• 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