Competition mechanism of multiple four-wave mixing in highly nonlinear fiber: spatial instability and satellite characteristics

doi:10.1007/s12200-012-0280-z

Front Optoelec

2012, Vol. 5

Issue (4) : 414-428 https://doi.org/10.1007/s12200-012-0280-z

RESEARCH ARTICLE

Competition mechanism of multiple four-wave mixing in highly nonlinear fiber: spatial instability and satellite characteristics

Liang ZHAO¹(

), Junqiang SUN², Xinliang ZHANG², Cong CHEN³

1. Wuhan Foreign Languages School, Wuhan 430022, China; 2. Wuhan National Laboratory for Optoelectronics, School of Optoelectronic Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China; 3. Naval University of Engineering, Wuhan 430033, China

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Abstract

Competition mechanism in multiple four-wave mixing (MFWM) processes is demonstrated theoretically. Provided considering only two waves injected into a highly nonlinear fiber (HNLF), there are three modes displaying comprehensive dynamic behaviors, such as fixed points, periodic motion, and chaotic motion. Especially, Mode C of MFWM is emphasized by analyzing its phase-space trajectory to demonstrate nonlinear wave-wave interactions. The study shows that, when the phase-space trajectory approaches or gets through a saddle point, a dramatic power depletion for the injected wave can be realized, with the representative point moving chaotically, but when phase-space trajectories are distributed around a center point, the power for the injected wave is retained almost invariable, with the representative point moving periodically. Finally, the evolvement of satellite wave over an optical fiber is investigated by comparing it with the interference pattern in Young’s double-slit experiment.

Keywords highly nonlinear fiber (HNLF) periodic motion representative point Young’s double-slit experiment

Corresponding Author(s): ZHAO Liang,Email:liangshao_acool@smail.hust.edu.cn

Issue Date: 05 December 2012

Cite this article:

Liang ZHAO,Junqiang SUN,Xinliang ZHANG, et al. Competition mechanism of multiple four-wave mixing in highly nonlinear fiber: spatial instability and satellite characteristics[J]. Front Optoelec, 2012, 5(4): 414-428.

URL:

https://academic.hep.com.cn/foe/EN/10.1007/s12200-012-0280-z
https://academic.hep.com.cn/foe/EN/Y2012/V5/I4/414

Fig.1 Schematic diagram for the decomposition of MFWM

Tab.1 Contribution of all the FWM terms to the injected and sideband waves

Fig.2 Phase-space portraits with abnormal dispersion (see (a), (b) and (c)) and normal dispersion (see (d), (e) and (f)) regimes. (a) = -7; (b) = -3; (c) = -1; (d) = 10; (e) = 5; (f) = 1. Physical limits require that -1≤cos≤1 and -1≤sin≤1

Fig.3 Illustration of distribution of singular points with different values of . (a) Plot for singular point I (, ) = (( + 6)/12, 0), singular point II (, ) = ((-2)/4, 0) and singular point III (, ) = (0, 0); (b) plot for singular point IV

Fig.4 Illustration of distribution of singular points with different values of . (a) Plot for singular point ; (b) plot for singular point (, ) = (±, 0)

Fig.5 Illustration for phase-space portraits with (a) = -3; (b) = 3.5 and (c) = 7. Physical limits require that -1≤cos≤1 and -1≤sin≤1

Fig.6 (a) Sideband power as a function of with different values of ; (b) fractional power loss as a function of

Fig.7 Illustration of phase-space trajectories representing (a) an unstable saddle point with = -1 and (d) a stable center point with = 4. vs. with (b) = -1 and (e) = 4. cos vs. with (c) = -1 and (f) = 4

Fig.8 (a) Potential well energy () vs. normalized power with = 1 and different values of ; (b) potential well energy () vs. normalized power with = 1 and different values of Hamiltonian parameter ; (c) 3D plot for potential well energy () as function of normalized power and linear phase mismatch when = 1. Physical limits require that 0≤≤1

Fig.9 (a) Comparison of Young's double-slit experiment and (b) evolvement of satellite wave over an optical fiber

Tab.2 Comparison of Young’s double-slit experiment and evolvement of satellite wave over an optical fiber

Fig.10 Simulations for satellite power as a function of fiber length. (a) The red dash line represents the numerical result while the green dots denote the analytical solution. The related parameters are = 1555 nm, = 1545 nm, = 20 mW, = 10 mW and = 500 m; (b) The green and red dots correspond to interfered-destructive points satisfying the condition of = 4π/( - ) and = (4 2)π/( - ) respectively, the blue dots correspond to interfered-constructive points satisfying the condition of = (2 1)π/( - ). The related parameters are = 1555 nm, = 1548 nm, = 10 mW, = 5 mW and = 1000 m

Fig.11 Satellite power as function of fiber length with different injected wavelengths: (a) = 1555 nm, = 1548 nm; (b) = 1560 nm, = 1548 nm; (c) = 1550 nm, = 1545 nm; (d) = 1550 nm, = 1540 nm. The other parameters are = 10 mW, = 5 mW

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