- Email: [email protected]
Analysis and simulation of single-frequency Raman fiber amplifiers
Optics Communications 284 (2011) 2997–3003
Contents lists available at ScienceDirect
Optics Communications j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / o p t c o m
Analysis and simulation of single-frequency Raman fiber amplifiers Jinyong Leng ⁎, Shengping Chen ⁎, Wuming Wu, Jing Hou, Xiaojun Xu College of Optoelectronic Science and Engineering, National University of Defense Technology, Changsha, Hunan, 410073, China
a r t i c l e
i n f o
Article history: Received 22 November 2010 Received in revised form 31 January 2011 Accepted 31 January 2011 Available online 12 February 2011
a b s t r a c t High power operation of single-frequency Raman fiber amplifiers is usually limited by the onset of stimulated Brillouin scattering. A theoretical investigation on single-frequency Raman fiber amplifier limited by stimulated Brillouin scattering is presented in this paper, based on the intensity equations combining stimulated Brillouin scattering and stimulated Raman scattering. A combination of methods is proposed to increase the output power of single-frequency Raman fiber amplifier. These methods include applying a suitable pump scheme according to the fiber length and seed signal power, using short gain fibers, utilizing a multiple-stage scheme and providing suppression of stimulated Brillouin scattering. © 2011 Elsevier B.V. All rights reserved.
1. Introduction
2. Theoretical model
Raman fiber amplifiers (RFAs) are known as stable high-power fiber light sources providing almost any wavelength in the near-IR range due to the broad gain spectrum and wavelength versatility of stimulated Raman scattering (SRS) [1]. Therefore, RFAs are very attractive for a variety of applications, especially in the fields of telecommunications [2] and supercontinuum generation [3]. However, RFAs are seldom utilized to generate high power single frequency output. Because hundred meters of fibers should be used to provide enough Raman gain in these sources which makes stimulated Brillouin scattering (SBS) easy to be initiated. The SBS effect limits the achievable powers of single frequency Raman fiber amplifiers (SF-RFAs) to a very low level. Nevertheless, researches on SF-RFAs remain continuously active [4–7], due to its attractive application potentials in aspects that need specific lasing wavelengths which cannot be easily achieved with conventional doped fiber amplifiers. Although efforts have been made to enhance the output power of SF-RFAs, the achievements rarely reach the practical requirements [6,7]. To date, most researches on single frequency RFAs focus on the experimental investigations. On the other hand, theoretical part has, to the best of our knowledge, not yet been elaborately investigated. The purpose of this paper is to provide a theoretical investigation on SF-RFAs, so as to find the ways of enhancing the output powers of SF-RFAs. A theoretical model is proposed in the paper, based on the intensity equations combining SBS and SRS. The impacts of pump scheme, fiber length, seed power level, and SBS suppression on the performance of SF-RFAs are discussed.
A typical RFA is illustrated in Fig. 1. The configuration is almost the same as a conventional fiber amplifier except that the gain is provided by SRS instead of stimulated rare earth ions. An 1178 nm source is selected as an example, due to its attractive potential ability to be frequency doubled to 589 nm for laser guide star in astronomical adaptive optics systems. The 1178 nm single frequency seed is amplified forward by SRS effect along the single mode fiber pumped at 1120 nm. The 1178 nm signal increases along the gain fiber and initiates backward SBS at a certain power level. SBS is easy to be initiated in this amplifier because of the narrow signal linewidth and the long gain fiber. An SBS frequency shift is usually at the order of ten gigahertz (less than 0.1 nm). So, the backward SBS exhibits a wavelength around 1178 nm, near the signal wavelength, which locates at the peak wavelength of the Raman gain profile with 1120 nm pump. Because the Raman gain is bidirectional effective along the fiber, the backward SBS will also be amplified by SRS effect. The backward amplified SBS will then compete with the signal, causing an unwanted amplifier power limitation. The intensity equations of SRS and SBS can be described as [8]:
⁎ Corresponding authors. E-mail addresses: [email protected] (J. Leng), [email protected] (S. Chen). 0030-4018/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2011.01.089
8 dISR > > < dz = gR IP ISR − αSR ISR υ > dI > : P = − p gR IP ISR −αP IP dz υSR 8 dISB > > = −gB IP ISB + αSB ISB < dz > > : dIP = −g I I −α I B P SB P P dz
ð1Þ
ð2Þ
where ISR and ISB are the intensity of Raman wave and Brillouin wave. IP is the pump intensity. gR and gB are the gain coefficients of Raman
2998
J. Leng et al. / Optics Communications 284 (2011) 2997–3003
Fig. 1. Schematic diagram of a Raman fiber amplifier.
scattering and Brillouin scattering. υP and υSR are the frequencies of pump and Raman wave. αP, αSR and αSB are the intrinsic background losses in the fiber for pump, Raman and Brillouin wave. z is the location along the fiber. Considering the described physical processes in Fig. 1, the intensity equations describing the SF-RFAs with SBS can be written as: υp υp dIþ þ þ þ − þ P =− g I I − g I I −αP IP dz υSR R P SR υSB R P SB
ð3aÞ
υp υp dI− − þ − − − P = g I I + g I I + αP IP dz υSR R P SR υSB R P SB
ð3bÞ
dIþ þ þ − þ SR = gR IP ISR −gB ISR ISB −αSR ISR dz −
dISB − þ − − = −gR IP ISB −gB ISR ISB + αSB ISB dz
ð3cÞ
ð3dÞ
where the superscript “+” stands for forward propagated waves and “−” stands for backward propagated waves in Eq. (3). The subscript “P”, “SR” and “SB” represent the 1120 nm pump light, the 1178 nm Raman signal light and the Brillouin scattering light near 1178 nm, − respectively. IP stands for I+ P + IP . υSB is the frequency of the Brillouin wave. Eq. (3a) and (3b) describe the power evolution of the 1120 nm pump light. The first two items at the right side of the equations correspond to the Raman consumption of the 1178 nm Raman signal light and the Brillouin scattering light near 1178 nm. Eq. (3c) describes the power variation of the 1178 nm Raman signal light. It is not only a signal light of the Raman scattering process, but also a pump light of the Brillouin scattering process. The three items at the right side of the equation correspond to the Raman gain, the Brillouin consumption and the intrinsic loss, respectively. Eq. (3d) describes the power evolvement of the Brillouin scattering light. It is a signal light of both the Raman and the Brillouin process. The three items at the right side of the equation correspond to the Raman gain, the Brillouin gain and the intrinsic loss, respectively. There are three assumptions in Eq. (3). The first one is that the difference between the Raman gain coefficients of υSR and υSB is negligible. That's well-founded because the wavelength shift of Brillouin wave is less than 0.1 nm away from the 1178 nm signal wavelength. The second one is that the Raman gain coefficients of both directions are the same [8]. The last one is that the spontaneous Raman noises of both directions are negligible. That is an evident conclusion for the forward direction because the seed of the spontaneous Raman scattering is negligible compared with the input seed. For the backward direction, spontaneous Raman scatterings only transfer a small fraction of 1120 nm pump to Raman scattering light. In another word, the pump power changes a little due to spontaneous Raman scattering. So the influence of spontaneous Raman scattering could be
neglected. The last assumption will be confirmed by simulation in the next section. Substituting power for intensity and considering the Brillouin gain spectrum, Eq. (3) should be changed as follow: þ
−
PSBi þ υp gR Pþ υp gR PP ∑ dPþ þ P P PSR i =− − −αP PP dz υSR A eff υSB A eff −
−
PSBi þ υp gR P− υp gR PP ∑ dP− − P P PSR i = + + αP PP dz υSR A eff υSB Aeff dPþ g P Pþ SR = R P SR − dz A eff
− Pþ SR ∑ gBi PSBi i
A eff
ð4aÞ
þ
−αSR PSR
ð4bÞ
ð4cÞ
dP− g P P− g Pþ P− − SBi = − R P SBi − Bi SR SBi + αSB PSBi dz A eff A eff
ð4dÞ
where Aeff is the effective area of the fiber core. The differences of frequencies, Raman gain coefficients and background losses of these discrete Brillouin waves are neglected in Eq. (4). SBS gain can be described by the following Lorentzian shaped profile with peak gain g0 and bandwidth ΩSBS [8]. 2
gB ðυi Þ = g0
ΩSBS 4ðυi −υ0 Þ2 + ΩSBS2
ð5Þ
where υ0 is the Brillouin frequency shift from the seed signal λSR, which is defined by υ0 = 2nνa /λSR with n the optical refractive index and νa the acoustic velocity. The boundary conditions of Eq. (4) are shown in Fig. 1. The initial powers for the discrete Brillouin waves initiated from noise, which could be thermally activated phonons, ASE, signal noise or back scattered light, could be written as PN = hυ0ΔυSB within the discrete linewidth [9,10]. The differential equations are two point boundary value problems which are solved by the modified relaxation method in this paper [11]. The fibers used in the model are single mode polarization maintaining silica fibers. The bandwidth of the 1178 nm seed signal is far below the Brillouin scattering bandwidth ΩSBS. Parameters used in the model are given in Table 1. Table 1 Parameters used in the model. λP = 1120 nm gR = 7 × 10−14 m/W αP = 0.003 m−1 ΩSBS = 58 MHz n = 1.45
λSR = 1178 nm g0 = 2.4 × 10−11 m/W αSR = αSB = 0.005 m−1 Aeff = 2.83 × 10−11 m2 νa = 5.96 km/s
J. Leng et al. / Optics Communications 284 (2011) 2997–3003
2999
3. Modeling results
3.1. Pump scheme
Based on the above theoretical model, the impacts of pump scheme, fiber length, seed power, and SBS suppression on the performance of the SF-RFAs are discussed in this section. Firstly, we confirm the third assumption in Eq. (3) that the influence of backward spontaneous Raman noise could be neglected. As an example, Fig. 2 illustrates the 1120 nm pump, 1178 nm signal and SBS power distributions along the 100 m fiber. A backward pump scheme is adopted. The signal power and pump power are set at 10 mW and 25 W, respectively. It can be seen from Fig. 2(a) that the signal grows slowly at the input port and increases rapidly at the output port. As a comparison, the powers of the backward scattered light amplified by SRS or SBS respectively are illustrated in Fig. 2(b). We can see that the growth process of the backward scattered power, starting from noise at the output port and propagating backward, can be divided into two parts. In the first part, while the 1178 nm signal power is high enough, SBS is in the majority. In the second part, while the signal power is too low to excite SBS, SRS is in the majority. In other words, the contribution of the backward scattered power growth could be divided into two parts. Compared with SBS, the power growth due to SRS is much lower which suggests that the backward spontaneous Raman noise is negligible.
Usually, bidirectional pump scheme is not used in SF-RFAs, because the large remnant pump light is dangerous for the pump resource on the opposite direction. So, only forward and backward pump schemes are considered here. The relationships between the output power and the pump power under different pump schemes with various fiber lengths and seed signal powers are illustrated in Fig. 3. It should be noted that there is a critical value for the pump power of the SF-RFA. Once the pump power exceeds the critical value, the Brillouin scattering light will deplete the signal light rapidly [12]. So the descending process of the output power cannot be depicted in Fig. 3. This corresponds to the situation that the second item on the right side of Eq. (4c) is higher than the first item. As a result, no amplified 1178 nm signal will be exported. The whole system actually becomes unstable under this condition. Time dependent items should be added into the model to describe the behavior of the RFA at this time, which might be considered in the future. The curves in Fig. 3 and succeeding figures are illustrated under the critical pump value. The y-axis values of the end points on the curves correspond to the maximum available output power. From Fig. 3 we can see that for the SF-RFA with a long fiber, maximal output power of the backward pumped amplifier is higher than that of the forward pumped one, such as 150 m and 100 m in Fig. 3(a) and
Fig. 2. (a) Pump, signal and (b) SBS power distribution inside the fiber.
Fig. 3. Output power as a function of pump power with different pump schemes. (a) seed power = 10 mW; (b) seed power = 50 mW.
3000
J. Leng et al. / Optics Communications 284 (2011) 2997–3003
100 m and 50 m in Fig. 3(b). As an illustration, Fig. 4(a) shows the differences between signal and SBS power distributions inside the 150 m fibers under different pump schemes with the same output power, in which the seed signal powers are 10 mW. From Fig. 4(a) we can see that the SBS power of the forward pumped RFA is much higher than that of the backward pumped RFA with the same output power, which means that the performance of SF-RFA with a forward pump scheme is easier to be limited by SBS. At the same time, for the SF-RFA with a short fiber in Fig. 3, maximal output power of the forward pumped amplifier is higher than that of the backward pumped one, such as 30 m in Fig. 3(a) and 15 m in Fig. 3(b). We attribute this to the difference of the SBS power evolution trendline under different pump schemes. From Fig. 3(a), we can see that the backward pumped RFA is limited by the onset of SBS at about 5.7 W output power and however the forward pumped RFA is not at this power level. It can be explained that although the SBS power of the forward pumped RFA is higher than that of the backward pumped RFA with the same output power, the difference between them is comparatively small, as shown in Fig. 4(b), in which the fiber lengths are 30 m and the seed powers are also 10 mW. At the same time, the pump power at the seed input port (z = 0) of the forward pumped RFA is also higher than that of backward pumped RFA and the differences between them are comparatively big. So the higher pump power at z = 0 insure the Raman gain is stronger than the Brillouin
Fig. 5. Output power and SBS power as a function of pump power with different fiber lengths.
consumption for the forward pump scheme, leading to the continuative increase of 1178 nm signal power. Unfortunately, the lower pump power at z = 0 fails to do that for the backward pump scheme. So the output power has reached its maximum. Suitable pump scheme should be chosen to get a higher output power, according to the fiber length. It should be emphasized that the output power of the forward pumped RFA is always higher than that of the backward pumped one at the same pump power, no matter how long the fiber is. So, when the needed output power can be obtained with both pump schemes, the forward pump scheme should be adopted to get higher efficiency. 3.2. Fiber length Fiber length is an important factor affecting the thresholds of SRS and SBS. Due to the low Raman gain coefficient, hundred meters of fibers should be used in SF-RFAs to amplify 1178 nm signal. On the other hand, SBS power grows rapidly while increasing the fiber length. Fig. 5 illustrates the 1178 nm signal and SBS power as a function of pump power with different fiber lengths. Fig. 6 shows the conversion efficiencies of the RFA with various fiber lengths. The seed
Fig. 4. Signal and SBS power distributions inside the fiber under different pump schemes. (a) Fiber lengths = 150 m; (b) fiber lengths = 30 m.
Fig. 6. Efficiency as a function of output power with different fiber lengths.
J. Leng et al. / Optics Communications 284 (2011) 2997–3003
signal powers are all 10 mW. Backward pump scheme is adopted in the two figures. It can be seen from the two figures that a shorter fiber length corresponds to a higher pump power threshold and a higher maximal output power, however with a relatively lower efficiency. A longer fiber length corresponds to a higher efficiency, however with a lower SBS limited output power. In other words, long fibers are not suitable for high power output. Short fiber length should be a good choice to build up high power RFA, although its efficiency is not high. However, it should be emphasized that in the condition of getting enough output power, the fiber length should be chosen as long as possible to get higher efficiency. Fig. 7 shows the maximal available output power and efficiency of the SF-RFAs as a function of fiber length. Different pump schemes and seed signal powers have been considered. Fig. 7(a) and (b) are illustrated with the seed signal power of 10 mW and 50 mW, respectively. In both figures, the forward pumped amplifier is more efficient than the backward pumped one with short fiber lengths. While with long fiber lengths, the backward pumped one is more efficient. Fig. 7(c) shows the maximal output power as a function of fiber length by combining the two curves shown in Fig. 7(a) and (b), despite of the pump scheme. It can be seen that the amplifier with higher seed signal power is easier to be power limited by SBS, so the maximal output power is relatively lower as compared with the low signal power seeded one when using the same fiber length. However, the efficiency of the high power seeded one is higher, as shown in
3001
Fig. 7(d). That is to say, the high power seeded RFA exhibits high efficiency, while the low power seeded one exhibits high available output power. It should be noted that the efficiencies in Fig. 7(d) are all got at the maximal output power, which correspond to the end points of the curves in Fig. 6. Therefore, in order to set up a high-power SF-RFA, one should firstly clarify the needed output power. According to the needed output power, the scope of fiber length is decided from Fig. 7(c). Then, proper pump scheme can be selected according to the fiber length. 3.3. Multi-stages amplifiers The influences of seed signal power on the performance of SF-RFAs have been mentioned above. The seed signal power of 1178 nm from a commercial DFB is usually at the level of about 10 mW. The 10 mW seed can be amplified directly to tens of watt or only to several watt and then to tens of watt. Fig. 8 shows the output power versus pump power with seed power of 10 mW and 1 W. The fiber lengths are 20 m and 9.5 m, respectively. The fiber lengths are chosen to get 10 W maximal output power. Pump scheme is chosen according to get the higher output power. So forward pump scheme is used with seed power of 10 mW. Backward pump scheme is used with seed power of 1 W. It can be seen from Fig. 8 that the pump powers needed for 10 W output power are about 150 W and 110 W, respectively for 10 m W
Fig. 7. The maximal available output power and efficiency as functions of fiber lengths.
3002
J. Leng et al. / Optics Communications 284 (2011) 2997–3003
a two-stages RFA to amplify 10 mW seed signal to 10 W output, giving a total conversion efficiency of 7.9%. This two-stage RFA is obviously more efficient than the one-stage RFA. The latter exhibits a conversion efficiency of 6.7% (10 W/150 W). It should be emphasized that the losses between the two amplifiers of two-stage SF-RFA are ignored in our discussion. Another problem emerges on how large should the middle power be. Fig. 9 shows the total efficiency of a two-stage amplifier as a function of the middle power with various total output powers. Fig. 9(b) is a close-up illustration of Fig. 9(a). The total efficiency has a maximum value corresponding to a certain middle power. We call this certain middle power the optimal middle power. This optimal middle power and the total efficiency both grow with the total output powers. So the middle power should be optimized according to the total output power, to get a maximal total efficiency. It should be emphasized that the above results are obtained without considering any SBS suppression. In the next section, we will show that the performance of RFA can be enhanced greatly with only simple SBS suppression. Fig. 8. Output power versus pump power with various seed powers.
3.4. SBS suppression and 1 W seed power. According to Fig. 3(a), the needed pump power in an amplifier with 150 m fiber length to amplify 10 mW seed to 1 W is about 17 W. That is to say, a total pump power of 127 W is needed in
From the simulation results above, we can draw the conclusion that the achievable powers of single-frequency Raman fiber amplifiers are usually limited by SBS. So the SBS suppression is the key factor for high-power single-frequency RFA. There has been much investigation on SBS suppression in single-frequency Yb-doped fiber amplifiers. Among those suppression methods, the temperature and strain gradients along the fibers can broaden the effective SBS linewidth and thereby reduce the effective gain which has been demonstrated to be a good approach to mitigate SBS [10,13]. This technique can be used in SF-RFA, in which the peak SBS gain g0 is inversely proportional to the SBS gain linewidth. If some special temperature and strain gradients are utilized to broaden the effective SBS linewidth in SF-RFA and thereby reduce the effective SBS peak gain, the performance of SF-RFAs will be improved. The results illustrated in Fig. 10 are gained by reducing g0 to g0/8. We can see that the maximal output powers are increased by a factor of ~3 compared to the RFA without any SBS suppression. 4. Conclusion In this paper, we present our theoretical investigation on SF-RFAs, based on the intensity equations combining SBS and SRS. The impacts of
Fig. 9. Total efficiency versus middle power with various total output powers.
Fig. 10. Improve the performance of RFA by SBS suppressing.
J. Leng et al. / Optics Communications 284 (2011) 2997–3003
pump scheme, fiber length, seed power, and SBS suppression on the performance of RFA are discussed. According to preferred embodiments, a combination of methods is used to increase the output power of SF-RFAs. These methods include: a suitable pump scheme should be provided according to the fiber length and seed signal power; a short fiber should be used in company with high pump power to get high output power; a multi-stage scheme should be adopted according to the laboratorial conditions to export high signal power with low pump power comparatively easily; and some measures should be used to reduce the effective peak SBS gain to improve the performance of RFA sharply. Acknowledgement This work was supported by the Projects of the National Natural Science Foundation of China under Grant no 10904173 and the China Postdoctoral Science Foundation. References [1] E.M. Dianov, I.A. Bufetov, M.M. Bubnov, et al., Opt. Lett. 25 (2000) 402. [2] N.S. Kim, M. Prabhu, C. Li, et al., Opt. Commun. 176 (2000) 219.
3003
[3] H. Masuda, K.-I. Suzuki, S. Kawai, et al., Electron. Lett 33 (1997) 753. [4] P. Dupriez, C. Farrell, M. Ibsen, J.K. Sahu, J. Kim, et al., Proc. SPIE 6102 (2006) 61021G. [5] L. Taylor, Y. Feng, D.B. Calia, Opt. Express 17 (2009) 14687. [6] Yan Feng, Luke R. Taylor, Domenico Bonaccini Calia et al. “39 W narrow linewidth Raman fiber amplifier with frequency doubling to 26.5 W at 589 nm”, in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2009), paper PDPA4. [7] Feng Yan, Luke R. Taylor, Domenico Bonaccini Calia, Opt. Express 17 (2009) 23678. [8] Govind P. Agrawal, Nonlinear Fiber Optics, 4th ed., Elsevier Pte Ltd, Singapore, 2009. [9] A. Liu, Opt. Express 17 (2009) 15201. [10] M. Hildebrandt, S. Büsche, P. Weßels, et al., Opt. Express 16 (2008) 15970. [11] A. Liu, Proc. SPIE. 6102 (2006) 61021R. [12] Feng Yan, Luke R. Taylor, Domenico Bonaccini Calia, Opt. Express 17 (2009) 19021. [13] J.E. Rothenberg, P.A. Thielen, M. Wickham, et al., Proc. SPIE. 6873 (2008) 687300.
Contents lists available at ScienceDirect
Optics Communications j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / o p t c o m
Analysis and simulation of single-frequency Raman fiber amplifiers Jinyong Leng ⁎, Shengping Chen ⁎, Wuming Wu, Jing Hou, Xiaojun Xu College of Optoelectronic Science and Engineering, National University of Defense Technology, Changsha, Hunan, 410073, China
a r t i c l e
i n f o
Article history: Received 22 November 2010 Received in revised form 31 January 2011 Accepted 31 January 2011 Available online 12 February 2011
a b s t r a c t High power operation of single-frequency Raman fiber amplifiers is usually limited by the onset of stimulated Brillouin scattering. A theoretical investigation on single-frequency Raman fiber amplifier limited by stimulated Brillouin scattering is presented in this paper, based on the intensity equations combining stimulated Brillouin scattering and stimulated Raman scattering. A combination of methods is proposed to increase the output power of single-frequency Raman fiber amplifier. These methods include applying a suitable pump scheme according to the fiber length and seed signal power, using short gain fibers, utilizing a multiple-stage scheme and providing suppression of stimulated Brillouin scattering. © 2011 Elsevier B.V. All rights reserved.
1. Introduction
2. Theoretical model
Raman fiber amplifiers (RFAs) are known as stable high-power fiber light sources providing almost any wavelength in the near-IR range due to the broad gain spectrum and wavelength versatility of stimulated Raman scattering (SRS) [1]. Therefore, RFAs are very attractive for a variety of applications, especially in the fields of telecommunications [2] and supercontinuum generation [3]. However, RFAs are seldom utilized to generate high power single frequency output. Because hundred meters of fibers should be used to provide enough Raman gain in these sources which makes stimulated Brillouin scattering (SBS) easy to be initiated. The SBS effect limits the achievable powers of single frequency Raman fiber amplifiers (SF-RFAs) to a very low level. Nevertheless, researches on SF-RFAs remain continuously active [4–7], due to its attractive application potentials in aspects that need specific lasing wavelengths which cannot be easily achieved with conventional doped fiber amplifiers. Although efforts have been made to enhance the output power of SF-RFAs, the achievements rarely reach the practical requirements [6,7]. To date, most researches on single frequency RFAs focus on the experimental investigations. On the other hand, theoretical part has, to the best of our knowledge, not yet been elaborately investigated. The purpose of this paper is to provide a theoretical investigation on SF-RFAs, so as to find the ways of enhancing the output powers of SF-RFAs. A theoretical model is proposed in the paper, based on the intensity equations combining SBS and SRS. The impacts of pump scheme, fiber length, seed power level, and SBS suppression on the performance of SF-RFAs are discussed.
A typical RFA is illustrated in Fig. 1. The configuration is almost the same as a conventional fiber amplifier except that the gain is provided by SRS instead of stimulated rare earth ions. An 1178 nm source is selected as an example, due to its attractive potential ability to be frequency doubled to 589 nm for laser guide star in astronomical adaptive optics systems. The 1178 nm single frequency seed is amplified forward by SRS effect along the single mode fiber pumped at 1120 nm. The 1178 nm signal increases along the gain fiber and initiates backward SBS at a certain power level. SBS is easy to be initiated in this amplifier because of the narrow signal linewidth and the long gain fiber. An SBS frequency shift is usually at the order of ten gigahertz (less than 0.1 nm). So, the backward SBS exhibits a wavelength around 1178 nm, near the signal wavelength, which locates at the peak wavelength of the Raman gain profile with 1120 nm pump. Because the Raman gain is bidirectional effective along the fiber, the backward SBS will also be amplified by SRS effect. The backward amplified SBS will then compete with the signal, causing an unwanted amplifier power limitation. The intensity equations of SRS and SBS can be described as [8]:
⁎ Corresponding authors. E-mail addresses: [email protected] (J. Leng), [email protected] (S. Chen). 0030-4018/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2011.01.089
8 dISR > > < dz = gR IP ISR − αSR ISR υ > dI > : P = − p gR IP ISR −αP IP dz υSR 8 dISB > > = −gB IP ISB + αSB ISB < dz > > : dIP = −g I I −α I B P SB P P dz
ð1Þ
ð2Þ
where ISR and ISB are the intensity of Raman wave and Brillouin wave. IP is the pump intensity. gR and gB are the gain coefficients of Raman
2998
J. Leng et al. / Optics Communications 284 (2011) 2997–3003
Fig. 1. Schematic diagram of a Raman fiber amplifier.
scattering and Brillouin scattering. υP and υSR are the frequencies of pump and Raman wave. αP, αSR and αSB are the intrinsic background losses in the fiber for pump, Raman and Brillouin wave. z is the location along the fiber. Considering the described physical processes in Fig. 1, the intensity equations describing the SF-RFAs with SBS can be written as: υp υp dIþ þ þ þ − þ P =− g I I − g I I −αP IP dz υSR R P SR υSB R P SB
ð3aÞ
υp υp dI− − þ − − − P = g I I + g I I + αP IP dz υSR R P SR υSB R P SB
ð3bÞ
dIþ þ þ − þ SR = gR IP ISR −gB ISR ISB −αSR ISR dz −
dISB − þ − − = −gR IP ISB −gB ISR ISB + αSB ISB dz
ð3cÞ
ð3dÞ
where the superscript “+” stands for forward propagated waves and “−” stands for backward propagated waves in Eq. (3). The subscript “P”, “SR” and “SB” represent the 1120 nm pump light, the 1178 nm Raman signal light and the Brillouin scattering light near 1178 nm, − respectively. IP stands for I+ P + IP . υSB is the frequency of the Brillouin wave. Eq. (3a) and (3b) describe the power evolution of the 1120 nm pump light. The first two items at the right side of the equations correspond to the Raman consumption of the 1178 nm Raman signal light and the Brillouin scattering light near 1178 nm. Eq. (3c) describes the power variation of the 1178 nm Raman signal light. It is not only a signal light of the Raman scattering process, but also a pump light of the Brillouin scattering process. The three items at the right side of the equation correspond to the Raman gain, the Brillouin consumption and the intrinsic loss, respectively. Eq. (3d) describes the power evolvement of the Brillouin scattering light. It is a signal light of both the Raman and the Brillouin process. The three items at the right side of the equation correspond to the Raman gain, the Brillouin gain and the intrinsic loss, respectively. There are three assumptions in Eq. (3). The first one is that the difference between the Raman gain coefficients of υSR and υSB is negligible. That's well-founded because the wavelength shift of Brillouin wave is less than 0.1 nm away from the 1178 nm signal wavelength. The second one is that the Raman gain coefficients of both directions are the same [8]. The last one is that the spontaneous Raman noises of both directions are negligible. That is an evident conclusion for the forward direction because the seed of the spontaneous Raman scattering is negligible compared with the input seed. For the backward direction, spontaneous Raman scatterings only transfer a small fraction of 1120 nm pump to Raman scattering light. In another word, the pump power changes a little due to spontaneous Raman scattering. So the influence of spontaneous Raman scattering could be
neglected. The last assumption will be confirmed by simulation in the next section. Substituting power for intensity and considering the Brillouin gain spectrum, Eq. (3) should be changed as follow: þ
−
PSBi þ υp gR Pþ υp gR PP ∑ dPþ þ P P PSR i =− − −αP PP dz υSR A eff υSB A eff −
−
PSBi þ υp gR P− υp gR PP ∑ dP− − P P PSR i = + + αP PP dz υSR A eff υSB Aeff dPþ g P Pþ SR = R P SR − dz A eff
− Pþ SR ∑ gBi PSBi i
A eff
ð4aÞ
þ
−αSR PSR
ð4bÞ
ð4cÞ
dP− g P P− g Pþ P− − SBi = − R P SBi − Bi SR SBi + αSB PSBi dz A eff A eff
ð4dÞ
where Aeff is the effective area of the fiber core. The differences of frequencies, Raman gain coefficients and background losses of these discrete Brillouin waves are neglected in Eq. (4). SBS gain can be described by the following Lorentzian shaped profile with peak gain g0 and bandwidth ΩSBS [8]. 2
gB ðυi Þ = g0
ΩSBS 4ðυi −υ0 Þ2 + ΩSBS2
ð5Þ
where υ0 is the Brillouin frequency shift from the seed signal λSR, which is defined by υ0 = 2nνa /λSR with n the optical refractive index and νa the acoustic velocity. The boundary conditions of Eq. (4) are shown in Fig. 1. The initial powers for the discrete Brillouin waves initiated from noise, which could be thermally activated phonons, ASE, signal noise or back scattered light, could be written as PN = hυ0ΔυSB within the discrete linewidth [9,10]. The differential equations are two point boundary value problems which are solved by the modified relaxation method in this paper [11]. The fibers used in the model are single mode polarization maintaining silica fibers. The bandwidth of the 1178 nm seed signal is far below the Brillouin scattering bandwidth ΩSBS. Parameters used in the model are given in Table 1. Table 1 Parameters used in the model. λP = 1120 nm gR = 7 × 10−14 m/W αP = 0.003 m−1 ΩSBS = 58 MHz n = 1.45
λSR = 1178 nm g0 = 2.4 × 10−11 m/W αSR = αSB = 0.005 m−1 Aeff = 2.83 × 10−11 m2 νa = 5.96 km/s
J. Leng et al. / Optics Communications 284 (2011) 2997–3003
2999
3. Modeling results
3.1. Pump scheme
Based on the above theoretical model, the impacts of pump scheme, fiber length, seed power, and SBS suppression on the performance of the SF-RFAs are discussed in this section. Firstly, we confirm the third assumption in Eq. (3) that the influence of backward spontaneous Raman noise could be neglected. As an example, Fig. 2 illustrates the 1120 nm pump, 1178 nm signal and SBS power distributions along the 100 m fiber. A backward pump scheme is adopted. The signal power and pump power are set at 10 mW and 25 W, respectively. It can be seen from Fig. 2(a) that the signal grows slowly at the input port and increases rapidly at the output port. As a comparison, the powers of the backward scattered light amplified by SRS or SBS respectively are illustrated in Fig. 2(b). We can see that the growth process of the backward scattered power, starting from noise at the output port and propagating backward, can be divided into two parts. In the first part, while the 1178 nm signal power is high enough, SBS is in the majority. In the second part, while the signal power is too low to excite SBS, SRS is in the majority. In other words, the contribution of the backward scattered power growth could be divided into two parts. Compared with SBS, the power growth due to SRS is much lower which suggests that the backward spontaneous Raman noise is negligible.
Usually, bidirectional pump scheme is not used in SF-RFAs, because the large remnant pump light is dangerous for the pump resource on the opposite direction. So, only forward and backward pump schemes are considered here. The relationships between the output power and the pump power under different pump schemes with various fiber lengths and seed signal powers are illustrated in Fig. 3. It should be noted that there is a critical value for the pump power of the SF-RFA. Once the pump power exceeds the critical value, the Brillouin scattering light will deplete the signal light rapidly [12]. So the descending process of the output power cannot be depicted in Fig. 3. This corresponds to the situation that the second item on the right side of Eq. (4c) is higher than the first item. As a result, no amplified 1178 nm signal will be exported. The whole system actually becomes unstable under this condition. Time dependent items should be added into the model to describe the behavior of the RFA at this time, which might be considered in the future. The curves in Fig. 3 and succeeding figures are illustrated under the critical pump value. The y-axis values of the end points on the curves correspond to the maximum available output power. From Fig. 3 we can see that for the SF-RFA with a long fiber, maximal output power of the backward pumped amplifier is higher than that of the forward pumped one, such as 150 m and 100 m in Fig. 3(a) and
Fig. 2. (a) Pump, signal and (b) SBS power distribution inside the fiber.
Fig. 3. Output power as a function of pump power with different pump schemes. (a) seed power = 10 mW; (b) seed power = 50 mW.
3000
J. Leng et al. / Optics Communications 284 (2011) 2997–3003
100 m and 50 m in Fig. 3(b). As an illustration, Fig. 4(a) shows the differences between signal and SBS power distributions inside the 150 m fibers under different pump schemes with the same output power, in which the seed signal powers are 10 mW. From Fig. 4(a) we can see that the SBS power of the forward pumped RFA is much higher than that of the backward pumped RFA with the same output power, which means that the performance of SF-RFA with a forward pump scheme is easier to be limited by SBS. At the same time, for the SF-RFA with a short fiber in Fig. 3, maximal output power of the forward pumped amplifier is higher than that of the backward pumped one, such as 30 m in Fig. 3(a) and 15 m in Fig. 3(b). We attribute this to the difference of the SBS power evolution trendline under different pump schemes. From Fig. 3(a), we can see that the backward pumped RFA is limited by the onset of SBS at about 5.7 W output power and however the forward pumped RFA is not at this power level. It can be explained that although the SBS power of the forward pumped RFA is higher than that of the backward pumped RFA with the same output power, the difference between them is comparatively small, as shown in Fig. 4(b), in which the fiber lengths are 30 m and the seed powers are also 10 mW. At the same time, the pump power at the seed input port (z = 0) of the forward pumped RFA is also higher than that of backward pumped RFA and the differences between them are comparatively big. So the higher pump power at z = 0 insure the Raman gain is stronger than the Brillouin
Fig. 5. Output power and SBS power as a function of pump power with different fiber lengths.
consumption for the forward pump scheme, leading to the continuative increase of 1178 nm signal power. Unfortunately, the lower pump power at z = 0 fails to do that for the backward pump scheme. So the output power has reached its maximum. Suitable pump scheme should be chosen to get a higher output power, according to the fiber length. It should be emphasized that the output power of the forward pumped RFA is always higher than that of the backward pumped one at the same pump power, no matter how long the fiber is. So, when the needed output power can be obtained with both pump schemes, the forward pump scheme should be adopted to get higher efficiency. 3.2. Fiber length Fiber length is an important factor affecting the thresholds of SRS and SBS. Due to the low Raman gain coefficient, hundred meters of fibers should be used in SF-RFAs to amplify 1178 nm signal. On the other hand, SBS power grows rapidly while increasing the fiber length. Fig. 5 illustrates the 1178 nm signal and SBS power as a function of pump power with different fiber lengths. Fig. 6 shows the conversion efficiencies of the RFA with various fiber lengths. The seed
Fig. 4. Signal and SBS power distributions inside the fiber under different pump schemes. (a) Fiber lengths = 150 m; (b) fiber lengths = 30 m.
Fig. 6. Efficiency as a function of output power with different fiber lengths.
J. Leng et al. / Optics Communications 284 (2011) 2997–3003
signal powers are all 10 mW. Backward pump scheme is adopted in the two figures. It can be seen from the two figures that a shorter fiber length corresponds to a higher pump power threshold and a higher maximal output power, however with a relatively lower efficiency. A longer fiber length corresponds to a higher efficiency, however with a lower SBS limited output power. In other words, long fibers are not suitable for high power output. Short fiber length should be a good choice to build up high power RFA, although its efficiency is not high. However, it should be emphasized that in the condition of getting enough output power, the fiber length should be chosen as long as possible to get higher efficiency. Fig. 7 shows the maximal available output power and efficiency of the SF-RFAs as a function of fiber length. Different pump schemes and seed signal powers have been considered. Fig. 7(a) and (b) are illustrated with the seed signal power of 10 mW and 50 mW, respectively. In both figures, the forward pumped amplifier is more efficient than the backward pumped one with short fiber lengths. While with long fiber lengths, the backward pumped one is more efficient. Fig. 7(c) shows the maximal output power as a function of fiber length by combining the two curves shown in Fig. 7(a) and (b), despite of the pump scheme. It can be seen that the amplifier with higher seed signal power is easier to be power limited by SBS, so the maximal output power is relatively lower as compared with the low signal power seeded one when using the same fiber length. However, the efficiency of the high power seeded one is higher, as shown in
3001
Fig. 7(d). That is to say, the high power seeded RFA exhibits high efficiency, while the low power seeded one exhibits high available output power. It should be noted that the efficiencies in Fig. 7(d) are all got at the maximal output power, which correspond to the end points of the curves in Fig. 6. Therefore, in order to set up a high-power SF-RFA, one should firstly clarify the needed output power. According to the needed output power, the scope of fiber length is decided from Fig. 7(c). Then, proper pump scheme can be selected according to the fiber length. 3.3. Multi-stages amplifiers The influences of seed signal power on the performance of SF-RFAs have been mentioned above. The seed signal power of 1178 nm from a commercial DFB is usually at the level of about 10 mW. The 10 mW seed can be amplified directly to tens of watt or only to several watt and then to tens of watt. Fig. 8 shows the output power versus pump power with seed power of 10 mW and 1 W. The fiber lengths are 20 m and 9.5 m, respectively. The fiber lengths are chosen to get 10 W maximal output power. Pump scheme is chosen according to get the higher output power. So forward pump scheme is used with seed power of 10 mW. Backward pump scheme is used with seed power of 1 W. It can be seen from Fig. 8 that the pump powers needed for 10 W output power are about 150 W and 110 W, respectively for 10 m W
Fig. 7. The maximal available output power and efficiency as functions of fiber lengths.
3002
J. Leng et al. / Optics Communications 284 (2011) 2997–3003
a two-stages RFA to amplify 10 mW seed signal to 10 W output, giving a total conversion efficiency of 7.9%. This two-stage RFA is obviously more efficient than the one-stage RFA. The latter exhibits a conversion efficiency of 6.7% (10 W/150 W). It should be emphasized that the losses between the two amplifiers of two-stage SF-RFA are ignored in our discussion. Another problem emerges on how large should the middle power be. Fig. 9 shows the total efficiency of a two-stage amplifier as a function of the middle power with various total output powers. Fig. 9(b) is a close-up illustration of Fig. 9(a). The total efficiency has a maximum value corresponding to a certain middle power. We call this certain middle power the optimal middle power. This optimal middle power and the total efficiency both grow with the total output powers. So the middle power should be optimized according to the total output power, to get a maximal total efficiency. It should be emphasized that the above results are obtained without considering any SBS suppression. In the next section, we will show that the performance of RFA can be enhanced greatly with only simple SBS suppression. Fig. 8. Output power versus pump power with various seed powers.
3.4. SBS suppression and 1 W seed power. According to Fig. 3(a), the needed pump power in an amplifier with 150 m fiber length to amplify 10 mW seed to 1 W is about 17 W. That is to say, a total pump power of 127 W is needed in
From the simulation results above, we can draw the conclusion that the achievable powers of single-frequency Raman fiber amplifiers are usually limited by SBS. So the SBS suppression is the key factor for high-power single-frequency RFA. There has been much investigation on SBS suppression in single-frequency Yb-doped fiber amplifiers. Among those suppression methods, the temperature and strain gradients along the fibers can broaden the effective SBS linewidth and thereby reduce the effective gain which has been demonstrated to be a good approach to mitigate SBS [10,13]. This technique can be used in SF-RFA, in which the peak SBS gain g0 is inversely proportional to the SBS gain linewidth. If some special temperature and strain gradients are utilized to broaden the effective SBS linewidth in SF-RFA and thereby reduce the effective SBS peak gain, the performance of SF-RFAs will be improved. The results illustrated in Fig. 10 are gained by reducing g0 to g0/8. We can see that the maximal output powers are increased by a factor of ~3 compared to the RFA without any SBS suppression. 4. Conclusion In this paper, we present our theoretical investigation on SF-RFAs, based on the intensity equations combining SBS and SRS. The impacts of
Fig. 9. Total efficiency versus middle power with various total output powers.
Fig. 10. Improve the performance of RFA by SBS suppressing.
J. Leng et al. / Optics Communications 284 (2011) 2997–3003
pump scheme, fiber length, seed power, and SBS suppression on the performance of RFA are discussed. According to preferred embodiments, a combination of methods is used to increase the output power of SF-RFAs. These methods include: a suitable pump scheme should be provided according to the fiber length and seed signal power; a short fiber should be used in company with high pump power to get high output power; a multi-stage scheme should be adopted according to the laboratorial conditions to export high signal power with low pump power comparatively easily; and some measures should be used to reduce the effective peak SBS gain to improve the performance of RFA sharply. Acknowledgement This work was supported by the Projects of the National Natural Science Foundation of China under Grant no 10904173 and the China Postdoctoral Science Foundation. References [1] E.M. Dianov, I.A. Bufetov, M.M. Bubnov, et al., Opt. Lett. 25 (2000) 402. [2] N.S. Kim, M. Prabhu, C. Li, et al., Opt. Commun. 176 (2000) 219.
3003
[3] H. Masuda, K.-I. Suzuki, S. Kawai, et al., Electron. Lett 33 (1997) 753. [4] P. Dupriez, C. Farrell, M. Ibsen, J.K. Sahu, J. Kim, et al., Proc. SPIE 6102 (2006) 61021G. [5] L. Taylor, Y. Feng, D.B. Calia, Opt. Express 17 (2009) 14687. [6] Yan Feng, Luke R. Taylor, Domenico Bonaccini Calia et al. “39 W narrow linewidth Raman fiber amplifier with frequency doubling to 26.5 W at 589 nm”, in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2009), paper PDPA4. [7] Feng Yan, Luke R. Taylor, Domenico Bonaccini Calia, Opt. Express 17 (2009) 23678. [8] Govind P. Agrawal, Nonlinear Fiber Optics, 4th ed., Elsevier Pte Ltd, Singapore, 2009. [9] A. Liu, Opt. Express 17 (2009) 15201. [10] M. Hildebrandt, S. Büsche, P. Weßels, et al., Opt. Express 16 (2008) 15970. [11] A. Liu, Proc. SPIE. 6102 (2006) 61021R. [12] Feng Yan, Luke R. Taylor, Domenico Bonaccini Calia, Opt. Express 17 (2009) 19021. [13] J.E. Rothenberg, P.A. Thielen, M. Wickham, et al., Proc. SPIE. 6873 (2008) 687300.