Desurvire, E. Erbium-Doped Fiber Amplifiers: Principles and Applications (Wiley, 1994).

Tse, M. et al. Quantum-enhanced advanced LIGO detectors in the era of gravitational-wave astronomy. Phys. Rev. Lett. 123, 231107 (2019).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Casacio, C. A. et al. Quantum-enhanced nonlinear microscopy. Nature 594, 201–206 (2021).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Madsen, L. S. et al. Quantum computational advantage with a programmable photonic processor. Nature 606, 75–81 (2022).

Article 
ADS 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Kawasaki, A. et al. Real-time observation of picosecond-timescale optical quantum entanglement towards ultrafast quantum information processing. Nat. Photon. 19, 271–276 (2025).

Article 
ADS 
CAS 

Google Scholar
 

Mears, R., Reekie, L., Jauncey, I. & Payne, D. Low-noise erbium-doped fibre amplifier operating at 1.54um. Electron. Lett. 23, 1026–1028 (1987).

Article 
ADS 

Google Scholar
 

Sobhanan, A. et al. Semiconductor optical amplifiers: recent advances and applications. Adv. Opt. Photon. 14, 571–651 (2022).

Article 

Google Scholar
 

Baumgartner, R. & Byer, R. Optical parametric amplification. IEEE J. Quantum Electron. 15, 432–444 (1979).

Article 
ADS 

Google Scholar
 

Jankowski, M., Mishra, J. & Fejer, M. M. Dispersion-engineered χ(2) nanophotonics: a flexible tool for nonclassical light. J. Phys. Photon. 3, 042005 (2021).

Article 
CAS 

Google Scholar
 

Ho, M.-C., Uesaka, K., Marhic, M., Akasaka, Y. & Kazovsky, L. 200-nm-bandwidth fiber optical amplifier combining parametric and Raman gain. J. Lightwave Technol. 19, 977–981 (2001).

Article 
ADS 

Google Scholar
 

Kobayashi, T. et al. 103-ch. 132-Gbaud PS-QAM signal inline-amplified transmission with 14.1-THz bandwidth lumped PPLN-based OPAs over 400-km G.652.D SMF. In Proc. Optical Fiber Communication Conference (OFC) 2023 Th4B.6 (Optica Publishing, 2023).

Shimizu, S. et al. Wideband optical parametric amplification of 8.375-THz WDM signal using cascaded PPLN waveguides with reused pump light. J. Lightwave Technol. 41, 7399–7407 (2023).

Article 
ADS 
CAS 

Google Scholar
 

Shimizu, S. et al. Hybrid lumped repeater using PPLN-based high-gain optical parametric phase conjugators and EDFAs for C+L-band transmission. J. Lightwave Technol. 42, 3580–3591 (2024).

Article 
ADS 
CAS 

Google Scholar
 

Kuznetsov, N. et al. An ultra-broadband photonic-chip-based parametric amplifier. Nature 639, 928–934 (2025).

Article 
ADS 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Yariv, A., Fekete, D. & Pepper, D. M. Compensation for channel dispersion by nonlinear optical phase conjugation. Opt. Lett. 4, 52–54 (1979).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Umeki, T. et al. Simultaneous nonlinearity mitigation in 92 × 180-Gbit/s PDM-16QAM transmission over 3840 km using PPLN-based guard-band-less optical phase conjugation. Opt. Express 24, 16945–16951 (2016).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Foo, B., Karlsson, M., Vijayan, K., Mazur, M. & Andrekson, P. A. Analysis of nonlinearity mitigation using phase-sensitive optical parametric amplifiers. Opt. Express 27, 31926–31941 (2019).

Article 
ADS 
PubMed 

Google Scholar
 

Kazama, T. et al. Over-30-dB gain and 1-dB noise figure phase-sensitive amplification using a pump-combiner-integrated fiber I/O PPLN module. Opt. Express 29, 28824–28834 (2021).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Ye, Z. et al. Overcoming the quantum limit of optical amplification in monolithic waveguides. Sci. Adv. 7, eabi8150 (2021).

Article 
ADS 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Wu, L.-A., Kimble, H. J., Hall, J. L. & Wu, H. Generation of squeezed states by parametric down conversion. Phys. Rev. Lett. 57, 2520–2523 (1986).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Nehra, R. et al. Few-cycle vacuum squeezing in nanophotonics. Science 377, 1333–1337 (2022).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Stokowski, H. S. et al. Integrated quantum optical phase sensor in thin film lithium niobate. Nat. Commun. 14, 3355 (2023).

Article 
ADS 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Butt, M., Janaszek, B. & Piramidowicz, R. Lighting the way forward: the bright future of photonic integrated circuits. Sens. Int. 6, 100326 (2025).

Article 

Google Scholar
 

Foster, M. A. et al. Broad-band optical parametric gain on a silicon photonic chip. Nature 441, 960–963 (2006).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Liu, X., Osgood, R. M., Vlasov, Y. A. & Green, W. M. J. Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides. Nat. Photon. 4, 557–560 (2010).

Article 
ADS 
CAS 

Google Scholar
 

Kuyken, B. et al. 50 db parametric on-chip gain in silicon photonic wires. Opt. Lett. 36, 4401–4403 (2011).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Wang, K.-Y. & Foster, A. C. Ultralow power continuous-wave frequency conversion in hydrogenated amorphous silicon waveguides. Opt. Lett. 37, 1331–1333 (2012).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Ooi, K. J. A. et al. Pushing the limits of CMOS optical parametric amplifiers with USRN:Si7N3 above the two-photon absorption edge. Nat. Commun. 8, 13878 (2017).

Article 
ADS 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Riemensberger, J. et al. A photonic integrated continuous-travelling-wave parametric amplifier. Nature 612, 56–61 (2022).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Ayan, A., Liu, J., Kippenberg, T. J. & Brès, C.-S. Towards efficient broadband parametric conversion in ultra-long Si3N4 waveguides. Opt. Express 31, 40916–40927 (2023).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Qu, Y. et al. Integrated optical parametric amplifiers in silicon nitride waveguides incorporated with 2D graphene oxide films. Light Adv. Manuf. 4, 437 (2023).

Article 

Google Scholar
 

Zhao, P. et al. Ultra-broadband optical amplification using nonlinear integrated waveguides. Nature 640, 918–923 (2025).

Article 
ADS 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Sohler, W. & Suche, H. Optical parametric amplification in Ti-diffused LiNbO3 waveguides. Appl. Phys. Lett. 37, 255–257 (1980).

Article 
ADS 
CAS 

Google Scholar
 

Serkland, D. K., Fejer, M. M., Byer, R. L. & Yamamoto, Y. Squeezing in a quasi-phase-matched LiNbO3 waveguide. Opt. Lett. 20, 1649–1651 (1995).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Umeki, T., Tadanaga, O., Takada, A. & Asobe, M. Phase sensitive degenerate parametric amplification using directly-bonded PPLN ridge waveguides. Opt. Express 19, 6326–6332 (2011).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Kashiwazaki, T. et al. Fabrication of low-loss quasi-single-mode PPLN waveguide and its application to a modularized broadband high-level squeezer. Appl. Phys. Letters 119, 251104 (2021).

Article 
ADS 
CAS 

Google Scholar
 

Jankowski, M. et al. Quasi-static optical parametric amplification. Optica 9, 273–279 (2022).

Article 
ADS 

Google Scholar
 

Ledezma, L. et al. Intense optical parametric amplification in dispersion-engineered nanophotonic lithium niobate waveguides. Optica 9, 303–308 (2022).

Article 
ADS 

Google Scholar
 

Li, X. et al. Two-stage lithium niobate nonlinear photonic circuits for low-crosstalk and broadband all optical wavelength conversion. APL Photon. 10, 076121 (2025).

Article 
ADS 
CAS 

Google Scholar
 

Chen, M. et al. High-gain optical parametric amplification with a continuous-wave pump using a domain-engineered thin-film lithium niobate waveguide. Optica 12, 1242–1249 (2025).

Article 
ADS 
CAS 

Google Scholar
 

Santandrea, M., Stefszky, M. & Silberhorn, C. General framework for the analysis of imperfections in nonlinear systems. Opt. Lett. 44, 5398–5401 (2019).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Zhao, J. et al. Unveiling the origins of quasi-phase matching spectral imperfections in thin-film lithium niobate frequency doublers. APL Photon. 8, 126106 (2023).

Article 
ADS 
CAS 

Google Scholar
 

Zhang, M., Wang, C., Cheng, R., Shams-Ansari, A. & Lončar, M. Monolithic ultra-high-Q lithium niobate microring resonator. Optica 4, 1536–1537 (2017).

Article 
ADS 
CAS 

Google Scholar
 

Khalatpour, A., Qi, L., Fejer, M. M. & Safavi-Naeini, A. Roughness-limited performance in ultra-low-loss lithium niobate cavities. Adv. Optical Mater. https://doi.org/10.1002/adom.202502355 (2025).

Kashiwazaki, T. et al. Over-8-dB squeezed light generation by a broadband waveguide optical parametric amplifier toward fault-tolerant ultra-fast quantum computers. Appl. Phys. Lett. 122, 234003 (2023).

Article 
ADS 
CAS 

Google Scholar
 

McKenna, T. P. et al. Ultra-low-power second-order nonlinear optics on a chip. Nat. Commun. 13, 4532 (2022).

Article 
ADS 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Zhao, Y. et al. Large regenerative parametric amplification on chip at ultra-low pump powers. Optica 10, 819–825 (2023).

Article 
ADS 
CAS 

Google Scholar
 

Menotti, M. et al. Nonlinear coupling of linearly uncoupled resonators. Phys. Rev. Lett. 122, 013904 (2019).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Wang, Z.-Y. et al. Toward ultimate-efficiency frequency conversion in nonlinear optical microresonators. Sci. Adv. 11, eadu7605 (2025).

Article 
ADS 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Carmon, T., Yang, L. & Vahala, K. J. Dynamical thermal behavior and thermal self-stability of microcavities. Opt. Express 12, 4742–4750 (2004).

Article 
ADS 
PubMed 

Google Scholar
 

Hu, C. et al. High-efficient coupler for thin-film lithium niobate waveguide devices. Opt. Express 29, 5397–5406 (2021).

Article 
ADS 
PubMed 

Google Scholar
 

Baney, D. M., Gallion, P. & Tucker, R. S. Theory and measurement techniques for the noise figure of optical amplifiers. Opt. Fiber Technol. 6, 122–154 (2000).

Article 
ADS 

Google Scholar
 

Cestier, I. et al. Chip-scale parametric amplifier with 11dB gain at 1550nm based on a slow-light GaInP photonic crystal waveguide. Opt. Lett. 37, 3996–3998 (2012).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Kishimoto, T., Inafune, K., Ogawa, Y., Sasaki, H. & Murai, H. Highly efficient phase-sensitive parametric gain in periodically poled LiNbO3 ridge waveguide. Opt. Lett. 41, 1905–1908 (2016).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Lamont, M. R. et al. Net-gain from a parametric amplifier on a chalcogenide optical chip. Opt. Express 16, 20374–20381 (2008).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Sua, Y. M., Chen, J.-Y. & Huang, Y.-P. Ultra-wideband and high-gain parametric amplification in telecom wavelengths with an optimally mode-matched ppln waveguide. Opt. Lett. 43, 2965–2968 (2018).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Guo, X., Zou, C.-L. & Tang, H. X. 70 dB long-pass filter on a nanophotonic chip. Opt. Express 24, 21167–21176 (2016).

Article 
ADS 
PubMed 

Google Scholar
 

Guo, Q. et al. Femtojoule femtosecond all-optical switching in lithium niobate nanophotonics. Nat. Photon. 16, 625–631 (2022).

Article 
ADS 
CAS 

Google Scholar
 

Siegman, A. E. Lasers (University Science Books, 1986).

Levine, J. A simplified calculation of power-broadened linewidths, with application to resonance ionization mass spectrometry. Spectrochim. Acta Part B At. Spectrosc. 69, 61–66 (2012).

Article 
CAS 

Google Scholar
 

Chen, P.-K. et al. Adapted poling to break the nonlinear efficiency limit in nanophotonic lithium niobate waveguides. Nat. Nanotechnol. 19, 44–50 (2024).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Xin, C. J. et al. Wavelength-accurate and wafer-scale process for nonlinear frequency mixers in thin-film lithium niobate. Commun. Phys. 8, 136 (2025).

Article 

Google Scholar