The variation of the output power of Ytterbium-doped fiber lasers (YDFLs) with temperature has been evaluated. Temperature-dependent rate equations of ytterbium fiber laser based on Fabry-Perot design have been discussed. The results demonstrate that the output power decrease with the increase of temperature. The effect of the temperature on the output performance increases by increasing the pump power. The effect of temperature can be ignored only for lower pump power. The theoretical result is in agreement with the published experimental results

El-Nahal, Fady I.

Husein, Abdel Hakeim M.

Institutional Repository of the Islamic University of Gaza

   JOURNAL OF ENGINEERING RESEARCH AND TECHNOLOGY, VOLUME 3, ISSUE 1, MARCH 2016   1   Temperature Dependency of Ytterbium-Doped Fiber Laser (YDFL) Based on Fabry-Perot Design Operating at 915 nm and 970 nm High Power Pumping Configuration  Fady I. El-Nahal1, Abdel Hakeim M. Husein2  1Electrical Engineering Department, Islamic University of Gaza, Gaza, Palestine fnahal@iugaza.edu.ps 2Physics Department, Al Aqsa University, Gaza, Palestine.  Abstract— The variation of the output power of Ytterbium-doped fiber lasers (YDFLs) with temperature has been evaluated. Temperature-dependent rate equations of ytterbium fiber laser based on Fabry-Perot design have been discussed. The results demonstrate that the output power decrease with the increase of temperature. The effect of the temperature on the output performance increases by increasing the pump power. The effect of temperature can be ignored only for lower pump power. The theoretical result is in agreement with the published experimental results. Index Terms— Ytterbium-doped fiber laser, Temperature-dependent rate equation. 1. INTRODUCTIONSince the first report in 1962 of laser achievement in ytterbi-um ion (Yb3+) doped silicate glass [1]. Ytterbium (Yb)-doped fiber lasers (YDFLs) have attracted great interest be-cause they offer the advantages of compact size and struc-ture, high gain, guided mode propagation, highly stable pro-cesses, their outstanding thermo-optical properties and high doping levels are possible [1-6]. Moreover, It does not have some of the drawbacks associated with other rare-doped fiber such as excited state absorption phenomenon that can reduce the pump efficiency and concentration quenching by interionic energy transfer. Thus, it offers high output power (or gain) with a smaller fiber length. YDFA’s have a simple energy level structure and provide amplification over a broad wavelength range from 915 to 1200 nm. Furthermore, YDFA’s can offer high output power and excellent power conversion efficiency [1,7,8].   Lately, interest has been shown in Yb3+ as a laser ion, in the form of Yb3+-doped silica and fluoride fiber lasers [9]. YD-FLs have been widely used in advanced manufacturing, high energy physics and military defense [10]. There are several theoretical analyses of the YDFL based on rate equations and power differential transmission with fixed or variant parameters of the fiber laser, the results of which are im-portant for optimization of fiber lasers. The numerical analy-sis of thermal distribution and its effects on the high power YDFLs have been studied, as thermal damage, refractive index variation of the gain fiber, and output wavelength [11]. Several papers studied the temperature effects on the output performance of YDFLs. It is reported that the central wave-length of output laser shifts to longer wavelength and the output power decrease with increase of temperature [12, 13]. Brilliant et. al. showed their experimental results of tempera-ture tuning in a dual-clad ytterbium fiber laser, they varied the temperature of the fiber from 0 to 100◦C and found im-portant changes in operating wavelength, power and thresh-old [14].  Today, the wavelength shift can be controlled with the using of fiber grating. Thus the temperature-dependence study about fixed wavelength is required. The effect of tempera-ture on the optical properties of YDF lasing at different wavelengths has been analyzed [15]. Nevertheless, to our knowledge, there is no articles that discuss the effect of tem-perature on the best possible conditions of YDFLs theoreti-cally so far. In this article, the temperature-dependency model based on ions’ rearrangement emerging from tem-perature variation for YDFLs with two-end Fabry-Perot mir-rors has been presented. In this model, the output perfor-mance can be studied (slope efficiency and the output pow-er) depending on the temperature. In addition, the heat dis-tribution along the laser cavity, and the numerical results of slope efficiency are combined. The optimal fiber length is obtained by taking into account the variation of temperature.    2- THEORETICAL MODEL  The energy level system for Yb having possible transitions is shown in Figure 1 [16]. The effect of the temperature on the ion distribution between upper and lower energy level within a manifold is considered. However, the redistribution of ions between the excited manifold 2F5/2 and the ground manifold 2F7/2 is ignored. This can be justified because of the large energy gap between these two manifolds, on the basis of Boltzmann distribution and the energy level diagram. The standard rate equations for two-level systems are used to describe the gain and propagation characteristics of the fiber EL-NAHAL:  TEMPERATURE DEPENDENCY OF YTTERBIUM-DOPED FIBER LASER  2 2  laser because the ASE power is negligible for a high power amplifier with sufficient input signal (about 1 mW). After the overlap factors are introduced and the fiber loss ignored, the simplified two-level rate equations and propagation equations are given as follow [17]                                                      212 12 1 21 21 21 2( ) ( )p lp s up p up s us usdNW f W f N W f W f A f Ndt      (1)                               where W12 and W21 are  the  stimulated absorption and stimu-lated emission transition probability, respectively. They can be given as:                                              12 12 ;        p ap p s as sp sp sP PW WAh Ah          (2)                                                                                  21 21 211 ; ;  p ep p s es sp sp sP PW W AAh Ah          (3)                        where ( , ),  ( , )s pP z t P z t  are the signal and pump power respectively.   as esand   are the signal absorption and emission  cross  sections.  and s p   are the frequencies of signal and pump light, respectively. h is Planck’s constant.  A is the doped area of the fiber. A21 is the spontaneous radiation transition probability and  is the upper state lifetime. s  and p  are  the overlapping factor of laser power and the pump power, respectively. ( )s s  is given by 1- e1-V ,where V can be obtained by 22 / sa NA  , where NA is the numerical aperture. p  can be approximately got by (a/b)2. a and b refer to the radius of the fiber core and the radius of the inner cladding of the YDF [18].    Figure  1  Energy level diagram of Yb in silica with 976 nm, 1040 nm, and 1064 nm transitions labeled. Source: [24]   The Yb- dopant concentration is  Nt, and given by[19];                           1 2 tN N N        (4) where N1 and N2 are the ground and upper-level populations.  The energy level diagram for Yb in silica may vary with each individual fiber. Because of the splitting of the levels depends on the glass composition, concentration of dopants and co-dopants, and the degree of structure disorder of the glass network. The absorption and emission cross-sections for Yb in silica are related to the temperature and the energy of the levels[20]. The saturation of ytterbium absorbing transition occurs when population of two stark levels involving in the transition are matched. The photon energy is the energy difference between the highest Stark level of the ground state 2F7/2 (4) and the lowest Stark level of the excited state 2F5/2 (1) of the Yb3+ ion in phosphate glass. Therefore, we assume in the model that just these two sublevels and calculate the Boltzmann occupation factors fli and fui of lower  and  upper  manifolds for lower and upper levels from measured stark splitting  Ei and Ej and  they can be expressed as [21-23]                       //41 i BE K Tj BE K Tliiefe For Yb ground state                                             (5)                        //31 i BE K Tj BE K Tuijefe For Yb excited state                                              (6) KB is Boltzmann’s constant and equals 231.38 10  J/K.  At steady state, 2 / 0dN dt  , then                                                    12 122 121 21 21( )( )upp slpup us usp sW f W fN NW f W f A f                                                                   (7)                                          EL-NAHAL:  TEMPERATURE DEPENDENCY OF YTTERBIUM-DOPED FIBER LASER  3 3  12 12221 1 21 1 21 21 21( )( )p lp s lsp lp s ls p up s us usW f W fNN W f N W f N W f W f A f        (8) where the subscripts s and p represent laser and pump, respec-tively. At the same time, by considering the scattering losses both for pump and laser, and then the power time independency differ-ential transmission equations considering temperature by ignor-ing the amplified spontaneous emission (ASE) can be expressed as follows:  2( )( ) ( )pp up lp ep up up lp p p pdP zN f f f N P z P zdz              (9)                          2( )( ) ( )s s as es es us as es s s sdP zN f f f N P z P zdz            (10) with the boundary condition                                   1(0) (0),s sP R P                                  (11)                                                                                                   2( ) ( )s sP L R P L                                 (12)                                     where the superscript of sP and Pp represent the propagation direction for the power along the fiber, the positive superscript represents forward direction and the negative superscript repre-sents backward direction of laser beam and L is the fiber length. p  and s  are scattering loss coefficients of pump light and laser light respectively. R1 and R2 are the power reflectivity of Fabry Perot reflectors at laser wavelength at z = 0 and z = L, respectively. From above equations, the numerical results of power distribution along the fiber laser can be calculated. The temperature distribution of fiber core T1 and fiber cladding T2 respectively, as a function of fiber radius and fiber length and can be given as [24]:                       2 212( )( , ) ( )4( )ln (0 )2ccQ zT r z T a rQ z da       r aa dh                 (13)                          222( )( , ) ln ln2( )( )2ccQ z a d rT r z Ta aQ z a      a r ddh                      (14) where Q(z) is the heat power density,  represents thermal conductivity, Tc is environment temperature and hc is the heat transmission coefficient of the fiber surface.  3- RESULTS AND DISCUSSION  Numerical simulations are carried out by solving the rate equa-tions to study the effects of temperature variation on the per-formance of high power YDFLs. The parameters used in the simulations are included in Table 1. The variations of output power with pump power for 915 nm and 970 nm signals at dif-ferent temperatures 253k, 293k and 333k are shown in Figure 2 and 3 respectively. It is clear from the results that increasing the pump power will increase the output power. At the same time the output power decreases with increasing temperature from 253k to 333k which agrees with previous results and can be explained by the fact that as the population of the sublevel “a” decreases with the increase in temperature, while the population of sublevel “c” increases, that is the absorption of pump de-clines and the absorption of laser rises [13,14].  The variations of output power with fiber length for 915 nm and 970 nm signals at different temperatures (243k & 363k) with the pump power of 1500 W are shown in Figure 4 and 5 respec-tively. It is clear from the results that the optimal fiber length is about 12 m. According to Figs. 3 and 4, when the fiber length is longer, the difference of output power at difference temperature becomes smaller and smaller as shown in Figures 4 and 5 re-spectively. This indicates that the effect of temperature is the smallest when the pump power is absorbed entirely.  Table 1   Parameters used in the simulation. Parameters Value Signal wavelength (λs) 1100nm Pump wavelength (λp)  915,970nm Yb ion density (N) 80 x 1024 m-3 Numerical aperture (NA) 0.2nm Excited-state lifetime (τ) 0.8ms Core radius 2.5µm Environment temperature (Tc) 298k Heat transmission coef-ficent (hc) 17W/(m2K) Thermal conductivity ( ) 1.38 W/(mK) Scattering loss coefficient of laser light ( ) 5 x 10-3 Scattering loss coefficient of pump light ( ) 3 x 10-3 Absorption cross section at pump wavelength (σap) 2.5 x 10-24 m2 Absorption cross section at laser wavelength (σas) 1.5 x 10-26 m2 Emission cross section at pump wavelength (σep) 2.5 x 10-24 m2 Emission cross section at laser wavelength (σes) 3.2 x 10-25 m2    spEL-NAHAL:  TEMPERATURE DEPENDENCY OF YTTERBIUM-DOPED FIBER LASER  4 4   Figure 2 Output power as a function of pump power (915nm) for different temperature when L = 3 m. Figure 3 Output power as a function of pump power (970nm) for different temperature when L = 3 m.  Figure 4 The output power as a function of fiber length for different temperature when Pump power = 1500 W for 915nm signal           Figure 5 The output power as a function of fiber length for different temperature when Pump power = 1500 W for 970nm signal  The variation of the output power with the fiber length for different pump power for 915nm and 970nm signals are shown in Figures 6 and 7 respectively. It is clear from the results that the output power increases with increasing pump power. The optimal length for different pump power is around 12m. Figure 6 The output power as a function of fiber length at room temperature (273k) for 915nm signal.   Figure 7 The output power as a function of fiber length at room temperature (273k) for 970nm signal.    EL-NAHAL:  TEMPERATURE DEPENDENCY OF YTTERBIUM-DOPED FIBER LASER  5 5  4- CONCLUSION  This paper has described in detail a temperature-dependent model for (YDFL) based on Fabry-Perot design. The output performance mainly the output power of YDFL variation with temperature is investigated. It is clear from the results that the output power decreases with the increase of temperature. More-over, the variation of output power with temperature increases with the increase of the pump power. The theoretical results obtained here is in agreement with the published experimental result. These results show that the temperature effect must be considered especially when the laser is operated at higher pump power.  REFERENCES: [1] H. W. Etzel, H. W. Candy. and R. J. Ginther, “Stimulated emission of infrared radiation from ytterbium-activated silicate glass,” Appl. Opt., vol. 1, pp. 534, 1962. [2] R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, Ytterbium-Doped Fiber Amplifiers, IEEE journal of quantum electronics, vol. 33, no. 7, pp. 1049-1056, JULY 1997. [3] J. Chen, Z. Sui, F. Chen and J. Wang, Output characteristics of Yb3+-doped fiber laser at different temperatures, Chin. 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Temperature Dependency of Ytterbium-Doped Fiber Laser (YDFL) Based on Fabry-Perot Design Operating at 915 nm and 970 nm High Power Pumping Configuration

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Temperature Dependency of Ytterbium-Doped Fiber Laser (YDFL) Based on Fabry-Perot Design Operating at 915 nm and 970 nm High Power Pumping Configuration

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