FM Mode-Locking Fiber Laser

Abstract

In this paper the study of Frequency Modulation Harmonic Mode-locking for Ytterbium Doped Fiber Laser is presented. The model studied, uses ytterbium-doped, single mode fiber pumped by 976 nm laser source is used with 150 mW pumping power to produce 1055 nm output laser and Frequency Modulation Harmonically Mode-Locked by MZI optical modulator. The effect of both normal and anomalous dispersion regimes on output pulses is investigated. Also, modulation frequency effect on pulse parameters is investigated by driving the modulator into different frequencies values. This study shows the stability of working in anomalous dispersion regime and the pulse compression effect is better than counterpart normal regime, due to the combination effect of both negative(Group velocity dispersion), GVD and nonlinearity. Also it shows the great effect of modulation frequency on pulse parameters and stability of the system. Model-locking fiber laser master equation is introduced, and using the assumed pulse shapes for both dispersion regimes after modifying (Ginzburg-Landau equation), GLE and by applying the moment method, a set of five ordinary differential equations are introduced describing pulse parameters evolution during each roundtrip.To solve these equations numerically using fourth-fifth order, Runge-Kutta method is performed through MatLab 7.0 program. ‫ﺍﻟﻤﻘﻔﻠﺔ‬ ‫ﺫﻭﺍﻷﻨﻤﺎﻁ‬ ‫ﺍﻟﺒﺼﺭﻴﺔ‬ ‫ﺍﻷﻟﻴﺎﻑ‬ ‫ﻟﻠﻴﺯﺭ‬ ‫ﺍﻟﺘﺭﺩﺩﻱ‬ ‫ﺍﻟﺘﻀﻤﻴﻥ‬ ‫ﺍﻟﺨﻼﺼـﺔ‬ ‫ﺍﻷﻨﻤ‬ ‫ﻗﻔل‬ ‫ﺩﺭﺍﺴﺔ‬ ‫ﺘﻡ‬ ‫ﻫﺫﺍﺍﻟﺒﺤﺙ‬ ‫ﻓﻲ‬ ‫ﺒﻌﻨﺼﺭ‬ ‫ﺍﻟﻤﺸﺎﺏ‬ ‫ﺍﻟﺒﺼﺭﻱ‬ ‫ﺍﻟﻠﻴﻑ‬ ‫ﻟﻠﻴﺯﺭ‬ ‫ﺍﻟﺘﺭﺩﺩﻱ‬ ‫ﻟﻠﺘﻀﻤﻴﻥ‬ ‫ﺍﻟﻤﺘﻨﺎﻏﻡ‬ ‫ﺎﻁ‬ ‫ﺍﻟﻴﻭﺘﺭﺒﻴﻭﻡ‬. ‫ﺒﻤﺼﺩﺭ‬ ‫ﺍﻟﻤﻀﺦ‬ ‫ﺍﻷﺤﺎﺩﻱ‬ ‫ﺍﻟﻨﻤﻁ‬ ‫ﻟﻠﻴﻑ‬ ‫ﺍﻟﻴﻭﺘﺭﺒﻴﻭﻡ‬ ‫ﻤﺸﺎﺏ‬ ‫ﻴﺘﻀﻤﻥ‬ ‫ﺍﻟﻤﺩﺭﻭﺱ‬ ‫ﺍﻟﻨﻤﻭﺫﺝ‬ ‫ﻟﻴﺯﺭﻱ‬) 976nm (‫ﻀﺦ‬ ‫ﻗﺩﺭﺓ‬ ‫ﻤﻊ‬) 150mW (‫ﻟﻴﺯﺭﻱ‬ ‫ﺨﺭﺝ‬ ‫ﻴﻨﺘﺞ‬) 1055mW (‫ﺍﻟﻨﻤﻁ‬ ‫ﺒﻘﻔل‬ ‫ﻤﺘﻨﺎﻏﻡ‬ ‫ﺘﺭﺩﺩ‬ ‫ﻭﺘﻀﻤﻴﻥ‬ ‫ﺘﺩﺍﺨل‬ ‫ﺠﻬﺎﺯ‬ ‫ﺒﺎﺴﺘﺨﺩﺍﻡ‬) Mach-Zender Interferometer (‫ﺒﺼﺭﻱ‬ ‫ﻜﻤﻀﻤﻥ‬. ‫ﺘﺄﺜﻴﺭﺍﻟﺘﺸﺘﺕ‬ ‫ﺘﻔﺴﻴﺭ‬ ‫ﻜﻤﺎﺘﻡ‬ ‫ﺍﻟﺨﺎﺭﺠﺔ‬ ‫ﺍﻟﻨﺒﻀﺔ‬ ‫ﻓﻲ‬ ‫ﻭﺍﻟﺸﺎﺫ‬ ‫ﺍﻷﻋﺘﻴﺎﺩﻱ‬. ‫ُﺩﻨﺎﺍﻟﻤﻀﻤﻥ‬ ٌ ُ ‫ﹸ‬ ‫ﻗ‬ ‫ﺤﻴﺙ‬ ‫ﺍﻟﻨﺒﻀﺔ‬ ‫ﻋﻭﺍﻤل‬ ‫ﺍﻟﺘﺭﺩﺩﻱ‬ ‫ﺍﻟﺘﻀﻤﻴﻥ‬ ‫ﺘﺄﺜﻴﺭ‬ ‫ﺘﻔﺴﻴﺭ‬ ‫ﻜﻤﺎﺘﻡ‬ ‫ﺍﻟﺘﺭﺩﺩﺍﺕ‬ ‫ﻤﻥ‬ ‫ﻤﺨﺘﻠﻔﺔ‬ ‫ﻟﻘﻴﻡ‬. ‫ﺍﻟﺸﺎﺫ‬ ‫ﺍﻟﺘﺸﺘﺕ‬ ‫ﻤﺩﻯ‬ ‫ﻓﻲ‬ ‫ﺍﻟﻌﻤل‬ ‫ﺃﺴﺘﻘﺭﺍﺭﻴﺔ‬ ‫ﺍﻟﺩﺭﺍﺴﺔ‬ ‫ﺃﻅﻬﺭﺕ‬) ‫ﺍﻷﻋﺘﻴﺎﺩﻱ‬ ‫ﻏﻴﺭ‬ (‫ﺍﻟ‬ ‫ﻀﻐﻁ‬ ‫ﻭﺘﺄﺜﻴﺭ‬ ‫ﻤﻨﻬﺎﻓﻲ‬ ‫ﻨﺒﻀﺔﺃﻓﻀل‬ ‫ﺍﻟﻤﺸﺘﺭﻙ‬ ‫ﺍﻟﺘﺄﺜﻴﺭ‬ ‫ﻭﺒﺴﺒﺏ‬ ،‫ﺍﻷﻋﺘﻴﺎﺩﻱ‬ ‫ﺍﻟﺘﺸﺘﺕ‬ ‫ﻤﺩﻯ‬ GVD ‫ﻭﺍ‬ ‫ﺍﻟﺴﺎﻟﺏ‬ ‫ﻟ‬ ‫ﻼﺨﻁﻴﺔ‬. ‫ﺍﻟﻜﺒﻴﺭ‬ ‫ﺍﻟﺘﺄﺜﻴﺭ‬ ‫ﺍﻟﺩﺭﺍﺴﺔ‬ ‫ﺃﻅﻬﺭﺕ‬ ‫ﻜﺫﻟﻙ‬ ‫ﺍﻟﻤﻨﻅﻭﻤـﺔ‬ ‫ﻭﺃﺴﺘﻘﺭﺍﺭﻴﺔ‬ ‫ﺍﻟﻨﺒﻀﺔ‬ ‫ﻋﻭﺍﻤل‬ ‫ﻓﻲ‬ ‫ﺍﻟﺘﺭﺩﺩﻱ‬ ‫ﻟﻠﺘﻀﻤﻴﻥ‬. ‫ﻤﻘﻔل‬ ‫ﺍﻟﻠﻴﻑ‬ ‫ﻟﻠﻴﺯﺭ‬ ‫ﺍﻟﺭﺌﻴﺴﻴﺔ‬ ‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬ ‫ﻭﻟﻘﺩﺃﺩﺨﻠﺕ‬ ‫ﻨ‬ ‫ﻟﻜﻼ‬ ‫ﺍﻷﻓﺘﺭﺍﻀﻴﺔ‬ ‫ﺍﻷﺸﻜﺎل‬ ‫،ﻭﺒﺄﺴﺘﺨﺩﺍﻡ‬ ‫ﺍﻟﻨﻤﻁ‬ ‫ﻤﻌﺎﺩﻟﺔ‬ ‫ﺘﻌﺩﻴل‬ ‫ﺒﻌﺩ‬ ‫ﺍﻟﺘﺸﺘﺕ‬ ‫ﻭﻋﻲ‬) Ginzburg-Landau equation (‫ﻋﻭﺍﻤل‬ ‫ﺤل‬ ‫ﺘﺼﻑ‬ ‫ﺘﻔﺎﻀﻠﻴﺔ‬ ‫ﻤﻌﺎﺩﻻﺕ‬ ‫ﺨﻤﺴﺔ‬ ‫ﻤﻥ‬ ‫ﻤﺠﻤﻭﻋﺔ‬ ‫ﺍﻟﻁﺭﻴﻘﺔﺍﻷﻋﺘﻴﺎﺩﻴﺔ،ﻜﻤﺎﺃﺩﺨﻠﺕ‬ ‫ﻭﺃﺴﺘﺨﺩﺍﻡ‬ ‫ﺩﻭﺭﺓ‬ ‫ﻜل‬ ‫ﺨﻼل‬ ‫ﺍﻟﻨﺒﻀﺔ‬. ‫ﻫﺫﻩ‬ ‫ﺤل‬ ‫ﺃﺠل‬ ‫ﻤﻥ‬ ‫ﺍﻟﻤﻌ‬ ‫ﺎ‬ ‫ﻋﺩﺩﻴﺎ‬ ‫ﺩﻻﺕ‬ " ‫ﺘﻡ‬ ‫ﺍﻟﻤﺭﺘﺒﺔ‬ ‫ﻁﺭﻴﻘﺔ‬ ‫ﺃﺴﺘﺨﺩﺍﻡ‬-‫ﺍﻟﺭﺍﺒﻌﺔ‬-‫ﺍﻟﺨﺎﻤﺴﺔ‬ ‫ل‬) Runge-Kutta (‫ﻤﻥ‬ ‫ﺒﺭﻨﺎﻤ‬ ‫ﺨﻼل‬ ‫ﺞ‬ MatLab 7.0 .