SIMUTIO OF THE GI CHRCTERISTICS OF EDF guyen Hong Suong and Pham Quoc Ho Deartment of Telecommunication, Pot and Telecommunication Intitute of Technology (PTIT), Ho Chi Mh City, Vietnam BSTRCT In thi tudy, one of the mot imortant characteritic of Erbium-Doed Fiber mlifier (EDF), ga i imulated and analyed. In ued licg method, Erbium-doed fiber (EDF) i divided to many mall lice which the Er 3+ oulation denitie of EDF at metatable tate and ground tate i aumed to be unchanged. Simulation reult how that EDF ga i affected by ome arameter uch a fiber length, ignal wavelength, um wavelength, ut ignal ower and um ower. Generally, the EDF ga i the non-lear function of thee arameter. Each ha different effect on the ga. Thee reult are conitent with ublihed material.. ITRODUCTIO Erbium-doed Fiber mlifier (EDF) i an otical amlifier which ha had a ignificant imact on otical fiber communication ytem [], eecially Wavelength Diviion Multilexg (WDM) ytem. With the characteritic uch a olariationdeendent ga, low terchannel crotalk, wide otical bandwidth and low-noie generation [], it ha been ued to comenate for ignal roagation lo along high eed gle mode fiber otical lk. mong the characteritic of EDF, ga i one of the mot imortant one. Together with aturation ower and noie, it i often referred the literature a EDF erformance []. The highet ga i exected. However, the ga of EDF i unequal at different oeration condition. It deend on ome arameter uch a ignal wavelength, um wavelength, ut ignal ower, um ower and the length of Erbium-doed Fiber (EDF). Therefore, undertandg the effect of thee arameter on ga characteritic and EDF erformance generally i required to tudy and imrove it erformance otical fiber communication ytem. In thi tudy, the ga characteritic of EDF are imulated and analyed. To achieve thi uroe, licg method which EDF i divided to many mall lice i ued. It will be reented more detail the Section. Baed on thi method, by changg aroriately the value of ignal wavelength, um wavelength, ignal ower, um ower and the length of EDF, the characteritic of ga veru thee arameter are imulated and analyed. The imulation reult of thee characteritic will be reented the Section 3.. METHODOOGY Fig. Erbium-doed fiber i rereented a a erie of dividual ga lice The method ued thi tudy i hown Fig.. In thi method, Erbium-doed fiber (EDF) i divided to many mall lice with the length of. In each lice, the oulation denity at metatable tate () and the
oulation denity at ground tate () are aumed to be unchanged. a reult, an EDF i conidered a a concatenation of many amlifier of the cremental length []. The ga g() and the um lo α () a lice of fiber can be determed a follow []: g ) = Γ [ σ σ ( )] () ( e, α ) = Γ [ σ σ ( )] () ( e, where Γ i the overla factor between field and erbium ion oulation; σ e and σ a are imulated emiion and abortion cro-ection, reectively. In the dicuion, ubcrit and refer to ignal and um, reectively. Simulated emiion and the abortion croection rereent the trength of tranition. In other word, they rereent the ability to roduce ga and abortion []. Thee croection deend on the kd of EDF and the wavelength of light. The abortion and emiion cro-ection of Er 3+ ion of l-ge- Er codoed ilica fiber [3] which i ued to imulate and analye the ga characteritic of EDF thi tudy are hown Fig.. ( ) / ω e R Γ = (3) where R i Er 3+ ditribution radiu; ω i ot ie which i determed a follow [5]: a.69.879 ω = 0.65 + +.5 6 (4) V V where a i core radiu of fiber and V i normalied frequency of fiber. () and () can be determed a follow [3]: τσ Γ τσ Γ P + P = τ ( σ + σ e, ) Γ τ ( σ + σ e, ) Γ P + P (5) ( ) = ( ) (6) where P () and P () are ignal ower and um ower at the oition of the fiber; i effective cro-ectional area; τ i the lifetime of Er 3+ at the metatable tate 4 I 3/, i the total ion oulation denity; ν and ν are otical um and ignal frequencie, reectively; h i Planck contant. The ga of EDF with length i comoed of the contribution of all the ga element of n lice along the amlifier fiber [3]: 0 { } g ( ) g ( ) g ( n = e e e )... G = lim = ex g( ) d (7) 0 Fig. bortion and emiion croection of Er 3+ ion of l-ge-er codoed ilica fiber [3]. Overla factor can be calculated by followg equation [4]: The ga of EDF can alo be determed a follow [3]: G = ex[( σ e, σ ) Γ ] (8) where, are the average ion oulation denitie at ground and metatable tate,
reectively. They can be calculated a follow [3]: 0 = ( ) d (9) ion at thi wavelength i highet a hown Fig.. We have a good agreement between imulation reult and ublihed work [3] hown thi figure. Er 3+ 0 = d (0) The equation from () to (0) how that EDF ga i changed along the fiber. It deend on material and tructural arameter of EDF (abortion and emiion croection, effective cro-ectional are Er 3+ ditribution radiu ), fiber length, um wavelength, ignal wavelength, ignal ower and um ower. By changg the value of thee arameter, the erformance of EDF ga at different oeration condition will be imulated. Simulation reult are reented the ection 3. 3. SIMUTIO RESUTS: The imulation reult of ga characteritic of EDF are hown the figure from Fig.3 to Fig.6. In imulation, the l-ge-er codoed ilica fiber with the abortion and emiion cro-ection of Er 3+ a hown Fig. i ued. Thi fiber ha tructural arameter a follow: core radiu a=.4µm, numerical aerture =0.8, Er 3+ ditribution radiu R=.05µm, total oulation denity =5.5x0 4 m -3. Thee material and tructural arameter of imulated EDF are imilar to thoe of EDF reented [3]. Therefore, to validate the imulation reult, ublihed reult of [3] are alo hown the figure. In Fig.3, the characteritic of EDF ga veru ignal wavelength and um wavelength i reented. It i imulated with fiber length =4m, um ower P =40mW and ut ignal ower P =-40dBm. We can ee that the ga i not equal over wavelength range. It i highet at nearly 530nm when um wavelength are 980nm or 480nm. The nearly 530nm wavelength i enitive to um ower becaue emiion cro-ection of Fig. 3 Simulation reult and ublihed reult [3] for ga veru um wavelength and ignal wavelength with P =40mW, =4m and P = -40dBm. From Fig.3, we can alo ee that the EDF ga at 980nm um wavelength i higher than that at 480nm um wavelength. Therefore, verion factor at 980nm i higher than that at 480 nm. Thi reult i conitent with the theory of EDF reented [4], [5]. Fig.4 Simulation reult ( ) for ga veru outut ignal ower with P =6dBm, =0m, λ =550nm, λ =480nm and ublihed reult [3] (---) The characteritic of EDF ga veru outut ignal ower i reented Fig.4. It i imulated with P =6dBm, =0m, ignal wavelength λ =550nm and um wavelength
λ =480nm. It how that ga i nearly 33dB when outut ignal ower i mall. When the outut ignal ower creae over 0dBm, ga decreae raidly. The reaon i that when ut ignal ower i high, verion level decle raidly and umg rate can not adat to high ut ignal rate. The ot at which ga reduce a half or 3dB i called aturation ot. Outut ignal ower at the aturation ot i called outut aturation ower, which i the other imortant characteritic of EDF []. There i dicreancy between imulation reult and ublihed reult [3] hown Fig.4. However, thi dicreancy i mall and accetable. Fig.5 Simulation reult for ga veru um ower with P =-40dBm, =4m, λ =550nm, λ =480nm. The characteritic of ga veru um ower i hown Fig.5. We can ee that when the um ower i very low (le than 5dBm), ga i le than 0 db. In the other word, ignal attenuate after ag the EDF. When um ower creae, ga creae almot learly with um ower. However, when um ower reache about 0dBm, ga creae more lowly and nearly unchanged when um ower i over 5dBm. It i becaue oulation verion i low when um ower i low. When um ower creae, oulation verion creae and o doe ga. However, when um ower exceed a certa level, oulation verion eem unchanged becaue of the Er 3+ oulation tability. Thi reult i conitent with the theory of EDF. Fig.6 Simulation reult for ga veru EDF length at the two um wavelength of 480nm and 980nm with P =0mW, P =-40dBm, λ =550 nm. The characteritic of ga veru Erbiumdoed fiber length i hown Fig.6. It i imulated at two um wavelength of 480 nm and 980 nm with P =0mW, P =-40dBm, λ = 550 nm. It how that when fiber length i hort, ga at the um wavelength of 980 nm i higher than that of 480 nm. However, when fiber length creae more, ga at 480 nm i higher and reduce more lowly than that at 980 nm. It i conitent with [3], [7]. The Fig.6 alo how that with certa ut um ower, ga creae when fiber length creae. It reache maximum value at a certa fiber length, o called otimum fiber length ot []. For fiber length > ot, ga decreae. In the other word, ignal i reaborbed along the fiber, a a reult of the abence of oulation verion thi fiber ection. Thi reult i conitent with []. 4. COCUSIO In thi tudy, the ga characteritic of EDF were imulated and analyed. The ued imulation method wa licg method which Erbium-doed fiber (EDF) wa divided to many mall lice with the length of. In each lice, the oulation denitie at
metatable tate and ground tate are aumed to be unchanged. a reult, an EDF i conidered a a concatenation of many amlifier of the cremental length. Baed on thi method, the imulation of ga characteritic of EDF wa done. The imulation reult how that the ga of EDF deend on many different arameter uch a material and tructural arameter of EDF, um wavelength, ignal wavelength, ut um ower, ignal ower and fiber length. The fluence of thee arameter on the EDF ga i different. Therefore, relyg on the requirement of alication, the value of thee arameter hould be choen reaonably to achieve deired ga. Thee imulation reult are conitent with ublihed material. REFERECES. Derickon, Denni, (998), Fiber Otic Tet and Meaurement, Prentice Hall.. Deurvire, Emmanuel, (994), Erbium- Doed Fiber mlifier Prcile and lication, John Wiley & Son. 3. Becker, P.C., Olon,.. and Simon, J.R., (999), Erbium-Doed Fiber mlifier Fundamental and Technology, cademic Pre. 4. Bjarklev, nder, (993), Otical Fiber mlifier Deign and Sytem lication, rtech Houe. 5. Vu Van San, (997), Otical Communication Technology, Technology and Science Publiher. 6. Ramawami, R., and Sivarajan, K.., (00), Otical etwork, Morgan Kaufmann Publiher. guyen Hong Suong wa born 98. She received the B.Eng degree Telecommunication from Pot and Telecommunication Intitute of Technology (PTIT), Ho Chi Mh City, Vietnam, 005 (email: uonghanh@yahoo.com). Pham Quoc Ho wa born 976. He received the B.Eng degree Telecommunication from Ho Chi Mh City Univerity of Technology, Vietnam, 999, the M.Eng degree Telecommunication from ian Intitute of Technology (IT), Bangkok, Thailand, 003. He i currently a lecturer Telecommunication Deartment, Pot and Telecommunication Intitute of Technology (PTIT), Ho Chi Mh City, Vietnam (email: qho@tithcm.edu.vn).