J. Basic. Appl. ci. Res., (3)834-84,, TextRoad Publication IN 9-434 Journal of Basic and Applied cientific Research www.textroad.co A Dynaic iulink Model For Erbiu-Doped Fiber Aplifiers Overodulation in Presence of Aplified pontaneous Eission Effect Hossein ariri¹, Mohaad ehdi Karkhanehchi², Ali Mohaadi¹, Fariburz Parandin¹ ¹ Eslaabad-E-Gharb branch, Islaic Azad University, Eslaabad-E-Gharb, Iran ² Departent of Electronics, Faculty of Engineering, Razi University, Keranshah-Iran ABTRACT This paper presented a ethod for investigating EDFA dynaics using the tools and iulink. We investigate the ect of AE on the gain odulation in EDFAs. The gain odulation is the low-frequency ( khz) aplitude odulation of the EDFA pup and the counication signal used for propagating line onitoring Inforation. We develop, the previous odels by including aplified spontaneous eission. The derivation of an analytical odel for EDFA overodulation response has been presented. This odel provide analytic expressions for the pup and input signal overodulation responses, respectively. These expressions describe the output signal odulation index aplitude and phase, assuing sall sinusoidal steady-state oscillations of the ean pup or input signal power. In this paper We show that AE have soe ect on predictions in the high gain/low saturation regie. KEYWORD: AE (aplified spontaneous eission), Erbiu-doped fiber aplifier (EDFA), Gain odulation, Overodulation. I. INTRODUCTION Erbiu doped fiber aplifier (EDFA) is an iperative eleent in DWDM networks. This all-optical aplifier enables siultaneous aplification of ultiple wavelengths in regard of electronic regeneration, direct optical aplification using erbiu-doped fiber aplifiers offers any advantages for long haul repeatered transission. First, the repeater can be quite siply configured regardless of the line signal bit rate. This feature becoes ore significant as the line signal bit rate exceeding Tb/s at which speed electronic regeneration requires high-speed electronic circuits, thereby resulting in increase in hardware cost and power consuption. Therefore, optical aplifiers are particularly useful in subarine repeaters that have severe space and power constraints. econd, optical aplifiers are flexible as regard bit rate and odulation forat, and support wavelength division ultiplexed signal transission. Infact Their deployent in WDM systes after 995 revolutionized the field of fiber-optic counications [],[]. tandard EDFA odels, which are typically static, are not well suited to investigating gain odulation, which is a dynaic ect. o we ust use dynaic odels. Novak and Moesle [3] () developed the perturbation concept of Freean and Conradi (993), using ethods described by Bononi and Rusch (998) for odeling transient ects in EDFAs, which are in turn based on the tie-varying gain equation of un et al. (996).Their odel did not take into account aplifier spontaneous eission. In practice aplifier saturation has to be included in view of the copetition between the aplified spontaneous eission (AE) and the signal for the power available fro the optical aplifiers. In this paper, we develop the odel of Novak and Moesle, by including aplified spontaneous eission (AE) in the odel. II. BACKGROUND The aplifier is odeled as a three-level syste [4], having Three populations of erbiu atos are of interest here: ) the ground state with population density n ; ) etastable level with population density n ; and 3) pup level with population density n 3. In practice, transitions fro 3 to are uch ore likely than transitions back to the ground state (3 to ) or the rate of spontaneous eission fro state. Under these assuptions, n 3.The rate equations describing the ects of the pup ( P P ),signal ( P ),and AE ( P AE ) power reduces to the following for n : n z, t s s n p 3 Ps PAE PAE n Ps PAE PAE n Pp Pp n () t h A h A h A s s p A is the ective cross-sectional area of the core. The s are known absorption and eission cross-section data for the erbi-u fiber. The s are the ode confineent factors for the pup and signal waves. The superscript + designates pup and *Corresponding Author: Hossein ariri, Eslaabad-E-Gharb branch, Islaic Azad University, Eslaabad-E-Gharb, Iran. 834
ariri, AE copropagating with the signal, and - when they counterpr- opagate to the signal. In odern fibers we can neglect scattering and other losses,so the convective equations describing the spatial developent of the pup, signal and AE in the fiber are[4]: P z, t PP z, t PP n n PP P 3n3 z z () PAE z, t PAE n n h n. z Equations () and () are the basic equations describing an EDFA. III. DYNAMICAL MODEL For dynaical odelling, first () is substituted into () and then integrated over Z to reove the length dependence of erbiu-doped fiber [5]. This results in a dynaic equation for the excited state population N, which in turn deterines the dynaics of the output pup and counication signals. P P n A PAE na h n. t z z z (3) In equation (3) we include only copropagating pup and AE. Integrating (3) over Z, we have,,,, N,, N N P t P L t P t P L t P t P L t h. P P t AE AE A (4) Where N is the nuber of erbiu ions in the excited state. P (,t) and Pp(,t) represent the tie-dependent input powers for the pup and signal. The output powers P (L,t) and Pp(L,t) are explicit functions of N. N N P, t expb N C P, t exp B N C h n G h N. P P P sp (5) t A This is the key equation for considering dynaic gain ects in the EDFA including AE. In equation (5) G is the gain, βs is the eission per unit length, Δν and ν refer to the wavelength deviation of the AE power around λ, h is Plank s constant, and nsp is the population-inversion factor which is diensionless [6]. In an EDFA, coplete inversion can only be obtained when being puped at 98 n; at 98 n βp = and therefore nsp =. o a pup wavelength of 98 n is assued. The B and C are given in ters of the confineent factors s and P, the absorption and eission cross sections (,, and 3 ), the density of erbiu atos, the length L, and the ective cross sectional area A of the erbiu-doped fiber. τ is the rate of spontaneous eission, and r is the ective radius of the fiber core. IV.GAIN MODULATION To odel the ipact of odulation, we add perturbations to the pup and signal transition rates. Overodulation is introduced as a sinusoidal tie variation of the pup or signal power [3], described by Here,, t cos P P t (6) P, P, P, P is the ean power (pup or signal) at the input (z=) and p, s is the input odulation index. Note the overodulation frequency is assued sall (~khz) copared with the counications signal data rate (~Gb/s) and can be considered siply as an analog odulation iposed on the ean signal power power. The EDFA overodulation behavior is then obtained by solving (5) with tie-dependent inputs of the for of (6). As a first step, we expand N (t) about its ean (unodulated) steady-state solution N : N t cos t N (7) 835
J. Basic. Appl. ci. Res., (3)834-84, -Pup and signal Modulation Using the ethod described by Novak and Mosle, the equations for the aplitude and phase of the pup-to-signal transfer function are given by B P P L P P P P Where tan P P L P L n GB P sp A And for the aplitude and phase of the signal-to-signal transfer function are given by (8) (9) K with K B P P L and tan K () These expressions describe the output signal odulation index aplitude and phase, assuing sall sinusoidal steady-state oscillations of the ean pup or input signal power. V. iulink EDFA odule for EDFA dynaics The iulink EDFA odules are shown in Figs. to 3 by the nubers beside the block connecting lines. In this case there is one signal wavelength and one pup wavelength. The EDFA odule in Fig. is called fro the ain iulink odel where the input signal power is 57.8 w. cope P U M P Output power Input power EDFA Gain E D F A <> <> cope3 cope 3 cope Deux 5 Fcn Deux 6 Fcn3 cope6 cope7 Fcn Mux cope8 cope5 e cope9 Deux 4 Fcn Mux cope4 Fig.. Overodualtion odule. 836
ariri, Input power cope cope Product Output power [C(),C()] Fcn [B(),B()] Fcn EDFA Gain u Mux u4 *h*nu_s_53*delta_nu -/tau a K Ts z- Discrete-Tie Integrator cope -/tau *h*nu_s_53*beta_s_53*delta_nu/(ro*a) q Fig.. iulink EDFA odule for EDFA dynaics. ine Wave Gain Mux Pp Input pup power Ps53 Input signal power Out Out cope Fig.3. Puping odule. VI. IMULATION REULT In this section, we copare our results fro our expanded o- del with the Novak and Moesle s odel. The results are given in ters of the output signal odulation index aplitude and phase response caused by overodulating the EDFA pup or input signal.the wavelength of pup and signal are 98 and 53n respectively.the necessary data are indicated in the table. p 3.3 db / s 4.9 db / s 4.4 db / 6.3 4 3.5s L.5 r. 6 3 GHz(5 n) input odulation index for both pup and signal = 5 % ean signal input powers = 57.8 W Table 837
J. Basic. Appl. ci. Res., (3)834-84, -Effect of AE and copression Level on output odulation indexes. The copression level is defined to be the difference between the sall signal gain and the gain at soe specified signal power [3]. Fig. 4 shows the gain versus signal input behavior for the EDFA at the wavelength of 53n. The solid line are OAIX results. In Fig. 4, we also show the predictions of the Novak odel (dashed line),which neglect AE and our odel (solid line) which include AE. The three odels agree at high copression.the Novak s odel differ by db or less at low copression. But our odel is atch to the OAIX. We now apply the analytic odel to predict the overodulation behavior for three saturation conditions at 53 n, corresponding to ean input signal power levels of - 3,-, and -8 db (gain saturation levels ~ -,-6,and -6dB). The pup overodulation aplitude response is given in Fig. 5. In Figs. 6 and 7 we show the signal overodulation aplitude and phase response, respectively. In the figures, the solid lines represent the odel that we include AE, and dotted lines represents tha results in wich, we neglect AE. Fig. 4. Gain versus ean input signal power for the EDFA in ection VI. OAIX predictions (red) including AE are copared with Novak odel predictions (green) and our odel predictions (blue). Fig. 5. ensitivity of output odulation index aplitude and phase responses to pup overodulation under no copression (-3dB), 6-dB opression (-db), 6-dB copression (-8dB),. ignal wavelength is 53 n. Coparison of including AE (solid) with neglecting AE (dotted). 838
ariri, In Fig. 5 for pup odulations, if ean input signal power is low (low copression) e.g. -3dB including AE ake that output odulation index be ore than the neglecting AE condition. But if input signal power increase (high copression) e.g. -8dB, including or excluding AE have no ect on output odulation index. Figs. 6 and 7 show the signal overodulation aplitude and phase response, respectively. In the figures, the doted lines represent essentially no AE and solid lines represent AE take in to account. In Fig. 6 we show the output odulation index aplitude responses to signal overodulation under no copression (-3dB), -6dB copression (-db), -6dB copression (-8dB). If ean input signal power is low,the result for including AE is ore than,neglecting AE. for the phase response (Fig. 7) if the copression level is low, the solid line (including AE) is less than dotted line(neglecting AE).For both figures(figs.7,8) when copression level is high, two lines(solid and dotted) atch together. Fig. 6. ensitivity of output odulation index aplitude responses to signal overodulation under 3 input signal level at 53 n. Coparison of including AE (solid) with neglecting AE (dotted). Fig. 7. ensitivity of output odulation index phase responses to signal overodulation under no copression (-3dB), 6-dB opression (- db), 6-dB copression (-8dB),. ignal wavelength is 53 n. Coparison of including AE (solid) with neglecing AE (dotted). In an ort to better understand the reversal and its dependence on copression levels, we looked at the pup and signal output odulation indexes at as a function of ean input signal power. Results are shown in Fig. 8, where odulation indexes are noralized to their axiu values. The ean input signal powers at which reversal occurs for pup and signal overodulation are very close. Fig.8-a shows that, noralized odulation indexes for the signal atches for both odel. And, Fig.8-b shows that, noralized odulation indexes for the pup,in solid line (including AE) is ore than doted line (neglecting AE) by.4 at low copression and atches at high copressions. Noralized Output odulation index.8.6.4. signal including AE neglecting AE -5-4 -3 - - signal power(db) Noralized Output odulation index.8.6.4 pup. including AE neglecting AE -5-4 -3 - - signal power(db) Fig. 8. Noralized output odulation index for: (a)signal and (b)pup AE take in to account(solid lines),and AE neglect (dotted lines). is an ective corner frequency [7], equation (9). Fig. 9, shows the high copression, but differ at low copression. versus input signal power. The two odels agree at 839
84 J. Basic. Appl. ci. Res., (3)834-84, And finaly in Fig. the generated AE power in db is indicated for wavelength range fro 5 n to 57n. As shown in this figure, 53 n has the axiu AE power. -7.8-7.9 A E p ow e r (d B ) -8-8. -8. -8.3 Fig. 9. sensitivity of to ean input signal power.in solid line we includ AE,and in doted line we neglect AE. -8.4 5 55 53 535 54 545 55 555 56 565 57 wavelength (n) Fig.. AE power to wavelength. VII. UMMARY AND CONCLUION The derivation of an analytical odel for EDFA overodulation response that include AE, based on Novak odel [3], and desurvire odel [4], has been presented. Because of including AE, our odel agree at both low and high copression with OAIX but Novak s odel differ at low copression because they neglect AE. No other approxiations are ade and the odel is believed to capture the overodulation dynaics of an EDFA well as the saturation level is increased or decreased. REFERENCE [] M. Murakai,T. Iai, and M. Aoyaa, A reote supervisory syste based on subcarrier overodulation for subarine optical aplifier systes, J. Lightwave Technol., vol. 4, pp. 67 677, May 996. [] Agrawal, G. P, Fiber-Optic Counication ystes 3nd Ed, John Wiley and ons,ydney,,pp. 5-6. [3]. Novak and A. Moesle, Analytic odel for gain odulation in EDFAs, J. Lightwave Technol., vol., pp. 975 985, June. [4] C.Giles, and Eanuel Desurvire Propagation of ignal and Noise in Concatenated Erbiu-Doped Fiber Optical Aplifiers J. Lightwave Te- chnol., vol. 9. NO.. FEBRUARY 99 [5] A. Bononi and L. A. Rusch, Doped-fiber aplifier dynaics: A syste perspective, J. Lightwave Technol., vol. 6, pp. 945 956, May 998. [6] P.C. Becker, N.A. Olsson, and J.R. ipson, Erbiu-Doped Fiber Apl- ifiers Fundaentals and Technology. an Diego: Acadeic Press, 999. [7] J. Freean and J. Conradi, Gain odulation response of erbiu-doped fiber aplifiers, IEEE Photon. Technol. Lett., vol. 5, pp. 4 6, Feb. 993.