Инд. авторы:	Medvedev S., Bednyakova A.
Заглавие:	Hamiltonian approach for optimization of phase-sensitive double-pumped parametric amplifiers
Библ. ссылка:	Medvedev S., Bednyakova A. Hamiltonian approach for optimization of phase-sensitive double-pumped parametric amplifiers // Optics Express. - 2018. - Vol.26. - Iss. 12. - P.15503-15518. - ISSN 1094-4087.
Внешние системы:	DOI: 10.1364/OE.26.015503; РИНЦ: 35779167; SCOPUS: 2-s2.0-85048357664; WoS: 000435068300059;
Реферат:	eng: In this work we applied a Hamiltonian formalism to simplify the equations of non-degenerate nonlinear four-wave mixing to the one-degree-of-freedom Hamiltonian equations with a three-parameter Hamiltonian. Thereby, a problem of signal amplification in a phase-sensitive double-pumped parametric fiber amplifier with pump depletion was reduced to a geometrical study of the phase portraits of the one-degree-of-freedom Hamiltonian system. For a symmetric case of equal pump powers and equal signal and idler powers at the fiber input, it has been shown that the theoretical maximum gain occurs on the extremal trajectories. However, to reduce the nonlinear interaction of waves, we proposed to choose the separatrix as the optimal trajectory on the phase plane. Analytical expressions were found for the maximum amplification, as well as the length of optical fiber and the relative phase of interacting waves allowing this amplification. Using the proposed approach, we optimized of the phase-sensitive parametric amplifier. As a result, the optimal parameters of the phase-sensitive amplifier were found and the maximum possible signal amplification was realized in a broad range of signal wavelengths. (C) 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Ключевые слова:	AMPLIFICATION; FIBER; INSTABILITY; 3-WAVE;
Издано:	2018
Физ. характеристика:	с.15503-15518
Цитирование:	1. J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002). 2. M. E. Marhic, Fiber optical parametric amplifiers, oscillators and related devices (Cambridge University, 2008). 3. C. McKinstrie and S. Radic, “Phase-sensitive amplification in a fiber,” Opt. Express 12(20), 4973–4979 (2004). 4. C. McKinstrie, M. Raymer, S. Radic and M. Vasilyev, “Quantum mechanics of phase-sensitive amplification in a fiber,” Opt. Commun. 257(1), 146–163 (2006). 5. Z. Tong, C. Lundström, P. Andrekson, C. McKinstrie, M. Karlsson, D. Blessing, E. Tipsuwannakul, B. Puttnam, H. Toda and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011). 6. C. J. McKinstrie and G. G. Luther, “Solitary-wave solutions of the generalised three-wave and four-wave equations,” Phys. Lett. A 127(1), 14–18 (1988). 7. G. Cappellini and S. Trillo, “Third-order three-wave mixing in single-mode fibers: exact solutions and spatial instability e ects,” J. Opt. Soc. Am. B 8(4), 824–838 (1991). 8. S. Trillo and S. Wabnitz. “Dynamics of the nonlinear modulational instability in optical fibers,” Opt. Lett. 16(13), 986–988 (1991). 9. C. De Angelis, M. Santagiustina and S. Trillo, “Four-photon homoclinic instabilities in nonlinear highly birefringent media,” Phys. Rev. A 51(1), 774–791 (1995). 10. A. Bendahmane, A. Mussot, A. Kudlinski, P. Szriftgiser, M. Conforti, S. Wabnitz, and S. Trillo, “Optimal frequency conversion in the nonlinear stage of modulation instability,” Opt. Express 23(24), 30861–30871 (2015). 11. C. J. McKinstrie, “Stokes-space formalism for Bragg scattering in a fiber,” Opt. Commun. 282(8), 1557–1562 (2009). 12. H. Ste ensen, J. R. Ott, K. Rottwitt, and C. J. McKinstrie, “Full and semi-analytic analyses of two-pump parametric amplification with pump depletion,” Opt. Express 19(7), 6648–6656 (2011). 13. J. R. Ott,H. Ste ensen, K. Rottwitt, and C. J. McKinstrie, “Geometric interpretation of four-wave mixing,” Phys. Rev. A 88(4), 043805 (2013). 14. A. A. Redyuk, A. E. Bednyakova, S. B. Medvedev, M. P. Fedoruk, and S. K. Turitsyn, “Simple geometric interpretation of signal evolution in phase-sensitive fibre optic parametric amplifier,” Opt. Express 25(1), 223–231 (2017). 15. J. M. Chavez Boggio, J. D. Marconi, S. R. Bickham, and H. L. Fragnito, “Spectrally flat and broadband double-pumped fiber optical parametric amplifiers,” Opt. Express 15(9), 5288–5309 (2007). 16. P. F. Byrd and M. D. Friedman, Handbook of Elliptic Integrals for Engineers and Scientists (Springer, 1971). 17. H. B. Dwight, Tables of Integrals and Other Mathematical Data (The Macmillan Company, 1961). 18. M. E. Marhic, A. A. Rieznik, and H. H. Fragnito, “Investigation of the gain spectrum near the pumps of two-pump fiber-optic parametric amplifiers,” J. Opt. Soc. Am. B 25(1), 22–30 (2008).