Behaviour of Non-ideal Saturable Absorber Doped on Active Fiber

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1 American Journal of Oics and Phoonics 16; 4(5): 46-5 h:// doi: /j.ajo ISSN: (Prin); ISSN: (Online) Behaviour of Non-ideal Saurable Absorber Doed on Acive Fiber Abdallah Ijjeh, Saed Thuneiba Dearmen of Elecrical and Elecronic Engineering, Al-Balqa` Alied Universiy / Al-Huson Universiy College, Irbid, Jordan address: To cie his aricle: Abdallah Ijjeh, Saed Thuneiba. Behaviour of Non-ideal Saurable Absorber Doed on Acive Fiber. American Journal of Oics and Phoonics. Vol. 4, No. 5, 16, doi: /j.ajo Received: Seember 3, 16; Acceed: Ocober 5, 16; Published: December, 16 Absrac: In his aer, a non-ideal saurable absorber doed wih an acive fiber device is considered. The differenial equaions ha describe he behavior of he device are simlified and solved numerically. The resuls show ha as he non-ideal erm (loss) increases, he laser erformance degradaion increases. Keywords: Mulile Pulsing, Pulsed Lasers, Semiconducor, Saurable Absorbers 1. Inroducion In he fiber laser wih a non-ideal disribued saurable absorber (FLDSA), wo differen yes of aricles are disribued hrough he fiber core. These wo yes of aricles inerac via he elecric field in he fiber core [1, ]. Differen work has been done in FLDSA due o he fac ha FLSDA is a simle srucure ha exhibis laser ulsing behavior, Q-swiching, and mode locking in he range of icoseconds [3-11]. In addiion, he FLSDA srucure is comaible wih he exising fiber neworks. Passive mode locking relies on he acion of he disribued saurable absorber where is maerial becomes more ransaren o ligh as he ligh inensiy increases. As a resul, if a saurable absorber is laced inside he fiber laser caviy, i roduces modulaed loss a a searaion frequency of l c, where l is he fiber lengh and c is he seed of ligh. In he revious work wo differen aroaches have been used o describe he ulsing behavior under he assumion ha he saurable absorber is locaed as a bulk cell near he end of he fiber and he absorber is an ideal one. In he firs aroach, he elecric field, acive medium, and assive medium loss were exanded by Taylor exansion abou he maximum o deermine he exansion coefficiens from he self-consisency condiion [7-1]. In he second aroach a funcional form for he ulse rofile was chosen and hen is arameers on he basis of a second order aroximaion was deermined [11, 1]. In his aer he assive mode locking in he non-ideal saurable absorber is described wih a mahemaical model for ulsing behavior. In his case, he ulse widh is usually many orders shorer han he mode searaion. A non-ideal saurable absorber is inroduced for ulse evaluaion, and disribued uniformly in he fiber core hereby reducing he searaion frequency beween modes. In his aroach he hree couled nonlinear differenial equaions ha describe he field inside he fiber, acive medium gain, and assive medium loss, are simlified using he slowly varying field aroximaion. The resuling sysem is solved numerically.. Mahemaical Model I is assumed ha he acive medium is a wo level homogeneously broadening sysem which inroduces gain only and disribued uniformly inside he fiber core. The same assumions aly o non-ideal saurable absorber, exce ha i inroduces aenuaion insead of gain wih nonideal erm. The governing equaions ha describe he roagaion of he ime deenden elecric field ulse A, he acive medium gain and he assive enveloe medium losses are given by []: A( T, η) TRT T 4g d d g + ( B iδ A ) L + id A( T, η) dη dη Where T RT is he recovery ime for generaed ulses, g is (1)

2 47 Abdallah Ijjeh and Saed Thuneiba: Behaviour of Non-ideal Saurable Absorber Doed on Acive Fiber he gain medium arameer, ωa is he bandwidh of he linear resonan filer, δ is he self-hase modulaion and L is he consan fiber losses, including Fresnel losses faces, scaering, and absorion losses wihin he fiber core (addiional losses), and he erms: 4g d g + A( T, η), describes he gain medium, dη while ( δ ) B i ) A A( T, η), describes he saurable absorber medium wih self-hase modulaion (SPM), and d L + id A( T, η), describes he fiber caviy loses dη wih grou velociy disersion (GVD). The saurable balanced agains gain can be used as a ulse forming mechanism []. Le us define τ SA and τ sol as [4]: τ (8 g / ω )/ σ A SA 16g a σ ω apavg TRT () sol ( D / A ) 4 D /( Pavg TRT ) (3) τ δ δ o accoun for he effecs of SPM and GVD, and he effecs of absorion wih gain, resecively. Due o he fac haτ SA τ sol, hen he ulse shae is no srongly influenced by he sauraion absorber seed; slower saurable absorber can be used o obain shor ulses []. The saurable absorber balance agains gain can be obained by droing he imaginary erms ha corresonds o SPM and GVD from equaion (1): A( T, η) 4g d TRT g + B L A( T, η) T dη The gain medium is described by []: dg 1 I Gs g ( g1 g ) + d d TRT I1sa d Where g O is he small signal gain or oally unsauraed gain, g 1 is he oally sauraed gain, I1sa is he sauraion inensiy of he acive medium, and I( ) is he ligh inensiy of he ouu mode locking ulse which can be normalized (4) (5) and wrien as []: I() A( ) (6) The non-ideal sauraion absorber can be recognized in he form: σ B + S (7) Where S is he non-ideal absorion erm, and σ is he saurable erm given by: Then, α σ (8) + B 1 I/ ISAT α 1 + I/ ISAT + G s () is he um arameer given in [9] by, S (9) Gs() g I ( ) d (1) Where I () is he um ulse inensiy funcion which is assumed o be in he form: I () I o sech (11) Where I o is he um ulse amliude and is he um ulse duraion. The gain for acive medium far from sauraion can be reresened by: g g 1 G sech A s1 I 1sa (1) where G s1 is a new consan equal o gt RT. Using he slowly varying field aroximaion for equaion (4), and using equaions (6-1) he resuling equaions afer some maniulaions can be wrien as [1-3]. a d 1 d g L B A wa d wa d (13) A A d d wa( g g L α α S) + a1 + A wags sec h (14) I1sa Isa d d Le a ( α ) w g L S a (15) 1 1 wa( α g ) b Isa I1sa (16) and Then equaion (14) can be rewrien as:

3 American Journal of Oics and Phoonics 16; 4(5): d d aa + ba + a1 A A d + w sec ags h (17) d Which describes he acive fiber wih non-ideal absorber. R w G, hen equaion (17) can be rewrien as: If a s decreases, however, S (non-ideal erm) affecs only arameer a. 3 d d aa + ba + a1 A A d + Rsec h (18) d Equaion (18) can be solved numerically for roer values of media consans, acive fiber medium, and non-ideal absorber medium. The nonlinear erm in equaion (18) 3 involving A lays an imoran role in deermining he 3 secral roeries of he laser field. However, if A is negleced, he secrum of A ( ) will corresond o a uming ulse going hrough a linear resonan filer wih a bandwidh ωa. This is he case below he hreshold where he cubic erm can be negleced [14]. 3. Resuls and Discussions The behavior of non-ideal saurable absorber doed on acive fiber can be described accuraely by equaion 18. This equaion accouns for he effecs of assive/acive fiber mediums, and he uming characerisics. Figure 1 shows he yical saurable absorber behavior for ideal and non-ideal absorbers. I is clear ha as he irradiance increases, he absorion coefficien decreases. The reducion rae for he non-ideal absorber is less han ha for he ideal absorber. Figure. Amliude of ulse versus ime (in arbirary unis). a1, R1 and.1. Figure 3. Amliude of ulse versus ime (in arbirary unis) a b1, R1 and.1. Figure 4 shows he effec of R on ulsing behavior. As execed, as R increases he ulse amliude is also increases in he ulsing region, and he ulse widh decreases. This aroach can be used o generae ulses wih small duraion. Figure 1. Tyical saurable absorber behavior for ideal and non-ideal absorbers. Figures () and (3) show he yical ulses obained by solving equaion (18) for differen values of arameers a and b resecively. I is clear ha as a or b increases he amliude and he widh of he obained ulses decrease. The effec of α and S on he obained ulses can be seen clearly from equaions (15) and (16). As α (ideal erm) increases, boh arameers a and b of equaion (18) Figure 4. Pulse amliude versus ime (in arbirary unis). b1, a1 and.1.

4 49 Abdallah Ijjeh and Saed Thuneiba: Behaviour of Non-ideal Saurable Absorber Doed on Acive Fiber The effec of linear disersion arameer a 1 on he side ulses can be clearly seen in figures 5, 6, 7 and 8. As a 1 decreases, he side ulses increase faser Figure 8. Pulse inensiy versus (in arbirary unis). a1, b1, a 1, R5 and Conclusion Figure 5. Pulse inensiy versus ime (in arbirary unis). a1, b1, a 11, R15 and.9. Using acive fiber laser wih non-ideal absorber, he behavior of generaed ulse is srongly deending on he absorber arameers. As he non-ideal (non-saurable) erm increases, he ulse erformance degradaion increases; ulse amliude deceases and ulse widh increases. The effec of non-saurable arameer and fiber loss on arameer a is he same. This makes he ossibiliy o use high loss fiber wih very small non-saurable erm or vice versa. By inroducing he linear disersion arameer, he ideal erm increases and he effec of non-ideal erm is comensaed. References [1] Siegman, A. E. (1986). Lasers. Universiy science books, sausalio, California. Figure 6. Pulse inensiy versus (in arbirary unis). a1, b1, a 11, R5 and.9. [] Boyd, R. W., Raymer, M. G., Narducci, L. M.. (1986). Oical Insabiliies. Cambridge universiy ress, Cambridge. [3] Keller, U., Weingaren, K. J., Karner, F. X., Kof, D., Braun, B., Jung, I. D., Fluck, R., Honninger, C., Mauschek, N., Aus der Au, J. (1996). Semiconducor saurable absorber mirrors (SESAM's) for femosecondo nanosecond ulse generaion in solid-sae lasers. IEEE Journal of Seleced Toics in Quanum Elecronics,, [4] Kurner, F. X., der Au, J. A., Keller, U. (1998). Mode-locking wih slow and fas saurable absorbers-wha's he difference?. IEEE Journal of Seleced Toics in Quanum Elecronics, 4, [5] Ijjeh, A. (1995) Invesigaion of ulsing oeraion in Rare earh doed fiber. roceedings Russian, Telecom S- Peersburg Figure 7. Pulse inensiy versus (in arbirary unis). a1, b1, a 15, R5 and.9. In he absence of a 1 (see figure 8), he side ulses remain aroximaely fixed wih ime. Increasing a 1 is equivalen o increasing he ideal absorber erm α. [6] Galkin, S. L. (1991). Fiber oic devices based on Acive fibers. Proc. Is Foc 91. Leningrad [7] New, G. H. C., Caherall, J. M. (1984). Problems in he selfconsisen rofile aroach o he heory of laser modelocking. Oics Communicaions, 5, [8] New, G. C., Zeneno, L. A., Radmre, P. M. (1983). New echniques in he heory of acive mode locking. Oics Communicaions, 48,

5 American Journal of Oics and Phoonics 16; 4(5): [9] Clemens, J. M., Najbar J., Bronsein-Bone I., Hochsrasser, R. M. (1983). Dual icosecond Dye-lasers, synchronously umed by A mode locked CW. YAG laser Oics Communicaions, 47, [1] Graf F., Low, C., Penzkofer A. (1983). Passively mode-locked Nd-glass laser wih arially suressed naural mode selecion. Oics Communicaions, 47, [11] Haus H. A. (1975). Theory of mode locking wih a slow saurable absorber. IEEE J. of Quanum Elecronics, 11, [13] Chen, Yao, e al. "Oically driven black hoshorus as a saurable absorber for mode-locked laser ulse generaion." Oical Engineering 55.8 (16). [14] Yariv A. (1975). Quanum Elecronics. John Willy and Sons. Inc [15] Terrien, Soizic, e al. "Mulisable dynamics in a microillar laser wih saurable absorber and delayed oical feedback." Nonlinear Phoonics. Oical Sociey of America, 16. [1] Caherall, J. M., New, G. H. C., Radmore, P. M. (198). Aroach o he heory of mode locking by synchronous uming," Oics Leers. 7, 319. Biograhy Dr. Abdullah Ijjeh has received his BSc in Elecrical Engineering from Kuwai Universiy in He received his M.Sc. in communicaion engineering from Yarmouk Universiy, Jordan in He received his PhD in communicaion engineering from The Bonch-Bruevich Sain - Peersburg Sae Universiy of Telecommunicaions, S. Peersburg, Russia Currenly he is working a he Dearmen of communicaion engineering a Al-Balqa` Alied Universiy, Jordan. His research ineress are fiber oics and wireless and communicaion sysems. Dr. Saed Thuneiba is currenly working as an associae rofessor a he dearmen of Elecrical and Elecronic Engineering a he Al-Huson Universiy College, Al-Balqa Alied Universiy, Jordan. He secializes in research and eaching in oical and Digial elecommunicaion sysems, Comuer Neworks. His research ineress include Oical Fiber Performance, Digial Communicaion Sysems and Neworks.