Parameters optimization of high efficiency discrete Raman fiber amplifier by using the coupled steady-state equations. L
Optics Communications 273 (2007) 149–152 www.elsevier.com/locate/optcom
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, Ming Li a, Yi-Tseng Lin b, Anshi Xu
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Liang Dou a, Shien-Kuei Liaw
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Parameters optimization of high efficiency discrete Raman fiber amplifier by using the coupled steady-state equations a Department of Electronics, Peking University, Beijing 100871, China Department of Electronic Engineering, National Taiwan University of Science and Technology, No. 43, Sec. 4, Keelung Road, Taipei 106, Taiwan
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Received 5 October 2006; received in revised form 22 December 2006; accepted 10 January 2007
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Abstract
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By using the coupled steady-state equations, we have numerically studied the characteristics optimization of Raman fiber amplifier (RFA) in a signal/pump double-passes-the-gain-medium scheme. The simulation results are in very good agreement with those of experimental data. Given a constant pumping power, the length of dispersion compensation fiber (DCF) in a RFA could be determined. The optimum design shows that the best length of the DCF is at around 3.8 ± 0.2 km in our study. This could provide both the highest signal output power and the lowest noise figure among all conditions we choose. 2007 Elsevier B.V. All rights reserved.
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Keywords: Raman fiber amplifiers; Coupled steady-state equations; Dispersion compensation fiber; Double pass
1. Introduction
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Raman fiber amplifiers (RFAs) have become increasingly important in optical communication systems and optical networks to compensate for the fiber loss and/or splitting loss. Comparing to the conventional rare-earth doped fiber amplifiers, RFAs have flexible signal gain band and low noise figure (NF) level [1]. Several system experiments demonstrated the benefits of Raman amplification including repeater-less undersea experiments [2], highcapacity terrestrial [3], submarine system transmission [4], shorter span single-channel system [5] and soliton system [6]. However, the pump efficiency of the conventional RFA is low when compared to that of the conventional erbium doped fiber amplifier (EDFA) [7]. Recently, we reported an RFA with signal/pump double-passes-thegain-medium scheme by utilizing an optical circulator (OC) as a signal/pump reflector [8]. The pump efficiency improvement and the NF suppression can be realized *
Corresponding author. Tel.: +886 2 2737 6384; fax: +886 2 2737 6424. E-mail address:
[email protected] (S.-K. Liaw).
0030-4018/$ - see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2007.01.028
simultaneously. Although it is crucial to numerically predict the characteristics of RFA such as signal power and NF versus pump wavelength, pump power, gain medium characteristic and so on, the optimum design of RFA parameters has not yet been addressed. In this paper, we preliminary describe the numerical simulation method to estimate the characteristics of signal/pump double-pass RFA, and then we verify the simulation results with the experimental data in [8] to confirm if they are closely matched with each other. Finally, we conclude that the optimized length of the dispersion compensation fiber (DCF), under a certain pump power and pump wavelength, could be predicted to get the largest output signal power and the lowest NF. 2. Theory and simulation Fig. 1 depicts the similar configuration of RFA which has signal/pump power dual-passed the gain medium in [8]. Here, the Raman pump laser is launched into the dispersion compensation module (DCM) via a wavelength division multiplexing (WDM) coupler. The OC 2 in
L. Dou et al. / Optics Communications 273 (2007) 149–152
where P+(z,vi) and P(z,vi) are the optical power of the forward and the backward propagating waves within infinitesimal bandwidth around vi, respectively. a, g, h, k and T are attenuation coefficient, Rayleigh backscattering coefficient, Plank’s constant, Boltzmann constant and temperature, respectively; Aeff is the effective area of the optical fiber at frequency mm, g(mi mm) is Raman gain parameter at frequency mm due to pump laser at frequency mm, the factor C accounts for polarization randomization effect with the value lies between 1 and 2. In [10], it is reasonable to assume that the ASE level combines other noises is 30 dB lower than that of the input signal, so we may calculate the pump and the signal without considering the combined noise. Thus, Eq. (1) can be simplified as " # i1 m X X dP i gR ðvj vi Þ vi gR ðvi vj Þ ¼ ai þ Pj P j P i; CAeff CAeff dz v j¼1 j¼iþ1 j
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Fig. 1. Configuration of the RFA is depicted to have signal/pump power dual-pass the gain medium as shown in [8].
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ði ¼ 1; 2; . . . :; mÞ;
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Fig. 2 shows a simplified scheme to represent the signal/ pump double-passed configuration in a RFA. Along the section of DCF, the four major players are the forward pump power, backward pump power, forward signal power and backward signal power. In order to apply the above equation, one must know the four power levels at one side. Unfortunately, only the forward pump power and the forward signal power at z = 0, as well as reflection coefficient at the other end of z = L are known. To solve this problem, distribution of the signal power and the pump power along the whole DCF is calculated base on the following procedures. Firstly, the backward pump and the backward signal at z = 0 are assumed to be zero. Then we calculate the equations above from z = 0 to z = L. Since the forward signals and the backward signals are determined by the reflected ratios, the assumed backward signal power and pumps power can be corrected according to the difference between the calculated reflected ratios and the real ones. After several iterations, distribution of all the signal power and pump power may converge to an acceptable range, for example, of less than 0.1% variation between the adjacent iterations. After we get the distribution of the pump power and signal power, the noise can be founded by the relaxation method. We assume that the initial noise of each channel is 70 dBm in a channel spacing of 0.2 nm, which is corresponding to the sensitivity limitation of an optical spectrum analyzer (OSA), and the backward noise along
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Fig. 1 is utilized as a reflected mirror both for the signal and pump laser to loop back into the DCM. The signal comes into port 2 of the OC 2, then travels from port 3 to port 1 via the connecting point, and then comes back to port 2. In such a configuration, signal and the Raman pump power double pass the DCM. While the DCM acts as a gain medium as well as a dispersion compensator. The residual pump laser in DCM is in counter direction with the incoming signal beam and hence increases the Raman gain. Without loss of generality, the Raman laser we used is lasing at 1495 nm. The experiments have successfully confirmed the pumping efficiency improvement for this kind of RFA is more efficiency than other types of RFAs. In such a signal/pump double-passed scheme, the analysis of signal round-trip propagation in the DCM is essential to predict RFA performance under various conditions. The method we use in simulation is based on a set of coupled steady-state equations that include spontaneous Raman emission and its temperature dependence, Rayleigh scattering, amplified spontaneous emission (ASE), stimulated Raman scattering (SRS), and arbitrary interaction between the pump laser and signals. The forward and backward power evolution of pump power, signals and ASE can be expressed in terms of the following equations [9]. dP ðz; vi Þ ¼ aðvi ÞP ðz; vi Þ gðvi ÞP ðz; vi Þ dz i1 X gR ðvm vi Þ P ðz; vi Þ P ðz; vi Þ þ P ðz; vi Þ CA eff m¼1
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i¼1 X gR ðvm vi Þ P ðz; vi Þ þ P ðz; vi Þ CA eff m¼1 hðvm vi Þ 1 kT 1 1þ e Dv P ðz; vi Þ
hvi
n X vi gR ðvi vm Þ P ðz; vi Þ þ P ðz; vi Þ v CA eff m¼iþ1 m
n X vi gR ðvi vm Þ CAeff v m¼iþ1 m hðvi vm Þ 1 Dl; 1 þ e kT 1
2hvi P ðz; vi Þ
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Fig. 2. A simplified equivalent design to present the signal/pump doublepass RFA for simulation purpose.
L. Dou et al. / Optics Communications 273 (2007) 149–152
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the whole section of DCF is negligible. Then, we put these values into Eq. (1) together with the forward and the backward signals and pump power at z = 0. After calculating Eq. (1) from z = 0 to z = L, we get an approximate value of the forward direction noise. We assume that the backward noise at z = L equals to 70 dBm with the same channel spacing as mentioned above. Eq. (1) is then iterated from z = L to z = 0 along with the approximate forward noise. Thus, we have finished a complete round-trip iteration for signals and pump sources with noise of both directions. After several iterations, all WDM channel signals are convergent as predict. 3. Simulation results
Fig. 3. The simulation results are in very good agreement with those of experimental data.
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where G is the amplification factor defined as the output power over the input power. PASE is the ASE noise appears at the output of a RFA, and m is the signal frequency. B0 is the resolution of the OSA. The second one is called equivalent noise figure (NFeq) which is similar to Eq. (3) except that Gonoff is used instead of G. Here, the Gonoff is defined as the difference of signal output power between the on/off states of the pump laser(s). In this paper, in order to optimize the length of the DCF to get the best performance, another suitable definition of the NF is introduced. First we define Geff as G minus the loss due to single mode fiber (SMFloss). Note that the latter is attributed by the SMF and other inherent loss such as interport insertion loss of the OC. Geff has a clear meaning as it represents the Raman gain when DCF is used. Then we put Geff into Eq. (3), the corresponding NF is mostly contributed by DCF. Because the length of the SMF is kept constant, we may assume it has equivalent loss impact to various lengths of DCFs. Thus, DCF length becomes the dominant variable parameter to affect the gain and NF of the RFA. To verify the algorithm above, the signal/pump doublepassed RFA as shown in Fig. 1 is simulated for further comparison with the experimental data. The parameters are set equal to those in Ref. [8]. Thus, the output power of the tunable laser is 1.53 dBm for all the tested wavelengths at 1591.9-, 1595.1- and 1598.3 nm, respectively. The length of the first spool SMF is 26.569 km while that of the second spool SMF is 26.555 km. Both of them have the same attenuation coefficient of 0.22 dB/km. The Raman pump laser is operating at 1495 nm with pump power being 23.76 dBm. The insertion loss of the WDM coupler is 0.6 dB within a broadband wavelength range. The average inter-port insertion loss of OC 2 is 0.8 dB. The Raman gain
is contributed by both SMF and DCF as condition in Ref. [11]. While the Rayleigh backscattering coefficient is 7 · 108 m1 and the Aeff is equal to 80 · 1012 m2. We assume that the Raman gain coefficient of DCF is identical to that in [9] and DCF also has the same Rayleigh-backscattering coefficient as SMF does. The attenuation coefficients are 0.6403-, 0.6547- and 0.6717 dB/km at 1591.9-, 1595.1- and 1598.3 nm, respectively. The simulation results shown in Fig. 3 are in very good agreement with those of experimental data. To show the optimum DCF length under a fixed pump power and pump wavelength, Fig.4 presents the calculated results for both the signal output power and NF versus DCF length at three signal wavelengths of 1585.5-, 1595.1-, and 1604.7 nm, respectively. Among them, the 1595.1 nm has the potential highest gain for this RFA which is consistent with Raman shift effect of 13 THz away from the pump laser to signal wavelength which has the maximum Raman gain. We find that the largest signal output power may appear as the length of DCF is 3.6 km. While the lowest NF could be found as
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1 2P ASE þ ; G GhvB0
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The most important parameters for a RFA are signal output power and NF. When the input signal power is fixed, signal gain and signal output power reach their maximum simultaneously. The NF of RFA has two different definitions. The first one is similar to that of EDFA and could be express as NF ¼
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Fig. 4. The calculated results for both signal output power and noise figure versus DCF length at three signal wavelengths of 1585.5-, 1595.1and 1604.7 nm, respectively.
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L. Dou et al. / Optics Communications 273 (2007) 149–152
by NSC project under Grant No. 94-2219-E-011-007, Taiwan. We thank Ms. Hua Li and Mr. Oliver Sung for their kindness help, and reviewer’s comments.
the DCF length is 4 km. In general, DCF has a larger gain coefficient than that of the SMF, but the attenuation coefficient of the former is also higher than that of the SMF. So, there is a trade-off when selecting the length of DCF. From the simulation results, we conclude that the optimum length of DCF is 3.8 ± 0.2 km. DCF length of around 3.8 km is an ideal value to realize the best characteristics for the RFA.
References
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Liang Dou, Ming Li and Anshi Xu are partially supported by NFSC under Project No. 60477002, China. Shien-Kuei Liaw and Yi-Tseng Lin are supported in part
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Acknowledgements
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4. Conclusion We have numerically studied the optimum characteristics of a RFA using the coupled steady-state equations. The RFA is in a signal/pump double-passed (the DCM) scheme under fixed pump power and pump wavelength. The simulation results are in very good agreement with those of experimental data. We also conclude that the optimum length of the DCF is 3.6 km for obtaining the highest output power while it is 4.0 km for obtaining the lowest NF. It is suggested that the length of the DCF be around 3.8 ± 0.2 km for providing nearly both the highest signal output power and the lowest NF.
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