Research Article Effect of Er +3 Concentration on the Small Signal Gain Coefficient and the Gain in the Erbium Doped Fiber Amplifier

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1 Reearch Journal of Applied Science, Engineering and Technology (): -, DOI:.9/rjaet.. ISSN: -9; e-issn: - Maxwell Scientific Publication Corp. Submitted: October, Accepted: November, Publihed: April 9, Reearch Article Effect of Er + Concentration on the Small Signal Gain Coefficient and the Gain in the Erbium Doped Fiber Amplifier O. Mahran, Mohammed S. Helmi, Gamal D. Roton, Naglaa El. Sayed and Engy M. Gerge Faculty of Science, Faculty of Education, Univerity of Alexandria, Egypt Abtract: The mall ignal gain coefficient and the gain of Erbium-Doped Fiber Amplifier (EDFA) in the wavelength range (- nm) for different erbium concentration and different amplifier length are calculated and tudied. A graded-index and erbium-doped concentration, are optimized for an EDFA in implified twolevel model. There i evidence to how that, the gain increae with the erbium concentration and the amplifier length. Where the relation between the gain and the amplifier length at different wavelength i linear with the maximum gain at λ = nm. Alo the temperature dependence of the mall ignal gain coefficient and the gain at the peak wavelength of EDFA wa tudied which how, lightly increae in the value of both with temperature. The value of the ignal wavelength wa choen in the gain window of EDFA at nm. Keyword: Core-index, EDFA, erbium concentration, gain, mall ignal gain coefficient INTRODUCTION Rare earth doped fiber amplifier and laer are important tool in undertanding and deigning new optical device. Erbium-Doped Fiber Amplifier (EDFA) are attractive device for ingle-mode fiber in optical communication ytem in the nm wavelength band which i known a a third window for fiber optic communication. EDFA have many advantage uch a high gain and low noie in optical communication network. EDFA are characterized by gain which depend on erbium concentration and thi feature i very intereting in the modern optical tranmiion ytem which ue Wavelength Diviion Multiplexing (WDM) (Kemtchou et al., 99). Erbium-Doped Fiber Amplifier (EDFA), a key component in Wavelength Diviion Multiplexing (WDM) ytem in optical telecommunication, have received great attention over the pat year. The rapid growth and the future commercial importance of multi-wave length optical networking create trong incentive for the development of EDFA with higher gain and broader bandwidth. Many intereting reearch reult were reported in recent year. For example, Chernyak and Qian () etablihed modeling highconcentration -band EDF A at high optical power baed on inverion function. Johanne () reported patial ditribution effect and laer efficiency in Er/Yb-doped fiber. Wei et al. () utilized a genetic algorithm to optimize multitage erbium-doped fiber amplifier ytem with complex tructure. A remark able modeling wa introduced by Gile and Deurvire (99), which etablihed the propagation and rate equation for a two-level homogeneou laer medium. Thi approximated model i uitable for analyzing open-loop optical fiber amplifier and alo the teadytate operation of the optical fiber network. For radial effect of the fiber on EDFA performance of the, there have been a few reearche reported in recent year. One of the reearche wa preented by Martin (), who tudied erbium tranveral ditribution influence on the effectivene of a doped fiber by introducing a imple mathematical function and ignificant gain difference were oberved in active fiber. It i apparent that the tranmiion performance are manipulated and optimized by controlling the optical and geometrical parameter in the fiber tructure. A a reult, any undeired variation in the fiber tructure parameter, can perturb the tranference performance. The refractive index variation a a function of temperature (dn/dt) i the important feature in the optical fiber. Thi factor determine the temperature characteritic of an optical fiber tranmiion ytem (Oama, a). Aerial optical ytem are expected to face change of temperature in everal area of the planet, which compel the eential demand to contemplate the thermal effect in the deign of high-peed optical communication ytem (Rotami and Makouei, ). In thi reearch the dependence of the erbium concentration on the graded refractive index i done, alo the mall ignal gain coefficient and the gain pectrum in the wavelength range (-) nm for Correponding Author: O. Mahran, Faculty of Science, Univerity of Alexandria, Egypt Thi work i licened under a Creative Common Attribution. International icene (UR:

2 Re. J. App. Sci. Eng. Technol., (): -, different erbium concentration and different amplifier length are tudied. So we can expect an increae for the gain with the erbium concentration and the amplifier length. Where the relation between the gain and the amplifier length at different wavelength i linear with the maximum gain at λ = nm. Alo the temperature dependence of the mall ignal gain coefficient and the gain at the peak wavelength of EDFA wa tudied which how, lightly increae in the value of both with temperature. Thi i calculated by theoretical model which made by the author. MATERIAS AND METHODS Thi theoretical reearch of the dependence of the erbium concentration on the graded refractive index i done. Model: There are everal functional form that can be choen to decribe the radial ditribution of the erbium ion. We ue an exponential function a follow (Oama, a): δ r β Er ( r) = Ero exp (β, δ>) () where, E ro i the center concentration, β and δ are the parameter required to be optimized in the genetic algorithm. Equation () can how variou radial profile with different value of β and δ. At r =, Er reache a maximum, which i coincident with actual erbiumdoped concentration. For the fiber with radial ditribution of the refractive index (i.e., graded-index fiber), ome parameter (e.g., cut-off frequency) decribing light propagation in a tep-index are no longer available ince the graded-index alter with the radiu. Some detail analye on thi apect were already developed and one of thee i a uual variational method (Cheng and Xiao, ), in which a graded-index i reduced into an equivalent tep-index. Here, a ueful formula for the refractive index i given by Oama (a): r n = nclad + nh (r a) () a Table : The optimized value of β, δ,, a and n of the EDFA Central concentration E ro (cm - ) β (µm) δ a (µm) n Table : Interpolated coefficient of the Eq. () K ( - ) J ( - ) λ g (µm) t ( - ) The relation between the erbium concentration and the refractive index of the can give by ubtituting the value of r in Eq. (), we can give: E ( n r ) = E ro a exp β n n n clad δ () The value of a, n,, β and δ are choen to optimizing an Erbium-Doped Fiber Amplifier (EDFA), (Oama, b) and are given in Table. The refractive index variation of the due to temperature and wavelength i conidered in thi ection. The method ued in thi tudy ha been introduced by Ghoh (Rotami and Makouei, ). Thi model i baed on the ubcription of both electron and optical phonon. The optical contant computed from thi model are then ued to calculate the refractive indexe at any operating temperature or wavelength for the optical fiber tranmiion ytem. Thermo-optic coefficient dn /dt contain the contribution of electron and optical phonon. Conequently, it can be decribed in the optical tranmiion range in term of linear expanion coefficient t and the temperature variation of energy gap (de/dt) by the following relation a Oama (b): dn n dt deg = χ e t.. E g dt E g ( E E ) g () where, χ e, E and E g are the electronic uceptibity, photon energy and the uitable energy gap lying in the vacuum ultraviolet region, repectively. Equation () can be rewritten in term of a normalized wavelength a: where, a i the fiber radiu and n i the relative refractive-index difference. The function H ha the following form Oama (b): r r H = << () a a Then the radiu can give a: n r = a n n () clad = (Rotami and Makouei, ) () dn n = KR + JR dt () where, the contant K and J are related, repectively to the thermal expanion coefficient ( t ) and the energy gap temperature coefficient (de g /dt) according to the relation preented in Oama (a) and their value are given in Table for ilica glae (Oama, b). Integrating Eq. (), we obtain:

3 ( KR + JR ) T n o Re. J. App. Sci. Eng. Technol., (): -, n = + (9) where, n o i contant equal the value of. The relation between the erbium concentration and the temperature can be obtained by ubtituting the Eq. (9) in (). Thi i given by: E r ( T ) = E ro a exp β n ( ( KR + JR ) T + no ) n clad δ () The mall ignal gain coefficient (g) a a function of erbium concentration E r (n ) i given from Eq. () and (9), with the optimized value of, β, δ and the relative inverion D =, which repreent a complete medium inverion (Cheng and Xiao, ): g = E ( n r { σ e( λk )( + D) σ a ( λk )( D)} ) () where, σ a (λ k ) and σ e (λ k ) are the aborption and emiion cro ection of the laer tranition at λ k, repectively. The amplifier gain, G, can be calculated a: ( ) ( ) = e a G exp ( N ( z) σ N( z) σ ) Γ dz () Equation () appear to ugget that the gain i a complex function of the hape of the inverion along the length of the fiber. In fact, the gain can be related imply to the average inverion. Define an average upper-tate population and imilarly for the lowertate population, which both are function of E r (n ) a Jander and Brockle (): Fig. : Profile of the refractive index Er-concentration (x 9 cm - ) β (µm) β= Core radiu, r (µm) Fig. : Effect of β on Er-concentration β= β=. β=. β=. β=. β=9 β= β=9. N = N ( z)dz () N = N ( z)dz () Equation () can then be implified to: ( e) ( a ) [( N N ) Γ ] G = exp σ σ () Thi how that, the ignal gain after traveral of the fiber i dependent only on the average inverion of the erbium ion in the fiber and doe not depend on the detail of the hape of the inverion a a function of poition along the fiber length. RESUTS AND DISCUSSION Table lit ome optimized reult of the EDFA (Oama, b) and the required radial ditribution of the refractive index i hown in Fig. which give a ymmetrical behavior of the refractive index in both poitive and negative ide of the radiu at =. (optimal value). The maximum value of n =.9 at which the erbium concentration are concentrated on the axi while it i decreae on the wing. For >., there i unymmetrical behavior of the refractive index in both the poitive and negative part. Figure how the effect of the parameter β (decribing erbium radial ditribution, a defined in Eq. () on the erbium concentration and conequently the gain bandwidth. Note that, the total erbium concentration, i.e., the area under the profile, i altered with variou β value. A a comparion, we adopt a uniform erbium concentration while keeping the total concentration the ame thi with different ditribution of erbium ion. The maximum value of erbium concentration i located at the axial radiu where r = and thi value decreae on the two ide where the radiu increae. Figure how alo

4 Re. J. App. Sci. Eng. Technol., (): -, gain coefficient, g (m - ) Er=.E+ Er=.9E+ Er=.E+ Er=.E+ Er=.9E+ Er=.999E+ Er=.E+ wave length,, λ (nm) Fig. : Effect of δ on Er-concentration Er-concentration(x 9 cm - ) =., β =., δ= Core refractive index, n Fig. : The optimized value of, β and δ on Er concentration with the effect of refractive index Fig. : Small ignal gain coefficient of erbium doped alumino-germanoilicate gla fiber amplifier at different Er-concentration that, the optimal value of β i. µm. Thi correpond to the optimal ditribution curve. At thi value of β the ditribution allow the ignal to make total internal reflection inide the fiber. Figure how the effect of the parameter δ on the erbium concentration profile. However, it i hown that for ome value of δ, the erbium concentration take a negative value which i not true. The optimal ditribution take place when δ =, which give the ame effect on the erbium concentration profile on the poitive and negative ide of the radiu with maximum value of the erbium concentration =. 9 /cm on the axi. The optimized value of, β and δ of the EDFA on the calculation of the erbium concentration a a function the refractive index according to Eq. () i hown in Fig.... = m Er=.E+ Er=.9E+ Er=.E+ Er=.E+ = m Er=.E+ Er=.9E+ Er=.E+ Er=.E+.. Er=.9E+ Er=.999E+ Er=.E+ Gain, G (db ) Er=.9E+ Er=.999E+ Er=.E+.. (a) (b)

5 Re. J. App. Sci. Eng. Technol., (): -,. 9. = m Er=.E+ Er=.9E+ Er=.E+ Er=.E+ = m Er=.E+ Er=.9E+ Er=.E+ Er=.E+... Er=.9E+ Er=.999E+ Er=.E+ Er=.9E+ Er=.999E+ Er=.E+. (c) (d) Fig. : Gain pectrum for erbium doped alumino-germanoilicate gla fiber amplifier, for different value of Er-concentration at the labeled amplifier length a in a, b, c and d ength, (m) λ (nm) ( λ= λ= λ= λ= λ= λ= λ= λ= λ= λ=9 λ= Fig. : The maximum gain pectrum for erbium doped alumino-germanoilicate gla fiber amplifier The relation between the mall ignal gain coefficient (g) m - and the wavelength (λ) nm around the. µm laer tranition of a typical Er + doped alumino-germanoilicate gla fiber amplifier at different value of erbium concentration, are illutrated in Fig.. Notice that when the erbium concentration increae the gain coefficient increae and how le broadening. Alo the maximum gain coefficient (peak) at the wavelength nm, thi peak i the reaon for chooing the erbium ion doped ilica fiber to be the mot widely ued device, becaue they have a tranition in the third telecommunication window, around nm. The relation between the gain, G (db), for erbium doped alumino-germano-ilicate gla fiber amplifier and the wavelength with different value of the amplifier length at different erbium concentration are gain coefficient, g (m - ) λ = nm Er-concentration (x m - ) Fig. : The effect of Er-concentration on the gain coefficient and the gain at wavelength nm (a) λ = nm Er-concentration (x m - ) (b)

6 Re. J. App. Sci. Eng. Technol., (): -, gain coefficient, g (m - ) λ= nm Temperature, T ( o C) (a) λ= nm ignal wavelength nm, according to the Eq. (9), () and (). Thi how lightly increae in the value of gain coefficient (g) m - and of Gain (G) db with Temperature (T) C. The value of the ignal wavelength wa choen in the gain window of EDFA at λ = nm. CONCUSION Radial effect of the graded-index and erbium doped concentration are tudied with the optimized parameter value, β and δ for an Erbium-Doped Fiber Amplifier (EDFA) in a two-level model. Alo the mall ignal gain coefficient and the gain pectrum in the wavelength range (-) nm for different erbium concentration and different amplifier length are tudied. There i evidence to how that, the gain increae with the erbium concentration and the amplifier length. Where the relation between the gain and the amplifier length at different wavelength i linear with the maximum gain at λ = nm. Alo the temperature dependence of the mall ignal gain coefficient and the gain at the peak wavelength of EDFA wa tudied which how, lightly increae in the value of both with temperature. The value of the ignal wavelength wa choen in the gain window of EDFA at nm.. Temperature, T ( o C) Fig. 9: The effect of temperature on the gain coefficient (a) and the gain at contant wavelength nm (b) tudied uing Eq. (). Figure how uch relation at =,,, m in the range of the wavelength from to nm. It i found that, a the erbium concentration increae, the amplifier gain increae and the curve how le broadening, the maximum gain take place at wavelength = nm. The gain i alo plotted with amplifier length at different value of wavelength and at n =.. In Fig., the relation i found to be linear between the gain and the length. Thi i clear from the relation of (G, ). Alo the maximum gain at wavelength = nm which i correponding to the peak of the erbium ion doped ilica fiber. The effect of erbium concentration on the gain coefficient and the gain at the peak of the erbium ion are calculated according to the Eq. () and () i plotted in Fig.. Figure 9 how the temperature dependence of the mall ignal gain coefficient and the gain at contant (b) 9 REFERENCES Cheng, C. and M. Xiao,. Optimization of an erbium doped fiber amplifier with radial effect. Opt. Commun., : -. Chernyak, V. and. Qian,. Modeling high concentration -band EDFA at high optical power baed on inverion function. IEEE J. Sel. Top. Quant., : 9. Gile, C.R. and E. Deurvire, 99. The propagation and rate equation for a two-level homogeneou laer medium. J. ightwave Technol., 9:. Jander, P. and W.S. Brockle,. Spectrocopy of yttria-alumina-ilica gla doped with thulium and erbium. IEEE J. Quantum Elect., : 9-. Johanne, K.,. Spatial ditribution effect and laer efficiency in Er/Yb-doped fiber. Proceeding of the SPIE Conference on Optical Component and Material, :. Kemtchou, J., M. Duhamel and P. ecoy, 99. Gain temperature-dependence of erbium-doped ilica and fluoride fiber amplifier in multichannel wavelength-multiplexed tranmiion-ytem. IEEE J. ightwave Technol., ():. Martin, J.C.,. Erbium tranveral ditribution influence on the effectivene of a doped fiber. Opt. Commun., 9:.

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