane (HSQ) resist. Then, argon-based reactive ion etch (RIE) is used to transfer the pattern from resist to lithium niobate. The lithium niobate redeposition formed during the RIE step is removed by submerging the chip in a mixture of hydrogen peroxide and ammonium hydroxide. Finally, the chip is annealed in nitrogen gas. The fabricated device is shown in Fig. 1(b), and high quality ridge waveguides with smooth sidewalls can be observed.
We use the setup shown in Fig. 3(a) to measure the fabricated device. The light from a telecom tunable laser is amplified by a erbium doped fiber amplifier (EDFA). We then couple light into and out of the waveguides using lensed fibers mounted on piezoelectric stages. A wavelength-division multiplexer (WDM) is used at the output to separate fundamental and second harmonic signals, which are detected by InGaAs and Si photodetectors respectively.
Fig. 3. (a) Schematic of second-harmonic generation measurement apparatus. (b) Second-harmonic signal with different telecom pump wavelengths. (c) Fundamental (upper) and second-harmonic (lower) signals with different HWP angles for type-II phase matching condition. (d) Fundamental (upper) and second-harmonic (lower) signals with different HWP angles for type-I phase matching condition. (e) Pump power dependence of second-harmonic signal for type-II phase matching condition. (f) Pump power dependence of second-harmonic signal for type-I phase matching condition.
When the input light has both TE and TM components, we observe two groups of strong second-harmonic signals when the wavelength of the tunable laser is swept (Fig. 3(b)). The splitting of second-harmonic signals into multiple peaks is due to the fluctuation of input polarization during the wavelength sweep. In order to verify the phase matching type, we fix the wavelength of the input light at 1552 nm and vary the input polarization. We accomplish this by inserting a polarized beam splitter (PBS) to ensure linearly polarized input light, a half-wave plate (HWP) to rotate the polarization, and a bandpass filter (BPF) to reduce the effects of ASE noise from the EDFA (Fig. 3(a)). The output power of the fundamental field changes periodically with the input polarization angle, as TE and TM modes have different coupling efficiencies between the lensed fiber and the waveguide. The period is 90 degrees rotation in HWP angle, which corresponds to a 180 degrees input polarization rotation. The second-harmonic signal also changes periodically with the input polarization angle, but with a period half of the fundamental field (45 degrees HWP, 90 degrees polarization, Fig. 3(c)). This verifies that type-II phase matching condition is realized at this wavelength. Next, we change the input wavelength to 1560 nm. When the input polarization angle changes, the fundamental and second-harmonic signals have the same period (90 degrees HWP, 180 degrees polarization, Fig. 3(d)). Therefore, type-I phase matching condition is realized at this wavelength.
The power of the input light can be varied by adjusting the fiber polarization controller before the PBS. As seen in Fig. 3(e) and (f), the second-harmonic signals of type-I and type-II phase matching conditions both follow a quadratic dependence on the power of the fundamental fields. We also observe that the second-harmonic efficiency of type-I phase matching condition is significantly larger than type-II phase matching condition, which is consistent with the theoretical values by considering both the differences in nonlinear coefficients ($d_{33}$ vs. $d_{31}$) and mode overlapping (TE2 vs. TM2 for second-harmonic field).
We further performed sum-frequency generation with the same device. A second telecom laser is added to the setup (Fig. 4(a)). After amplification with EDFA, the second light source is used as the pump. The first light source is used as the probe, and combined with this second one using a fiber PBS. Therefore, the pump and probe are combined in orthogonal polarizations, leading to type-II phase matching condition. In Fig. 4(b), we show the probe laser frequencies of highest sum-frequency signals with different pump laser frequencies. The linear fit with the slope of -1 verifies the energy conservation of the $\chi ^{(2)}$ nonlinear process.
Fig. 4. (a) Schematic of type-II sum-frequency generation apparatus. Polarizations of both telecom sources are optimized for maximum transmission through fiber PBS. (b) Probe frequencies with peak sum-frequency signal as a function of pump frequency.
4. Generation of correlated photons with spontaneous parametric down conversion
In order to facilitate spontaneous parametric down conversion (SPDC) on chip, a near-infrared laser with tunable wavelength near 780 nm is used as the pump. A long-pass filter at the output is used to remove the residue pump. A half-wave plate and a polarized beam splitter are used to analyze the polarization of the correlated photons, which are detected by two superconducting nanowire single photon detectors (SNSPD). The coincidence between the two SNSPDs is recorded by an electronic time tagger (Fig. 5(a)).
Fig. 5. (a) Schematic of SPDC experiment apparatus. (b) Simulation of mode converter with TM0 input at 775 nm. Geometry of mode converter is outlined using dashed white lines. (c) Normalized coincidence count as a function of time delay between two SNSPDs. Wavelength of visible laser was set to 776.24 nm, and had an output power of 23 mW. Collection time was around 15 hours. Input polarization was optimized using the polarization controller to yield the highest photon counts at the output. (d) SNSPD count rates as a function of HWP angle. (e) Simulated type-I and type-II wave-vector mismatch (upper) and SPDC bandwidths (lower).
The pump is launched into the waveguide as TM0 or TE0 mode. As the phase matching condition is realized with high-order modes (TE2 and TM2, Fig. 2), a mode converter is needed to convert the power from TM0 and TE0 modes to TM2 and TE2 modes. The mode converter used in our device is an interface between two waveguides, where the width of the output waveguide is three times larger than the width of the input waveguide (Fig. 5(b)). This mode converter yields a simulated conversion efficiency of 31.5% for TE polarization and 30.3% for TM polarization. The detection coincidence is counted between the two SNSPDs, showing that correlated photons are generated (Fig. 5(c)). The on-chip single photon generation rate is estimated around 500 kHz, with pump efficiency around 21 kHz/mW. With a 1-nm tunable bandpass filter, the bandwidth of the generated single photons is measured to be around 80 nm. This leads to sub-picosecond temporal bandwidth, which is much smaller than the SNSPD jitter ($\sim$100 ps). To determine whether the correlated photons are generated with type-I or type-II SPDC, we measured the photon count rate from each SNSPD while varying the HWP angle. The photon count rate of each SNSPD varies sinusoidally with a period of 90 degrees, which indicates the type-I SPDC dominates the correlated photon generation (Fig. 5(d)). The same dependence of photon count rates on HWP angle is observed even when the pump wavelength is tuned to 776 nm, which should be type-II phase matching based on the second-harmonic generation experiment (Fig. 3(b)). This is explained by the fact that the bandwidth for type-I SPDC is more than 8x larger than type-II SPDC, reaching 80 nm (Fig. 5(e)). Therefore, correlated photons generated from type-II SPDC is overlapped with type-I SPDC in frequency. Considering that type-I $\chi ^{(2)}$ processes are significantly more efficient than type-II, we mainly observe correlated photons generated from type-I SPDC.
5. Conclusion
In conclusion, we have designed and fabricated a thin-film lithium niobate waveguide that realizes type-I and type-II $\chi ^{(2)}$ nonlinear processes at the same time. We verified the presence of both type-I and type-II processes by measuring second-harmonic generation and sum-frequency generation signals while varying pump wavelength, polarization, and power. Correlated photons generated from SPDC processes are also observed. The flexibility of realizing different phase matching conditions with a single photonic device will be valuable for future multi-functional photonic devices.
Funding
Office of Naval Research (N00014-19-1-2190); Oak Ridge National Laboratory (4000178321); National Science Foundation (CCF-1907918).
Acknowledgments
We acknowledge the use of facilities within Micro/Nano Fabrication Cleanroom at the Unversity of Arizona, and INQUIRE testbed supported by NSF MRI grant (NSF ECCS-1828132).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data may be obtained from the authors upon reasonable request.
References
1. D. A. Kleinman, “Theory of second harmonic generation of light,” Phys. Rev. 128(4), 1761–1775 (1962). [CrossRef]
2. Y.-C. Huang, K.-W. Chang, Y.-H. Chen, A.-C. Chiang, T.-C. Lin, and B.-C. Wong, “A high-efficiency nonlinear frequency converter with a built-in amplitude modulator,” J. Lightwave Technol. 20(7), 1165–1172 (2002). [CrossRef]
3. L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, and W. Bosenberg, “Multigrating quasi-phase-matched optical parametric oscillator in periodically poled linbo3,” Opt. Lett. 21(8), 591–593 (1996). [CrossRef]
4. M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in type-ii optical parametric down-conversion,” Phys. Rev. A 50(6), 5122–5133 (1994). [CrossRef]
5. Z.-S. Yuan, X.-H. Bao, C.-Y. Lu, J. Zhang, C.-Z. Peng, and J.-W. Pan, “Entangled photons and quantum communication,” Phys. Rep. 497(1), 1–40 (2010). [CrossRef]
6. J. Aasi, J. Abadie, B. Abbott, R. Abbott, T. Abbott, M. Abernathy, C. Adams, T. Adams, P. Addesso, R. Adhikari, C. Affeldt, O. Aguiar, P. Ajith, B. Allen, E. Ceron, D. Amariutei, S. Anderson, W. Anderson, K. Arai, M. Araya, C. Arceneaux, S. Ast, S. Aston, D. Atkinson, P. Aufmuth, C. Aulbert, L. Austin, B. Aylott, S. Babak, P. Baker, S. Ballmer, Y. Bao, J. Barayoga, D. Barker, B. Barr, L. Barsotti, M. Barton, I. Bartos, R. Bassiri, J. Batch, J. Bauchrowitz, B. Behnke, A. Bell, C. Bell, G. Bergmann, J. Berliner, A. Bertolini, J. Betzwieser, N. Beveridge, and P. Beyersdorf, “Enhanced sensitivity of the ligo gravitational wave detector by using squeezed states of light,” Nat. Photonics 7(8), 613–619 (2013). [CrossRef]
7. C. L. Degen, F. Reinhard, and P. Cappellaro, “Quantum sensing,” Rev. Mod. Phys. 89(3), 035002 (2017). [CrossRef]
8. D. Bouwmeester, J.-W. Pan, and K. Mattle, “Experimental quantum teleportation,” Nature 390(6660), 575–579 (1997). [CrossRef]
9. H. de Riedmatten, I. Marcikic, H. Zbinden, and N. Gisin, “Creating high dimensional time-bin entanglement using mode-locked lasers,” Quant. Inf. Comp. (2002).
10. I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, “Time-bin entangled qubits for quantum communication created by femtosecond pulses,” Phys. Rev. A 66(6), 062308 (2002). [CrossRef]
11. R. Shimizu and K. Edamatsu, “High-flux and broadband biphoton sources with controlled frequency entanglement,” Opt. Express 17(19), 16385–16393 (2009). [CrossRef]
12. M. Chen, N. C. Menicucci, and O. Pfister, “Experimental realization of multipartite entanglement of 60 modes of a quantum optical frequency comb,” Phys. Rev. Lett. 112(12), 120505 (2014). [CrossRef]
13. T. Kim, M. Fiorentino, and F. N. C. Wong, “Phase-stable source of polarization-entangled photons using a polarization sagnac interferometer,” Phys. Rev. A 73(1), 012316 (2006). [CrossRef]
14. C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, “High-flux source of polarization-entangled photons from a periodically poled ktiopo4 parametric down-converter,” Phys. Rev. A 69(1), 013807 (2004). [CrossRef]
15. E. Megidish, A. Halevy, H. S. Eisenberg, A. Ganany-Padowicz, N. Habshoosh, and A. Arie, “Compact 2d nonlinear photonic crystal source of beamlike path entangled photons,” Opt. Express 21(6), 6689–6696 (2013). [CrossRef]
16. C. Simon, “Towards a global quantum network,” Nat. Photonics 11(11), 678–680 (2017). [CrossRef]
17. B. Korzh, “Provably secure and practical quantum key distribution over 307 km of optical fibre,” Nat. Photonics 9(3), 163–168 (2015). [CrossRef]
18. R. Ursin, F. Tiefenbacher, and T. Schmitt-Manderbach, “Entanglement-based quantum communication over 144 km,” Nat. Phys. 3(7), 481–486 (2007). [CrossRef]
19. J. yuan Zhang, J. Y. Huang, H. Wang, K. S. Wong, and G. K. Wong, “Second-harmonic generation from regeneratively amplified femtosecond laser pulses in bbo and lbo crystals,” J. Opt. Soc. Am. B 15(1), 200–209 (1998). [CrossRef]
20. D. Nikogosyan, “Beta barium borate (bbo),” Appl. Phys. A 52(6), 359–368 (1991). [CrossRef]
21. M. Fiorentino, S. M. Spillane, R. G. Beausoleil, T. D. Roberts, P. Battle, and M. W. Munro, “Spontaneous parametric down-conversion in periodically poled ktp waveguides and bulk crystals,” Opt. Express 15(12), 7479–7488 (2007). [CrossRef]
22. J. Zhang, Y. Chen, F. Lu, and X. Chen, “Flexible wavelength conversion via cascaded second order nonlinearity using broadband shg in mgo-doped ppln,” Opt. Express 16(10), 6957–6962 (2008). [CrossRef]
23. R. Akbari and A. Major, “Optical, spectral and phase-matching properties of bibo, bbo and lbo crystals for optical parametric oscillation in the visible and near-infrared wavelength ranges,” Laser Phys. 23(3), 035401 (2013). [CrossRef]
24. M. Fejer, G. Magel, D. Jundt, and R. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992). [CrossRef]
25. V. Pasiskevicius, S. J. Holmgren, S. Wang, and F. Laurell, “Simultaneous second-harmonic generation with two orthogonal polarization states in periodically poled ktp,” Opt. Lett. 27(18), 1628–1630 (2002). [CrossRef]
26. B. F. Johnston, P. Dekker, M. J. Withford, S. M. Saltiel, and Y. S. Kivshar, “Simultaneous phase matching and internal interference of two second-order nonlinear parametric processes,” Opt. Express 14(24), 11756–11765 (2006). [CrossRef]
27. A. Ganany-Padowicz, I. Juwiler, O. Gayer, A. Bahabad, and A. Arie, “All-optical polarization switch in a quadratic nonlinear photonic quasicrystal,” Appl. Phys. Lett. 94(9), 091108 (2009). [CrossRef]
28. R. Lifshitz, A. Arie, and A. Bahabad, “Photonic quasicrystals for nonlinear optical frequency conversion,” Phys. Rev. Lett. 95(13), 133901 (2005). [CrossRef]
29. A. W. Bruch, X. Liu, X. Guo, J. B. Surya, Z. Gong, L. Zhang, J. Wang, J. Yan, and H. X. Tang, “17 000%/w second-harmonic conversion efficiency in single-crystalline aluminum nitride microresonators,” Appl. Phys. Lett. 113(13), 131102 (2018). [CrossRef]
30. J. Lu, J. B. Surya, X. Liu, A. W. Bruch, Z. Gong, Y. Xu, and H. X. Tang, “Periodically poled thin-film lithium niobate microring resonators with a second-harmonic generation efficiency of 250, 000%/w,” Optica 6(12), 1455–1460 (2019). [CrossRef]
31. C. Wang, M. Zhang, X. Chen, M. Bertrand, A. Shams-Ansari, S. Chandrasekhar, P. Winzer, and M. Lončar, “Integrated lithium niobate electro-optic modulators operating at cmos-compatible voltages,” Nature 562(7725), 101–104 (2018). [CrossRef]
32. L. Fan, C.-L. Zou, N. Zhu, and H. X. Tang, “Spectrotemporal shaping of itinerant photons via distributed nanomechanics,” Nat. Photonics 13(5), 323–327 (2019). [CrossRef]
33. C. Wang, C. Langrock, A. Marandi, M. Jankowski, M. Zhang, B. Desiatov, M. M. Fejer, and M. Lončar, “Ultrahigh-efficiency wavelength conversion in nanophotonic periodically poled lithium niobate waveguides,” Optica 5(11), 1438–1441 (2018). [CrossRef]
34. L. Fan, C.-L. Zou, M. Poot, R. Cheng, X. Guo, X. Han, and H. X. Tang, “Integrated optomechanical single-photon frequency shifter,” Nat. Photonics 10(12), 766–770 (2016). [CrossRef]
35. L. Fan, C.-L. Zou, R. Cheng, X. Guo, X. Han, Z. Gong, S. Wang, and H. X. Tang, “Superconducting cavity electro-optics: a platform for coherent photon conversion between superconducting and photonic circuits,” Sci. Adv. 4(8), eaar4994 (2018). [CrossRef]
36. X. Guo, C.-l. Zou, C. Schuck, H. Jung, R. Cheng, and H. X. Tang, “Parametric down-conversion photon-pair source on a nanophotonic chip,” Light: Sci. Appl. 6(5), e16249 (2017). [CrossRef]
37. G. Fujii, N. Namekata, M. Motoya, S. Kurimura, and S. Inoue, “Bright narrowband source of photon pairs at optical telecommunication wavelengths using a type-ii periodically poled lithium niobate waveguide,” Opt. Express 15(20), 12769–12776 (2007). [CrossRef]
38. L. Arizmendi, “Photonic applications of lithium niobate crystals,” physica status solidi (a) 201(2), 253–283 (2004). [CrossRef]
39. M. Zhang, C. Wang, R. Cheng, A. Shams-Ansari, and M. Lončar, “Monolithic ultra-high-q lithium niobate microring resonator,” Optica 4(12), 1536–1537 (2017). [CrossRef]
40. E. Lomonte, M. A. Wolff, F. Beutel, S. Ferrari, C. Schuck, W. H. P. Pernice, and F. Lenzini, “Single-photon detection and cryogenic reconfigurability in lithium niobate nanophotonic circuits,” (2021).
41. R. Luo, Y. He, H. Liang, M. Li, and Q. Lin, “Highly tunable efficient second-harmonic generation in a lithium niobate nanophotonic waveguide,” Optica 5(8), 1006–1011 (2018). [CrossRef]
