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Numerical simulation on Fiber Brillouin Amplifier

Xiaorui Li, Huaping Gong∗, Shuhua Li, Jianfeng Wang Institute of Optoelectronic Technology, China Jiliang University, Hangzhou, China 310018

ABSTRACT

The theory of fiber Brillouin amplifier is investigated by numerical solution combinating interpolation method and Runge-Kutta method. Meanwhile, the most complete characterization and comparison of FBAs for pump power, initial signal power and fiber length is obtained. Through the analysis and comparison, the results show that the amplification efficiency can reach 90% based on the SBS and the most of the power transfer occurs within the first 20% of the fiber length. The output signal power is linear increased with increasing of the initial pump and initial signal, respectively. The high-gain Brillouin amplifier can be obtained when then fiber length is about 26km.

Keywords：FBA, SBS, numerical stimulation, gain

1. INTRODUCTION

Due to unique characteristics of SBS in the optical fiber, such as inherent low threshold power[1], high conversion efficiency and ultra narrow linewidth gain, fiber Brillouin amplifier (FBA) and fiber Brillouin fiber laser (BFL) have important applications in many fields[2-4]. The conversion efficiency of SBS magnification is extremely high, and firstly was used to light amplification. The SBS-produced gain in an optical fiber can be used to amplify a weak signal whose frequency is shifted from the pump frequency by an amount equal to the Brillouin shift. The pump and injected signal must propagate in opposite directions in the case of signal mode fibers if SBS were to transfer pump power to the signal. Such amplifiers were first studied during the 1980s[5,6] and are useful for sensing and other applications.

However, compared with the Raman gain bandwidth of 12 THz, the Brillouin gain bandwidth is only around tens of megahertz in optical fibers, which limits the applicable communication speed. For this reason, as a member of the optical amplifiers, fiber Brillouin amplifiers (FBAs) have been long-time ignored, and even disappeared from some fiber communication reference books. In recent years, Brillouin amplifier may be useful in practice for applications requiring selective amplification[6,7]. One such application consists of amplifying the carrier of a modulated signal selectively, while leaving its modulation sidebands unamplified. Another application of narrowband Brillouin amplifiers consists of using them as a tunable narrowband optical fiber for channel selection in a densely packed multi-channel communication system. If channel spacing exceeds but the bit rate is smaller than the bandwidth of Brillouin gain, the pump laser can be tuned to amplify a particular channel selectively.

∗ Email: [email protected]; phone:86-571-86835769

2011 International Conference on Optical Instruments and Technology: Optoelectronic Measurement Technology and Systems, edited by Xinyong Dong, Xiaoyi Bao, Perry Ping Shum, Tiegen Liu, Proc. of SPIE Vol. 8201, 82010A

© 2011 SPIE · CCC code: 0277-786X/11/$18 · doi: 10.1117/12.906943

Proc. of SPIE Vol. 8201 82010A-1

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2. FBA PRINCIPLE AND NUMERICAL MODEL

Stimulated Brillouin scattering (SBS) is one of the most efficient nonlinear amplification mechanism in optical fibers, It can also be used for making distributed fiber sensors capable of sensing temperature and strain changed over relatively long distances. The basic idea behind the use of SBS for fiber sensors can be understood form Equation (1) [8].

/ 2 2 /B B P Pv nπ λ= Ω = (1)

Where Bv is the Brillouin frequency shift, n is the refractive index of the fiber core, av is the longitudinal acoustic

velocity for the optical fiber, and Pλ is the free-space wavelength of the pump light. As the Brillouin shift depends on

the effective index of the fiber mode, it changes whenever the refractive index changes in response to local environmental variations. Both temperature and strain can change the refractive index of silica. By monitoring changes in the Brillouin shift or strain over long distances over which the SBS signal can be detected with a good signal-to-noise ratio. A tunable continuous wave (CW) probe laser and a pulse pump laser inject light at the opposite ends of a fiber. The CW signal is amplified through SBS only when the pump-probe frequency difference coincides exactly with the Brillouin shift. The time delay between the launch of the pump pulse and increase in the received probe signal indicates the exact location where Brillouin amplification occurs.

The pump light transfer to the backward Brillouin scattering light when the pump power is beyond the SBS threshold. However, SBS effect can be used to constitute fiber Brillouin amplifier (FBA).

Under steady-state conditions, SBS is described by the two coupled equations[9,10]:

⎪⎪⎩

⎪⎪⎨

⎧

−−=

+−=

PPPSBP

SSPSBS

dddd

IIIgzI

IIIgzI

α

α （2）

Where IS and IP are the light intensity of signal light and pump light transmitting together in fiber, Sα and Pα are the

fiber optic attenuation, respectively; gB is the Brillouin gain coefficient of the medium. Two simplifications can be made:

the first P Sω ω≈ owing to a respectively small value of the Brillouin shift and the second, for the same reason,

P Sα α α≈ ≡ , fiber losses are nearly the same for the pump and Stokes waves. With these changes equation (2)

becomes:

S BP S S

P BP S P

eff

eff

dP g P P Pdz A

dP g P P Pdz A

α

α

⎧ ⎛ ⎞= − +⎪ ⎜ ⎟⎜ ⎟⎪ ⎝ ⎠

⎨⎛ ⎞⎪ = − −⎜ ⎟⎪ ⎜ ⎟⎝ ⎠⎩

（3）



Where PS and PP are the power of signal light and pump light transmitting together in fiber, z is the propagation distance along the optical fiber of total length L, α is the fiber loss coefficient, , Aeff is effective area of fiber. The input powers of the pump Pp(z=0) and the seed Stokes waves Ps(z=L) serve as the boundary conditions of (3).

When a weak Stokes wave is amplified, i.e, the S PP P<< , pump depletion can be neglected. Solving coupled equations,

and integrating it over the fiber length L, the Stokes power is found to grow exponentially in the backward direction as:

{ }LALPgLPP α−= ]/)0([exp)()0( effPBSS (4)

Where Leff is effective length of fiber considering fiber loss and fiber absorbability:

eff1 [1 exp( )]L Lαα

= − (5)

Equation(4) shows how a Stokes signal incident at z=L grows in the backward direction because of Brillouin

amplification occurring as a result of SBS. In the critical pump power crPP regime, the Brillouin gain threshold is given

by

21/effcr

PB ≈ALPg (6)

Where gB is the peak of Brillouin gain. According to the principle of SBS amplifier, the simplified model of the Brillouin amplifiers is shown in Figure 1

Fig.1 Theoretical model of the Brillouin amplifiers

3. RESULTS AND DISCUSS

In this paper, Fourth-order-Runge-Kutta method combining with interpolation method is used to solve SBS intensity coupling equations to analyze the Brillouin amplification phenomenon in fiber. The parameters used in simulation are listed as follows: gain coefficient gB=5.0×10-11m/W[11], the attenuation coefficients of both pump light and signal light are 0.215dB/km[12] , namely 4.95×10-5/m, the difference of the attenuation coefficients can be ignored because their wavelength is close to. The effective sectional area of SMF is 80×10-12m2[13]. Meanwhile, the power pump signal and input signal is 10mW and 0.1mW, respectively.

The distribution of pump power and signal power along the fiber is presented in Figure 2, which are obtained by solving the SBS intensity coupling equations with input pump power 5mW, 10mW and15mW, and other parameters holding. Fig.2 shows how the Stokes power and pump power varies in a Brillouin amplifier along the fiber length when the input



w1/z U: U U U

MUJU(U)dd MUJU(U)dd MUJU(U)dd

U: w1/z

U MUJU(U)dd

- MUJU(U)dd

- MWU(U)dd

w1/z

MUJU(U)dd MUJU(U)dd MUJU(U)dd U:

signal is launched at z=L and the pump is incident at z=0. Because of pump depletion, the pump intensity is very small after 5km of fiber. The pump attenuation caused by the SBS effect and attenuation in the fiber make pump wave decrease fast on the first 5km of fiber. The pump power in the last 15km of fiber is low while the signal power after 5km of fiber is also low. Form Fig 2(a), we can see that pump light start to decrease fast at first 5km, however, the power decrease slow when the fiber length is more than 5km. Due to the nonlinear effect, the signal power increases slowly form 5km to 20km of fiber, while it increases rapidly in the other region of pumping strong. Fig.3 shows that the distribution of gain of signal along a 20km single mode optical fiber for different pumps. It is clearly seen that signal light transmits along the fiber form the end of the fiber, gradually increases owing to SBS amplification, and then increases fast near to pump input terminal. Therefore, it can be seen that the amplification efficiency based on SBS effect is high and about 90% of the pump power is transferred to the Stokes, and the most of the power transfer occurs within the first 20% of the fiber length.

(a) (b)

Fig.2 The distribution of pump power and signal power along the fiber (a) The distribution of pump power; (b)

The distribution of signal power

Fig.3 The distribution of signal gain along the fiber

Fig.4 (signal power Ps (0) =0.1mW, fiber length L=20km) shows relationship between input signal power and gain and pump wave for different pumps. Fig.5 (a) shows the power curve of signal light. In Fig.4 (a), the output signal power approximately increases linearly with the increasing of initial pump power. Fig.4 (b) shows the gain curve of signal light. When the fiber length is more than 5km, the increasing of signal gain starts to be slow.



MW

/Sd

Gai

n/dB

7 -80 -50 -40 -30 -20 -IS 0Signal Power/dBw

857580

50

40CD

20IS

-7 -80 -50 -40 -30 -20 -10Signal Power/dBw

(a) (b)

Fig.4 The relationship between signal and initial pump power (a) power curve; (b) gain curve

The influence of input signal power on output signal power is shown in Fig.5. The signal power increases gradually from the weak signal of 10-8mW to 1mw. The power is increased an order of magnitude each time to 0.01mw from 10-8mw, then it is increased 0.02mw each time to 0.1mw, and the power is changed 0.1mw from 0.1mw to 1mw. It can be seen that the higher of the input power is given, the more of the output signal power can be obtained. But its gain decreases linearly, which is determined by the gain definition. The smaller gain would be obtained when the better input signal is provided under the same conditions. In addition, with the increasing of the initial signal, the signal gain is to get saturation fast, meanwhile the depleting of the pump wave is more in the SBS process. Therefore, the increasing of signal power leads to the pump light fully utilizing, while it causes the gain of output signal to decrease.

(a) (b)

Fig.5 The relationship between signal and initial signal power (a) power curve; (b) gain curve

Fig.6 shows the relationship between signal and fiber length. Both the output signal power and gain increase first and then decrease with increasing of fiber length. At first 10 km, the signal power and gain increase fast and then turn slow. And the power and gain of signal are to get saturation gradually at 26 km, finally it decrease slowly after 26km. This phenomenon can be attributed to a fact that the high pump power which leads to the SBS effect in intensity during the first 10km fiber, most of pump wave is transferred to signal, and the pump power decreases very fast along the fiber. The signal power and gain get saturation due to the pump power weakens. After 26km of fiber, the pump power decreases further, which leads to the signal gain is less than attenuation in the fiber, therefore signal power and gain decrease. It



ID 28 38 48 68 88

Fiber Length/km

IF

17

:7 IS

IsIID 20 30 40 50 50

Fiber Length/km

means that the maximum output signal and gain can be obtained at about 26km of fiber.

(a) (b)

Fig.6 The relationship between signal and fiber length (a) power curve; (b) gain curve

4. CONCLUSION

The theoretical analysis and calculation of FBA in a long single mode optical fiber are presented in this paper. Through the analysis and comparison, we can draw some conclusions as following: (1) The amplification efficiency can reach 90% based on the SBS effect and the most of the power transfer occurs within the first 20% of the fiber length; (2) The output signal power is linear increased with increasing of the initial pump and initial signal power, while the output signal gain increases when the initial pump power increases. (3) The output signal power and gain increases first and then decreases along the fiber, and the maximum signal power and gain can be obtained when the fiber length is 26km. The results are of value to analyze performance of FBA and the optimization design.

ACKNOWLEDGEMENT

This work was supported by the Zhejiang Province Natural Science and Technology Fund (No. Y5090150, Y1110687)

REFERENCES

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[9] Zhou Ping, Guo Shaofeng, Lu Qishen, et al. “Steady-state analysis of transverse SBS in optical materials”, High Power Laser And Particle Beams. 16(1), 15-19(2004)

[10] Govind P. Agrawal, [Nonlinear Fiber Optics and Applications of Nonlinear Fiber Optics], Elsevier Science, USA, 188-238. (2001)

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