volume | PIER Journals

Abstract

Optical amplification by nonlinear wave mixing offers wideband high-gain amplification that is desirable for a variety of applications. When the wave mixing process occurs in an interaction medium with sufficient length, the attained gain per excitation pulse is usually higher than that can be attained by lasers. Furthermore, the bandwidth of amplification via nonlinear wave mixing is much higher than the bandwidth allowed by laser transitions of laser gain media. However, optical amplification by nonlinear wave mixing offers negligible gain in the micrometer scale, due to a very limited length of the interaction medium. In micro-resonators, such a short interaction length does not offer sufficient small signal gain to compensate the round-trip loss. In this study, we present a Fletcher-Reeves algorithm-based nonlinear programming of the wave mixing process that tunes the frequencies of the excitation pulses of the source device in order to provide an ultra-high optical gain in the micro-scale via maximizing the electric energy density in a micro-resonator. Using this smart wave mixing approach, we obtained a micro-resonator gain of 4.7x10⁷ for an input wave at 640 THz, and a gain of 1.5x10⁸ at 100 THz. The results of our mathematical formulation are compared with well-known experimental results, and a mean accuracy of 99% is observed. The study aims to show that optical amplifiers that are based on the principle of nonlinear wave mixing can be used in the micro-scale for wideband ultra-high gain operation.

1. Chung, I., J.-H. Song, J. I. Jang, A. J. Freeman, and M. G. Kanatzidis, "Na₂Ge₂Se₅: A highly nonlinear optical material," Journal of Solid State Chemistry, November 2012.

2. Rout, A., G. S. Boltaev, R. A. Ganeev, Y. Fu, S. K. Maurya, V. V. Kim, K. S. Rao, and C. Guo, "Nonlinear optical studies of gold nanoparticle films," Nanomaterials, Vol. 9, 291, 2019.
doi:10.3390/nano9020291

3. Wu, R., J. Collins, L. T. Canham, and A. Kaplan, "The influence of quantum confinement on third-order nonlinearities in porous silicon thin films," Appl. Sci., Vol. 8, 1810, 2018.
doi:10.3390/app8101810

4. Sakhno, O., P. Yezhov, V. Hryn, V. Rudenko, and T. Smirnova, "Optical and nonlinear properties of photonic polymer nanocomposites and holographic gratings modified with noble metal nanoparticles," Polymers, Vol. 12, 480, 2020.
doi:10.3390/polym12020480

5. Varin, C., R. Emms, G. Bart, T. Fennel, and T. Brabec, "Explicit formulation of second and third order optical nonlinearity in the FDTD framework," Computer Physics Communications, Vol. 222, January 2018.
doi:10.1016/j.cpc.2017.09.018

6. Zygiridis, T. T. and N. V. Kantartzis, "Finite-difference modeling of nonlinear phenomena in time-domain electromagnetics: A review," Applications of Nonlinear Analysis. Springer Optimization and Its Applications, Vol. 134, Rassias T. (eds), Springer, Cham., 2018.

7. Xu, L., M. Rahmani, D. Smirnova, K. ZangenehKamali, G. Zhang, D. Neshev, and A. E. Miroshnichenko, "Highly-efficient longitudinal second-harmonic generation from doublyresonant AlGaAs nanoantennas," Photonics, Vol. 5, 29, 2018.
doi:10.3390/photonics5030029

8. De Ceglia, D., L. Carletti, M. A. Vincenti, C. De Angelis, and M. Scalora, "Second-harmonic generation in Mie-resonant GaAs nanowires," Appl. Sci., Vol. 9, 3381, 2019.
doi:10.3390/app9163381

9. Rocco, D., M. A. Vincenti, and C. De Angelis, "Boosting second harmonic radiation from AlGaAs nanoantennas with epsilon-near-zero materials," Appl. Sci., Vol. 8, 2212, 2018.
doi:10.3390/app8112212

10. Nguyen, D. T. T. and N. D. Lai, "Deterministic insertion of KTP nanoparticles into polymeric structures for efficient second-harmonic generation," Crystals, Vol. 9, 365, 2019.
doi:10.3390/cryst9070365

11. Huang, Z., H. Lu, H. Xiong, Y. Li, H. Chen, W. Qiu, H. Guan, J. Dong, W. Zhu, J. Yu, Y. Luo, J. Zhang, and Z. Chen, "Fano resonance on nanostructured lithium niobate for highly efficient and tunable second harmonic generation," Nanomaterials, Vol. 9, 69, 2019.
doi:10.3390/nano9010069

12. Cheng, T., Y. Xiao, S. Li, X. Yan, X. Zhang, T. Suzuki, and Y. Ohishi, "Highly efficient second-harmonic generation in a tellurite optical fiber," Optics Letters, Vol. 44, No. 19, 2019.
doi:10.1364/OL.44.004686

13. Kumar, S. and M. Sen, "High-gain, low-threshold and small-footprint optical parametric amplifier for photonic integrated circuits," J. Opt. Soc. Am. B, Vol. 35, 362-371, 2018.
doi:10.1364/JOSAB.35.000362

14. APL Photonics, Vol. 4, 086102, 2019, https://doi.org/10.1063/1.5103272.

15. Milton, M. J. T., T. J. McIlveen, D. C. Hanna, and P. T. Woods, "A high-gain optical parametric amplifier tunable between 3.27 and 3.65 μm," Optics Communications, Vol. 93, No. 3–4, 186-190, 1992, ISSN 0030-4018.
doi:10.1016/0030-4018(92)90526-W

16. Wnuk, P., Y. Stepanenko, and C. Radzewicz, "High gain broadband amplification of ultraviolet pulses in optical parametric chirped pulse amplifier," Optics Express, Vol. 18, No. 8, 7911-7916, Apr. 2010.
doi:10.1364/OE.18.007911

17. Ooi, K., D. Ng, T. Wang, et al. "Pushing the limits of CMOS optical parametric amplifiers with USRN: Si₇N₃ above the two-photon absorption edge," Nat. Commun., Vol. 8, 13878, 2017.
doi:10.1038/ncomms13878

18. Wei, X., Y. Peng, X. Luo, T. Zhou, J. Peng, Z. Nie, and J. Gao, "High-efficiency mid-infrared optical parametric amplifier with approximate uniform rectangular pump distribution," Proc. SPIE 10436, High-Power Lasers: Technology and Systems, Platforms, and Effects, 104360I, Oct. 26, 2017.

19. Asırım, O. E. and M. Kuzuoglu, "Super-gain optical parametric amplification in dielectric micro-resonators via BFGS algorithm-based non-linear programming," Appl. Sci., Vol. 10, 1770, 2020.
doi:10.3390/app10051770

20. Asırım, O. E. and M. Kuzuoglu, "Enhancement of optical parametric amplification in micro-resonators via gain medium parameter selection and mean cavity wall reflectivity adjustment," Journal of Physics B: Atomic, Molecular and Optical Physics, Apr. 2020.

21. Coetzee, R. S., A. Zukauskas, J. M. Melkonian, and V. Pasiskevicius, "An efficient 2 μm optical parametric amplifier based on large-aperture periodically poled RB:KTP," Proc. SPIE 10562, International Conference on Space Optics — ICSO 2016, 105620L, Sep. 25, 2017.

22. Liu, X., R. Osgood, Y. Vlasov, et al. "Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides," Nature Photon, Vol. 4, 557-560, 2010.
doi:10.1038/nphoton.2010.119

23. Gonzalez, M. and Y. Lee, "A study on parametric amplification in a piezoelectric MEMS device," Micromachines (Basel), Vol. 10, No. 1, 19, 2018.
doi:10.3390/mi10010019

24. Al-Mahmoud, M., A. A. Rangelov, V. Coda, and G. Montemezzani, "Segmented composite optical parametric amplification," Appl. Sci., Vol. 10, 1220, 2020.
doi:10.3390/app10041220

25. Kida, Y. and T. Imasaka, "Four-wave optical parametric amplification in a raman-active gas," Photonics, Vol. 2, 933-945, 2015.
doi:10.3390/photonics2030933

26. Manzoni, C. and G. Cerullo, J. Opt., Vol. 18, 103501, 2016.

27. Wang, K.-Y. and A. C. Foster, J. Opt., Vol. 17, 094012, 2015.

28. Schmidt, B., N. Thire, M. Boivin, et al. "Frequency domain optical parametric amplification," Nat. Commun., Vol. 5, 3643, 2014.
doi:10.1038/ncomms4643

29. Dao, L., K. Dinh, and P. Hannaford, "Perturbative optical parametric amplification in the extreme ultraviolet," Nat. Commun., Vol. 6, 7175, 2015.
doi:10.1038/ncomms8175

30. Ilday, F. O. and F. X. Kartner, "Cavity-enhanced optical parametric chirped-pulse amplification," Opt. Lett., Vol. 31, 637-639, 2006.
doi:10.1364/OL.31.000637

31. Asırım, O. E. and M. Kuzuoglu, "Optimization of optical parametric amplification efficiency in a microresonator under ultrashort pump wave excitation," International Journal of Electromagnetics and Applications, Vol. 9, No. 1, 14-34, 2019.

32. Yang, M., et al., "An octave-spanning optical parametric amplifier based on a low-dispersion silicon-rich nitride waveguide," IEEE Journal of Selected Topics in Quantum Electronics, Vol. 24, No. 6, 1-7, Art No. 8300607, Nov.–Dec. 2018.
doi:10.1109/JSTQE.2018.2836992

33. Varin, C., G. Bart, T. Fennel, and T. Brabec, "Nonlinear Lorentz model for the description of nonlinear optical dispersion in nanophotonics simulations [Invited]," Opt. Mater. Express, Vol. 9, 771-778, 2019.
doi:10.1364/OME.9.000771

34. Boyd, R. W., Nonlinear Optics, 105-107, Academic Press, New York, 2008.

35. Saleh, B. E. A. and M. C. Teich, Fundamentals of Photonics, 885-917, Wiley-Interscience, New York, 2007.

36. Nocedal, J. and S. J. Wright, Numerical Optimization, 36-37, Springer, New York, 2006.

37. Asırım, O. E., Super-gain parametric wave amplification in optical micro-resonators using ultrashort pump waves, Middle East Technical University Library, 2020.

38. Paschotta, R., "Article on ‘optical parametric amplifiers’," Encyclopedia of Laser Physics and Technology, 1st Edition, Wiley-VCH, Oct. 2008, ISBN 978-3-527-40828-3.

39. Yang, Y., D. Zhu, W. Yan, et al. "A general theoretical and experimental framework for nanoscale electromagnetism," Nature, Vol. 576, 248-252, 2019.
doi:10.1038/s41586-019-1803-1

40. Abubakar, A. B., P. Kumam, H. Mohammad, A. M. Awwal, and K. Sitthithakerngkiet, "A modified Fletcher-Reeves conjugate gradient method for monotone nonlinear equations with some applications," Mathematics, Vol. 7, 745, 2019.
doi:10.3390/math7080745

41. Sellami, B. and M. C. E. Sellami, "Global convergence of a modified Fletcher-Reeves conjugate gradient method with Wolfe line search," Asian-European Journal of Mathematics, Vol. 13, No. 04, Jun. 2020.
doi:10.1142/S1793557120500813

42. Pang, D., S. Du, and J. Ju, "The smoothing Fletcher-Reeves conjugate gradient method for solving finite minimax problems," Science Asia, Vol. 42, 40-45, 2016.
doi:10.2306/scienceasia1513-1874.2016.42.040

43. Frazer, L., J. K. Gallaher, and T. W. Schmidt, "Optimizing the efficiency of solar photon upconversion," ACS Energy Letters, Vol. 2, No. 6, 1346-1354, 2017.
doi:10.1021/acsenergylett.7b00237

44. Seo, Y.-K., J.-H. Seo, and W.-Y. Choi, "Photonic frequency-upconversion efficiencies in semiconductor optical amplifiers," Photonics Technology Letters, Vol. 15, 751-753, IEEE, 2003.
doi:10.1109/LPT.2003.809970

45. Tan, W., X. Qiu, G. Zhao, et al. "High-efficiency frequency upconversion of 1.5 μm laser based on a doubly resonant external ring cavity with a low finesse for signal field," Appl. Phys. B, Vol. 123, 52, 2017.
doi:10.1007/s00340-016-6626-2

Dr. Özüm Emre Aşırım

Dr. Alim Yolalmaz