doped phosphate fiber amplifier - IEEE Xplore

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IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 39, NO. 10, OCTOBER 2003

Numerical Analysis of Concentration Quenching Model of Er3+-Doped Phosphate Fiber Amplifier Chun Jiang, Weisheng Hu, and Qingji Zeng

Abstract—Based on the homogenous model and inhomogeneous model of concentration quenching of erbium-doped fiber amplifier with high doping concentration, the rate equation and power evolution equation of erbium-doped phosphate fiber are solved numerically and analyzed. The dependence of the calculated gain and noise figure on pump power is compared with experimental data, and the results indicate that the combined model of the two models is in good agreement with experimental data. The relative number of clusters in erbium-doped phosphate fibers is estimated from the numerical analysis, and the optimal doping concentration and length of erbium-doped phosphate fibers are proposed in this paper. By numerical analysis, the results show that with 200-mW/980-nm pump power, an erbium-doped phosphate fiber amplifier with a doping concentration of 4.0 1026 ion m3 and length of 10 cm may reach 27.0-dB gain. Index Terms—Concentration quenching model, erbium-doped phosphate fiber amplifier, numerical analysis.

I. INTRODUCTION

O

VER the past decade, the demand for high-speed data transmission has increased tremendously. With the new development of internet applications, the demand for more and more bandwidth continues to grow. As a key device of dense wavelength division multiplexing (DWDM) and all optical networks, the erbium-doped fiber amplifier (EDFA) is a mature technology, yet its large size requires further research and development efforts to make it small, compact, and efficient. Short fiber amplifiers with high gain are ideal for integration with passive devices. In order to compensate losses due to passive devices, such as splitting loss, a gain larger than 10 dB within a few centimeters of length is required and erbium ion . In recent years, concentrations are the order of research and development efforts have been directed toward the design of an efficient and short erbium-doped amplifier with high doping concentration. However, concentration quenching interactions in highly erbium-doped caused by fibers and waveguides make the gain performance degrade [1], [2]. In erbium-doped silica-based fibers and waveguides, the cooperative up-conversion and pair-induced quenching were studied extensively [3]–[11], [20]. The results indicate that in erbium-doped silica-based fiber with doping concentration , the concentration quenching demore than 1.0 rives from pair-induced quenching (PIQ) or/and homogeneous Manuscript received February 10, 2003; revised June 9, 2003. This work was supported by the National Key Laboratory on Broadband Optical Fiber Transmission and Communication System Technology, Chengdu, China. The authors are with the State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiaotong University, Shanghai 200030, China (e-mail: [email protected]). Digital Object Identifier 10.1109/JQE.2003.817667

up-conversion process. Although excited-state absorption also provides gain performance reduction, the PIQ effect on gain performance is the strongest in all of these processes. Concentration quenching depends strongly on host materials. Various materials have already been investigated for fabrication of waveguide-based and fiber amplifiers [12]–[14]. Among all materials, phosphate glass is an attractive material because it not only has high solubility for rare-earth ions (more than ) but also high gain and good chemical sta1.2 bility and durability [15]–[17]. High solubility allows co-doping with that broadens the pump absorption and of leads to an efficient pump coupling while relaxing the stringent requirements on the pump wavelengths around 980 nm. Compared to erbium-doped silica-based fiber, the concentration quenching of erbium ion in phosphate glasses was reported in very limited papers [16], [17]. Cooperative up-conversion level in a phosphate glass are one coefficients of the order of magnitude smaller than the ones reported for silica glass [16]. The increase in the cooperative up-conversion coconcentration was found to efficient with the increasing be small [16]. The effects of cooperative up-conversion on the concentragain performance were analyzed for different tions. Given the small cooperative up-conversion coefficients in phosphate glass, concentration of 1.1 . Such high concentrations had reis as high as 4.0 sulted in a 5-dB per unit length at 244-mW pump power with a 7.1-cm-long fiber [16]. However, the concentration quenching model and the dependence of gain on doing concentration and fiber length has been still not reported systematically so far. In this paper, the investigations of the concentration quenching model and its comparison with experimental data in a high-concentration erbium-doped phosphate fiber amplifier are presented. Using numerical solution and numerical analysis of the concentration quenching model of an erbium ion in the fiber, the optimal parameters of an amplifier, such as doping concentration and fiber length, are also proposed in this paper. II. THE AMPLIFIER MODEL In this section, the three-level system of erbium-doped fiber amplifier is used for numerical solution and analysis. Fig. 1 shows the relevant energy levels for a highly doped erbium . Following system with doping concentration of ( this diagram, the multilevel system of rate equations can be classified as the homogeneous model and inhomogeneous model. The homogeneous model [3] assumes that the ions are evenly distributed and that the probability of an ion interacting with its

0018-9197/03$17.00 © 2003 IEEE

JIANG et al.: NUMERICAL ANALYSIS OF CONCENTRATION QUENCHING MODEL OF ER

-DOPED PHOSPHATE FIBER AMPLIFIER

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only one ion per cluster in the excited state. In this model, it is assumed that all the clusters are the same size and they contain the same number of ions, (for instance, for ion pairs, in most cases). For a total concentration of , the concentra, where is the relative tion of clustered ions is is the percentage of ions in clusters. number of clusters and . The avThe concentration of single ions is state is erage number of clustered ions in (5)

Fig. 1. Schematic energy levels for a highly doped erbium system with cooperative up-conversion.

neighbor increases in proportion to equation becomes

The average number of single ions in the

state is (6)

so that the rate

(1)

Therefore, in the inhomogeneous model, the total population number is given by (7)

and represent the number of erbium ion in where ground state and meta-stable state at the position along fiber, respectively, is the light intensity, is the pump signal, and are the absorption cross-section and emission cross-section, respectively, is the lifetime of the ion in the meta-stable state, is the concentration-independent and host-dependent and . two-particle up-conversion constant measured in When there is no concentration quenching, the population ) at the position of the fiber end is given by number (

In fact, in erbium-doped fibers with doping concentrations larger than the critical concentration in which clusters form, the interaction between erbium ions should include cooperative up-conversion and pair-ion quenching. Therefore, the degradation of gain performance caused by concentration quenching should arise from two contributions: cooperative up-conversion between single ions and cluster-induced quenching. In the combined model, the average number of single ions in the state ( ) is given by

(2) (8) With the addition of the new term, the steady-state solution of the homogenous model becomes

The average number of clustered ions in the given by

state (

) is

(3) (9) (4) is the population number of erbium ion in the metawhere is the light power at the position of the fiber stable level, represent erbium ion concentration, end, , , , and absorption coefficient, frequency, and saturation power, respecand are the effective area of fiber core and Plank tively, is the overlap integral between constant, respectively, and the doping ion and the optical mode and may be calculated from [10]. In the inhomogeneous model [6], [10], it is assumed that the ions are not evenly distributed. It assumes that there are clustered ions that always exchange energy so that a cluster of ions can never have more than one ion in the meta-stable level. In this case, there are two distinct species: clustered ions and single ions that cannot interact with each other. The clustered ions occupy only two energy states: all the ions in the ground state or

Therefore, the average number of erbium ions in the level becomes

state (10) (11)

is the number of erbium ions in the ground state. where The power evolution of each pump and signal beam in the uniformly erbium -doped fiber is given by (12) is for propagation in the positive direction and Where for propagation in the negative direction. For erbium is , is radius, and uniformly doped in fiber, , is erbium doping radius.

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TABLE I PARAMETERS OF ERBIUM-DOPED PHOSPHATE FIBER [18]

Fig. 3. Dependence of the calculated gain of the amplifier on pump power using combined model, inhomogeneous model, homogeneous model and no-concentration quenching model. Erbium ion doping concentration is 3.8 10 ion=m , cooperative up-conversion coefficient is m =s, fiber length 7.1 cm, signal wavelength is 1535 nm, and 1.1 10 signal input power is 30 dBm.

2

Fig. 2.

2 0

Absorption and emission spectra of erbium-doped phosphate glass.

The evolution of the power in amplified spontaneous emission (ASE) is given by

(13) is the effective bandwidth of ASE, where represents ASE, is as the same as in (12). and The noise figure (NF) is calculated by (14) Where is gain, is photon energy.

is the power spectral density of ASE,

III. NUMERICAL SOLUTION OF CONCENTRATION QUENCHING MODEL In this section, the gain and NF of EDFA are calculated by numerical solution of the (1)–(14) above. Table I shows the parameters of the erbium-doped phosphate fiber, and spectra in Fig. 2 [12] were used for all calculation. With Runge-Kutta algorithm, ideal model (no quenching), homogeneous model, inhomogeneous model and combined model are calculated and compared with experimental data in order to find the model suitable for erbium-doped phosphate fiber. The erbium-doped phosphate fiber

Fig. 4. Dependence of the calculated gain of the amplifier on pump power using combined model of concentration quenching model with different relative number of cluster in the erbium-doped phosphate fiber and constant cooperative m =s. Erbium ion doping concentration is up-conversion of 1.1 10 3.8 10 ion=m , fiber length 7.1 cm, signal wavelength is 1535 nm, and signal input power is 30 dBm.

2

2 0

was forward-pumped by 980 nm semiconductor laser. The fiber parameters are as same as that used in experiment [18]. Fig. 3 shows the dependence of the calculated gain and NF of the amplifier on the pump power with different quenching model. The input signal wavelength is 1535 nm and input power dBm, the fiber length is 7.1 cm, the erbium ion concenis , the cooperative up-conversion cotration is 3.8 , and the relative number of cluster efficient is 1.1 is 20%.It is shown that with increasing pump power, in the ideal model and the homogeneous model the saturation gain occur at 50 mW or so, in inhomogeneous model and combined model saturation gain do not occur within 250 mW. Fig. 4. shows the dependence of the calculated gain on pump power using the combined model with relative number of cluster


Fig. 5. Dependence of the calculated gain of the amplifier on pump power using combined model of concentration quenching model with different cooperative up-conversion and constant relative number of cluster (20%) in the erbium doped phosphate fiber. Erbium ion doping concentration is 3.8 10 ion=m , fiber length is 7.1 cm, signal wavelength is 1535 nm, and signal input power is 30 dBm.

2

0

ranging from 5% to 20% and fixed cooperative up-conversion . The result shows that with increasing of 1.1 pump power the gain increase by different value in the fiber with the different relative number of cluster. At 200–250 mW pump power, the gain difference between the 5% and 20% relative number is 9 dB or so. Fig. 5. demonstrates the variation of the calculated gain as pump power using combined model with different cooperative up-conversion coefficient and constant relative number of cluster (20%) in the erbium doped phosphate fiber. The result shows that with increasing pump power the gain increase by different value in the fiber with the different cooperative up-conversion coefficient. The maximum gain difference beand 2.0 up-conversion tween 0.5 coefficient occur at 80 mW or so. The comparison of the calculated gain and NF with experimental data [18] is shown in Fig. 6. In the combined model, the small signal gain increases as pump power increase and reaches 22.5 dB with 200 mW pump power. The NF decreases as pump power varies from 10 to 50 mW and then almost keep a constant (4–5 dB) with larger pump power. It is shown that with up-conand the relative number version coefficient of 1.1 of cluster of 20% in the fiber, the numerical results of the combined model is in good agreement with the experimental data. Therefore, it indicates that both cooperative up-conversion and pair-ion quenching exist at the erbium doped phosphate fiber. IV. NUMERICAL ANALYSIS AND DISCUSSION


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Fig. 6. Dependence of the calculated gain and NF of the amplifier on pump power using combined model of concentration quenching model. The experimental data from reference[18]. Erbium ion doping concentration is 3.8 10 ion=m , cooperative up-conversion coefficient is 1.1 10 m =s, fiber length 7.1 cm, signal wavelength is 1535 nm, and signal input power is 30 dBm.

2

2 0

Fig. 7. Variation of the calculated gain and NF of the amplifier with erbium ion doping concentration. Cooperative up-conversion is 1.1 10 m =s, the relative number of cluster is 20%, the erbium-doped phosphate fiber length is 10 cm, and pump power is 200 mW.

2

of cluster in the fiber is 1.1 , 20%. It is shown that with increasing erbium ion concentration, the small-signal gain increase can reach maximum (27.0 dB or so) at a doping , then decrease with further concentration of 4.0 increasing doping concentration. The NF ranges from 4.0 to and 5.0 dB within doping concentration of 6.5 increases dramatically beyond the concentration.

A. Dependence of Gain and NF on Doping Concentration

B. Dependence of Gain and NF on Fiber Length

With the combined model the dependence of the gain and NF of the amplifier on erbium ion doping concentration were calculated and shown in Fig. 7. In this calculation, the fiber length is 10 cm, pumping power is 200 mW, signal wavedBm. The length is 1550 nm, and signal input power is cooperative up-conversion coefficient and the relative number

With the combined model, the dependence of the gain and NF on fiber length were calculated and demonstrated in Fig. 8. , In this calculation, doping concentration is 4.0 pumping power is 200 mW and the signal wavelength is dBm. The up-conversion 1550 nm and input power is coefficient and the relative number of clusters in the fiber is

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Fig. 8. Variation of the calculated gain and NF of the amplifier with fiber m =s, the relative length. Cooperative up-conversion coefficient is 1.1 10 number of cluster is 20%, the erbium ion concentration is 4.0 10 ion=m , pump power is 200 mW.

2

2

1.1 , 20%, respectively. It is shown that with increasing fiber length, the small-signal gain increases and reaches maximum (27.0) dB at 10 cm. The NF ranges from 4 to 6 dB within 18.0 cm, and then increase as the length increases further. V. CONCLUSION By numerical solution and numerical analysis of the homogenous model and inhomogeneous model, and the combined model of concentration quenching of erbium-doped fiber amplifier with high erbium concentration, The dependence of gain and NF on pump power are compared with experimental data, and the results indicate the combined model is in good agreement with experimental data and is suitable for modeling erbium-doped phosphate fiber amplifier. The erbium ion cluster in erbium-doped phosphate fiber is estimated from the numerical analysis and the optimal doping concentration and length of erbium-doped phosphate fiber are proposed in this paper. By the numerical analysis, the results show that with a 200-mW/980-nm pump laser, an erbium-doped phosphate fiber amplifier with a doping concentration of 4.0 and length of 10 cm may reach 27.0-dB gain. REFERENCES [1] E. Desurvire et al., Erbium-Doped Fiber Amplifier Devices and System Developments. New York: Wiley, 2002, pp. 242–259. [2] P. C. Becker et al., Erbium Doped Fiber Amplifier Fundamentals and Technology. New York: Academic, 1999, pp. 195–197. [3] P. Blixt et al., “Concentration-dependent upconversion in Er -doped fiber amplifiers: Experiments and modeling,” IEEE Photon. Technol. Lett., vol. 3, p. 996, 1991. [4] Y. Kimura and M. Nakazawa, “Gain characteristics of erbium doped fiber amplifiers with high erbium concentration,” Electron. Lett., vol. 28, no. 15, pp. 1480–1481, July 1992. [5] H. Musuda, A. Takada, and K. Aida, “Modeling the gain degradation of high concentration doped erbium doped fiber amplifiers by introducing inhomogeneous cooperative up-conversion,” J. Lightwave Technol., vol. 10, Dec. 1992. [6] E. Delevaque et al., “Modeling of pair-induced quenching in erbium doped silicate fibers,” IEEE Photon. Technol. Lett., vol. 5, pp. 73–75, Jan. 1993.

[7] M. Federighi and I. Massarek, “Optical amplification in thin optical waveguide with high erbium concentration,” IEEE Photon. Technol. Lett., vol. 5, pp. 227–229, Feb. 1993. [8] J. Nilsson, B. Jaskorzynska, and P. Blixt, “Performance reduction and design modification of erbium doped fiber amplifier resulting rrom pair-induced quenching,” IEEE Photon. Technol. Lett., vol. 5, pp. 1427–1429, Dec. 1993. [9] F. Di Pasquale, M. Zoboli, M. Federighi, and I. Massarek, “Finite-element modeling of silica wave-guide amplifiers with high erbium concentration,” IEEE J. Quantum Electron., vol. 30, pp. 1277–1282, May 1994. [10] P. Myslinki, D. Nguyen, and J. Chrostowski, “Effect of concentration on the performance of erbium-doped fiber amplifiers,” J. Lightwave Technol., vol. 15, pp. 112–120, Jan. 1997. [11] P. Myslinki et al., “Performance of high-concentration erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett., vol. 11, pp. 973–975, Aug. 1999. [12] W. J. Miniscalco, “Erbium-doped glasses for fiber amplifiers at 1500 nm,” J. Lightwave Technol., vol. 9, pp. 234–250, Feb. 1991. [13] Y. C. Yan, A. J. Faber, H. deWaal, P. G. Kik, and A. Polman, “Erbiumdoped phosphate glass waveguide on silicon with 4.1 dB/ cm gain at 1.535 nm,” Appl. Phys. Lett., vol. 71, pp. 2922–2924, 1997. [14] Y. Hu et al., “Numerical analysis of the population dynamics and determination of the upconversion coefficients in a new erbium doped tellurite glass,” J. Opt. Soc. Amer. B, vol. 18, no. 12, pp. 1928–1934, May 2001. [15] S. Jiang, B. C. Hwang, T. Luo, K. Seneschal, F. Smektala, S. Honkanen, J. Lucas, and N. Peyghambarian, “Net gain of 15.5 dB from a 5.1 cm long Er -doped phosphate glass fiber,” Proc. Tech. Dig. Optical Fiber Communication Conf., Mar. 2000. [16] B.-C. Hwang et al., “Cooperative upconversion and energy transfer of new high Er and Er -Yb doped doped phopshate glasses,” J. Opt. Soc. Amer. B, vol. 17, no. 5, pp. 833–839, May 2000. [17] T. Ohtsuki, S. Honkanen, and S. I. Najafi, “Cooperative upconversion effects on the performance of Er -doped phosphate glass waveguide amplifiers,” J. Opt. Soc. Amer. B: Opt. Phys., vol. 14, no. 7, pp. 1838–1845, July 1997. [18] B.-C. Hwang et al., “Performance of high-concentration Er -doped phosphate fiber amplifiers,” IEEE Photon. Technol. Lett., vol. 13, pp. 197–199, Mar. 2001. [19] Y. D. Hu, S. Jiang, and T. Luo, “Performance of high-concentration Yb -Er -codoped phosphate fiber amplifiers,” IEEE Photon. Technol. Lett., vol. 13, pp. 657–659, July 2001. [20] V. Chernyak and L. Qian, “Modeling high-concentration L-band EDFA at high optical powers based on inversion function,” IEEE J. Select. Topics Quantum Electron., vol. 8, pp. 569–574, May/June 2002.

Chun Jiang received the M.S. and Ph.D degrees in photonics from Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai, China, in 1996 and 1999, respectively. In 1999, he joined Center for Broadband Optical Networking Technology (CBONT), Shanghai Jiao Tong University (SJTU), Shanghai, China, as postdoctoral Research Associate. Since 2001, he has been an Associate Professor with the State Key Laboratory of Advanced Optical Communication Systems and Networks, SJTU. His current research interests include the simulation of photonic devices, optical communication systems and networks, research and development of photonic devices including optical switches, optical fiber amplifiers, and dense wavelength multiplexer/demultiplexer components, and the spectroscopy and laser characteristics of rare-earth-doped glasses for photonics and optoelectronics application. He has authored over 40 papers, mainly in the fields of erbium-doped fiber amplifiers and fiber Raman amplifiers, and spectroscopy and laser characteristics of rare-earth doped glasses.

Weisheng Hu received the B.Sc degree from Tsinghua University, Beijing, China, the M.E. degree from Beijing University of Science and Technology, Beijing, China, and the Ph.D. degree fromNanjing University, Nanjing, China, in 1986, 1989, and 1997, respectively. He is currently a Professor at Shanghai Jiao Tong University, Shanghai, China, and the Director of the State Key Laboratory of Advanced Optical Communication Systems and Networks. His research includes all-optical networking, optical switching, optical add-drop multiplexing module, and automatically switched optical network. He has published about 50 papers and has applied for 15 patents.


Qingji Zeng graduated from Chengdu Electronics and Telecommunication Engineering College, Chengdu, China, in 1960. He is currently a Full Professor and Head of the Center for Broadband Optical Networking Technology (CBONT), Shanghai JiaoTong University (SJTU), Shanghai, China. He is also a member of the Board of Directors and a Chief Scientist of Shanghai All-Optical Networking Technology Co. Ltd., Shanghai, China. His current research interests include intelligent optical networks, optical routers and optical ethernet technologies. He has authored more than 140 papers in the field of optical networking technology. Dr. Zeng was awarded the Science and Technology Progress Prize by the State Education Ministry in China.


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