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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 25 — Dec. 5, 2011
  • pp: 25741–25748
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Analytical analysis of second-order Stokes wave in Brillouin ring fiber laser

H. A. Al-Asadi, M. H. Abu Bakar, M. H. Al-Mansoori, F. R. Mahamd Adikan, and M. A. Mahdi  »View Author Affiliations


Optics Express, Vol. 19, Issue 25, pp. 25741-25748 (2011)
http://dx.doi.org/10.1364/OE.19.025741


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Abstract

This paper details a theoretical modeling of Brillouin ring fiber laser which incorporates the interaction between multiple Brillouin Stokes signals. The ring cavity was pumped at several Brillouin pump (BP) powers and the output was measured through an optical coupler with various coupling ratios. The first-order Brillouin Stokes signal was saturated with the presence of the second-order Stokes signal in the cavity as a result of energy transfer between them. The outcome of the study found that the optimum point for the first-order Stokes wave performance is at laser power reduction of 10%. Resultantly, at the optimum output coupling ratio of 90%, the BFL was able to produce 19.2 mW output power at BP power and Brillouin threshold power of 60 and 21.3 mW respectively. The findings also exhibited the feasibility of the theoretical models application to ring-type Brillouin fiber laser of various design parameters.

© 2011 OSA

1. Introduction

Besides the generation of multiwavelength lasers, BFL can be used for single-wavelength lasers as well. There are some processes that depend solely on first-order Brillouin Stokes wave such as incoherent beam combining [9

9. T. H. Russell, W. B. Roh, and J. R. Marciante, “Incoherent beam combining using stimulated Brillouin scattering in multimode fibers,” Opt. Express 8(4), 246–254 (2001). [CrossRef] [PubMed]

] and beam cleanup [10

10. B. C. Rodgers, T. H. Russell, and W. B. Roh, “Laser beam combining and cleanup by stimulated Brillouin scattering in a multimode optical fiber,” Opt. Lett. 24(16), 1124–1126 (1999). [CrossRef] [PubMed]

]. Nevertheless, while the multiwavelength BFL revels in the generation of higher order Stokes, the production of single-wavelength BFL is hampered by this natural phenomenon as the energy from the first-order Stokes wave would be reduced and transferred to the second-order Stokes wave. As a result, single-wavelength BFL devices normally operate below their maximum capabilities in order not to exceed the threshold of the second-order Stokes signal.

Studies have been performed to study the threshold features of the second-order Stokes wave in several devices. While Russell and Roh concluded that second-order SBS was not a limiting factor in beam combiner [11

11. T. H. Russell and W. B. Roh, “Threshold of the second Stokes scattering in a fiber stimulated Brillouin scattering beam combiner,” in Conference Proceedings - Lasers and Electro-Optics Society Annual Meeting-LEOS (2001), 665–666.

], considerable power reduction was reported in the first-order Stokes signal due to the presence of higher order SBS component in distributed Raman amplifiers [12

12. K. D. Park, H. Ryu, W. K. Lee, S. K. Kim, H. S. Moon, and H. S. Suh, “Threshold features of a Brillouin Stokes comb generated in a distributed fiber Raman amplifier,” Opt. Lett. 28(15), 1311–1313 (2003). [CrossRef] [PubMed]

] and long distance all-Raman transmission system [13

13. D. Zhang, X. Zhang, X. Li, A. Xu, Z. Wang, F. Zhang, and Z. Chen, “Stimulated Brillouin scattering and Rayleigh cooperative process in 300 Km optical transmission,” Microw. Opt. Technol. Lett. 49(12), 2939–2941 (2007). [CrossRef]

]. No study however, has ever been conducted to estimate the optimum point to achieve maximum first-order Brillouin Stokes wave performance with the presence of second-order Stokes signal.

In this paper, we present an analytical model for the analysis of second-order Stokes wave of a continuous wave operation of a ring-cavity BFL. Using the analytical approach for the model allows the study of the ring laser behavior with the presence of the second-order Stokes wave, for the first time, to the best of our knowledge. A theoretical model was used to predict the best parameters to achieve optimum laser performance. Investigation was done on the effect of second-order Stokes wave for the performance of BFL at various output coupling ratios.

2. Modeling of ring cavity BFL

The schematic diagram of BFL considered for the analytical simulation and used for experimental verification is depicted in Fig. 1
Fig. 1 Schematic diagram for BFL. BS1 and BS2 denote the first- and second-order Stokes waves correspondingly.
. The configuration comprised of an external narrow-linewidth tunable laser source (TLS), an erbium-doped fiber amplifier (EDFA), a section of dispersion compensating fiber (DCF), an optical circulator and a tunable coupler. The EDFA gain block consisted of an erbium-doped fiber (EDF) of 8 meters long and wavelength division multiplexing (WDM) coupler. The EDF was pumped by a 1480 nm laser diode for the amplification of seed signal from TLS to be used as the Brillouin pump (BP) signal prior to entering the ring cavity.

This amplified narrow linewidth BP was injected into the DCF through port 1 to port 2 of the optical circulator. The optical circulator was also used to force unidirectional operation of the laser in the cavity. When the power of BP signal overcomes the threshold condition in DCF, a Stokes signal occurs at a lower frequency of approximately 11 GHz downshifted from the BP. The small DCF core induced higher nonlinearity effects that lowered the SBS threshold and allowed the generation of higher-order Stokes at lower BP power. This first-order Stokes signal then propagated inside the ring cavity through port 2 to port 3 of the optical circulator to form a laser. The circulating signal was taken out at the x% leg of the tunable coupler. This output coupling ratio (x) was varied from 10 to 95% to analyze the laser performance at different circulating power in the cavity.

In general thumb rule of laser, by further increasing the BP power, the amount of Stokes laser power was also increased. Under this circumstance, the first-order Stokes wave shown in Fig. 1 that propagated in the clockwise direction could also generate a second-order Stokes signal when its SBS threshold was met. This new signal propagated in the opposite direction of the first-order Stokes wave (anti clockwise direction). Subsequently, the energy of the initial Stokes wave was transferred to the new Stokes signal at the expense of the first-order Stokes signal performance degradation. This transition phase is our main research objective because the linear response of laser (in case of first-order Stokes wave) is no longer obeyed. The impact of the second-order Stokes wave presence is taken into our theoretical model to determine the performance characteristics of the first-order Stokes wave. In our experiment, the use of circulator limited the setup to a unidirectional operation, thus the second-order Stokes wave could not circulate and initiate its lasing process. Additionally, the unidirectional operation prohibited the second-order Stokes signal from being detected at the output; therefore, the Rayleigh backscattering component of the Stokes signal was observed instead in order to assess its evolution in the cavity.

Steady state differential equations including the effect of SBS in ring cavity BFL, can be represented by three waves mixing and absorptions on the coupling between the wave powers of BP, first-order Stokes signal, BS1 and second-order Stokes signal, BS2 as given by [14

14. N. F. P. Zel'dovich and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985).

];
PBP(z)z=(gB(v)AeffPBS1(z)(α12αspαcαfk))PBP(z),
(1a)
PBS1(z)z=(gB(v)AeffPBP(z)(α23αspαcαf(1k)))aPBS1(z),
(1b)
PBS2(z)z=(gB(v)AeffPBS1(z)(α12αspαcαfk))PBS2(z),
(1c)
where, α12 and α23 represent the loss factors of the optical circulator between ports 1 and 2, and ports 2 and 3, respectively. We introduced αc and αf as the coupler loss and total loss of DCF, respectively. αsp is the coefficient of the loss intensity due to a splice in a ring cavity and k is the output coupling coefficient. Aeffis the effective cross section area and gBis the Brillouin gain coefficient.

The wave power at the output coupler ports are interrelated as
Pout(z)=k(1γ)PBS1(z),
(2)
where γ is the intensity loss coupler coefficient.

Since the depletion of the backward propagating Stokes wave was ignored, the full analytical solutions to Eqs. (1a), (1b) and (1c) are given by,
PBP(z)=PBP(0)exp(α12αspαcαfkz),
(3a)
PBS1(z)=PBS1(L)exp(1α12αspαcαfkAeff(PBP(0)gB(eα12αspαcαfkzeα12αspαcαfkL)α12α23αsp2αc2αf2k(k1)Aeff(Lz))),
(3b)
PBS2(z)=PBS2(0)exp(12α122αsp2αc2αf2k2Aeff2(2gB2PBS1(L)PBP(0)(eα12αspαcαfkzα12αspαcαfkzeα12αspαcαfkL)2gBPBS1(L)(gBPBP(0)+Aeffα122αsp2αc2αf2k2z(α23αspαcαf(k1)(Lz2))1)2α123αsp3αc3αf3k3Aeff2z)),
(3c)
where, PBP(0), PBS1(L) and PBS2(0) represent the BP power coupled in the ring cavity through ports 1 and 2 of optical circulator, the initial values of first-order Stokes wave at z=Land the second-order Stokes wave at z=0of optical fiber ring cavity, correspondingly.

Substituting Eqs. (3a) and (3b) in Eq. (2), we arrive at the solution for the output wave power as a function of fiber length in ring cavity BFL in the form,

Pout(z)=k(1γ)PBS1(L)exp(1α12αspαcαfkAeff(PBP(0)gB(eα12αspαcαfkzeα12αspαcαfkL)α12α23αsp2αc2αf2k(k1)Aeff(Lz))),
(4)

3. Ring cavity BFL simulation results

The BFL analytical model requires input data that can be obtained through experimental configuration [15

15. N. A. M. A. Hambali, M. A. Mahdi, M. H. Al-Mansoori, M. I. Saripan, A. F. Abas, and M. Ajiya, “Effect of output coupling ratio on the performance of ring-cavity Brillouin fiber laser,” Laser Phys. 20(7), 1618–1624 (2010). [CrossRef]

]. The BFL setup characteristics are listed in Table 1

Table 1. Parameters used in the simulation work.

table-icon
View This Table
. The loss coefficient and effective area, together with other fiber parameters, the pump powers and the ratio of the optical coupler, represent the input data for the simulation results. The modeled BFL have the loss factors of optical circulator between ports 1 and 2 and ports 2 and 3, α12 =0.8 dB and α23 =0.7 dB, respectively and αsp =0.3 dB. The schematic of the ring cavity BFL considered for simulation results and used for experimental verification is depicted in Fig. 1.

Simulation results were compared to the experiment data obtained during the steady state for verification of our analytical model. The ring cavity was pumped at several BP power from 0 mW up to the maximum EDFA output of 24 mW with variations to the output coupling ratio.

Figure 2
Fig. 2 Theoretical (solid) and experimental (dash) results Brillouin output power of ring cavity BFL for various coupling ratio of optical coupler.
depicts the comparison between the theoretical results to the experimental output, which validates the analytical models used in this study. At 10% output coupling ratio, less than 2 mW of Stokes signal power was observed since 90% of the output power continued to propagate inside the cavity. Lasing can only occur when the cavity gain from SBS effect is equal to the cavity loss at the threshold condition. The lower output coupling ratio resulted in lower cavity loss and in turn reduced the BP power required to reach the threshold condition. Consequently, the Brillouin threshold for this output coupling ratio can be reached at low BP power of 0.9 mW. By increasing the output coupling ratio from 10% to 95%, the amount of cavity loss can also be elevated and at the highest output coupling ratio of 95%, the Brillouin threshold was higher as well, measuring at 2.6 mW. However, the highest Stokes signal power of 7.3 mW was not attained from the highest output coupling ratio but instead from the 90% output coupling ratio at BP power of 24 mW.

Figure 3
Fig. 3 Theoretical and experimental data on optimum Brillouin output power of ring cavity BFL for various coupling ratios of optical coupler.
illustrates the BFL optimum output Stokes power as a function of coupling ratio with 11 km long DCF. Also, it shows that as the coupling ratio was increased from 10% to 95%, the optimum Brillouin output power of BFL also rose until 90% reached 7.2 mW. When the coupling ratio is 95%, the optimum Brillouin output power decreased to 7.1 mW. This was due to the gain saturation which led to less available gain for amplification of the first-order Stokes wave and thus as a result, lower output powers were detected. The simulation results of our BFL analytical model show good comparison to the experimental data. Experimental observations at the output showed no Rayleigh backscattering component of BS2 present at BP less than 25 mW thus the effect of higher orders Stokes wave was assumed to be of minimal significance to the overall output of the laser. In the following paragraphs, this effect was considered to further evaluate the performance of single wavelength BFL.

After increasing the BP power, the backward propagating first-order Stokes wave reached the threshold for second-order Stokes wave generation in forward direction. Figure 4
Fig. 4 Theoretical power distribution of the first- and second-order Stokes waves as a function of Brillouin pump power of ring cavity BFL at 50% coupling ratio.
demonstrates the theoretical power distribution of the first- and second-order Stokes waves as a function of BP power. As the validity of the analytical models was already proven by Fig. 2 and Fig. 3, the models were then applied for theoretical BP power higher than 24 mW. Higher order Stokes waves can be expected from BFL if the BP power pushed further than 100 mW. Our model can be used to predict the performance of BFL with the presence of second-order Stokes wave. At the lower BP power, the first-order Stokes wave increased linearly. The first-order Stokes laser output power reached 6.3 mW before the second-order Stokes wave was generated at the output coupling ratio of 50%. After reaching the threshold of the second-order Stokes wave, the first-order Stokes laser power started to decrease as represented by the red line in Fig. 4. In this simulation, the output power was saturated at 17.1 mW. The critical pump power in which the BS signal power started to saturate was measured around 83 mW pump power for 50% output coupling ratio. This saturation characteristic is the evidence of energy transfer from the first-order Stokes signal to the second-order Stokes signal, which propagated in the same direction of BP power. Moreover, this phenomenon was due to the decreasing round trip gain in ring cavity as the BP power level was increased thus resulting in gain saturation. Since the use of circulator blocked the second-order Stokes wave from travelling on a complete round-trip, it did not resonate as a laser mode and the BFL was locked to first-order Stokes wave.

The amount of output power taken from the BFL system was dictated by the coupling ratio of the optical coupler used. Various coupling ratios have been used in our analytical modeling which yielded different output power. The coupling ratio dictated the tradeoff between the intra-cavity power and the output power. The optimum operating conditions of BFL for different output coupling ratios are shown in Fig. 5(a)
Fig. 5 Theoretical output power distribution of the BFL for various output coupling ratios; (a) threshold of second-order Stokes wave with the optimum BP power and (b) optimum and saturated output powers.
and 5(b).

4. Conclusion

Theoretical models of Brillouin fiber laser in a ring cavity were developed in this study. Analytic solutions of steady state differential equations of the optical waves interaction including the effect of SBS in ring cavity BFL have been provided. Additionally, the comparison between the modeling results with experimental results was made and good agreement between those results was found. This validated the feasibility of the analytical models application to ring-type BFL with different design parameters. The maximum power of 7.3 mW for the output power was obtained at BP power of 24 mW and 90% coupling ratio and 11 km DCF optical fiber length. By further increasing the BP slightly up to 100 mW, the amount of Stokes signal power can be increased. However, the generation of the second-order Stokes wave must be considered in our developed model. Our findings showed that at the optimum coupling ratio of 90%, the second-order SBS threshold power, the optimum BP and output powers are 21.3, 60 and 19.2 mW, respectively. Based on these findings, an optimum operating condition was determined to ensure that the output power is still high and its energy transfer to second-order Stokes signal is kept low.

Acknowledgments

This work was partly supported by the Ministry of Higher Education, Malaysia and the Universiti Putra Malaysia under research grant # 05-01-10-0901RU and Graduate Research Fellowship.

References and links

1.

M. F. Ferreira, J. F. Rocha, and J. L. Pinto, “Analysis of the gain and noise characteristics of fiber Brillouin amplifiers,” Opt. Quantum Electron. 26(1), 35–44 (1994). [CrossRef]

2.

S. P. Smith, F. Zarinetchi, and S. Ezekiel, “Narrow-linewidth stimulated Brillouin fiber laser and applications,” Opt. Lett. 16(6), 393–395 (1991). [CrossRef] [PubMed]

3.

K. Schneider and S. Schiller, “Narrow-linewidth, pump-enhanced singly-resonant parametric oscillator pumped at 532 nm,” Appl. Phys. (Berl.) 65(6), 775–777 (1997). [CrossRef]

4.

J. Geng, S. Staines, Z. Wang, J. Zong, M. Blake, and S. Jiang, “Highly stable low-noise Brillouin fiber laser with ultranarrow spectral linewidth,” IEEE Photon. Technol. Lett. 18(17), 1813–1815 (2006). [CrossRef]

5.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2007).

6.

T. A. Haddud, M. H. Al-Mansoori, A. K. Zamzuri, S. Shaharudin, M. K. Abdullah, and M. A. Mahdi, “24-Line of Brillouin-erbium fiber laser utilizing a Fabry-Perot cavity in L-band,” Microw. Opt. Technol. Lett. 45(2), 165–167 (2005). [CrossRef]

7.

M. H. Al-Mansoori, M. A. Mahdi, and M. Premaratne, “Novel multiwavelength L-band Brillouin-Erbium fiber laser utilizing double-pass Brillouin pump preamplified technique,” IEEE J. Sel. Top. Quantum Electron. 15(2), 415–421 (2009). [CrossRef]

8.

M. H. Al-Mansoori and M. A. Mahdi, “Multiwavelength L-band Brillouin-erbium comb fiber laser utilizing nonlinear amplifying loop mirror,” J. Lightwave Technol. 27(22), 5038–5044 (2009). [CrossRef]

9.

T. H. Russell, W. B. Roh, and J. R. Marciante, “Incoherent beam combining using stimulated Brillouin scattering in multimode fibers,” Opt. Express 8(4), 246–254 (2001). [CrossRef] [PubMed]

10.

B. C. Rodgers, T. H. Russell, and W. B. Roh, “Laser beam combining and cleanup by stimulated Brillouin scattering in a multimode optical fiber,” Opt. Lett. 24(16), 1124–1126 (1999). [CrossRef] [PubMed]

11.

T. H. Russell and W. B. Roh, “Threshold of the second Stokes scattering in a fiber stimulated Brillouin scattering beam combiner,” in Conference Proceedings - Lasers and Electro-Optics Society Annual Meeting-LEOS (2001), 665–666.

12.

K. D. Park, H. Ryu, W. K. Lee, S. K. Kim, H. S. Moon, and H. S. Suh, “Threshold features of a Brillouin Stokes comb generated in a distributed fiber Raman amplifier,” Opt. Lett. 28(15), 1311–1313 (2003). [CrossRef] [PubMed]

13.

D. Zhang, X. Zhang, X. Li, A. Xu, Z. Wang, F. Zhang, and Z. Chen, “Stimulated Brillouin scattering and Rayleigh cooperative process in 300 Km optical transmission,” Microw. Opt. Technol. Lett. 49(12), 2939–2941 (2007). [CrossRef]

14.

N. F. P. Zel'dovich and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985).

15.

N. A. M. A. Hambali, M. A. Mahdi, M. H. Al-Mansoori, M. I. Saripan, A. F. Abas, and M. Ajiya, “Effect of output coupling ratio on the performance of ring-cavity Brillouin fiber laser,” Laser Phys. 20(7), 1618–1624 (2010). [CrossRef]

OCIS Codes
(190.4370) Nonlinear optics : Nonlinear optics, fibers
(190.5890) Nonlinear optics : Scattering, stimulated
(290.5900) Scattering : Scattering, stimulated Brillouin

ToC Category:
Nonlinear Optics

History
Original Manuscript: October 11, 2011
Revised Manuscript: November 17, 2011
Manuscript Accepted: November 21, 2011
Published: December 1, 2011

Citation
H. A. Al-Asadi, M. H. Abu Bakar, M. H. Al-Mansoori, F. R. Mahamd Adikan, and M. A. Mahdi, "Analytical analysis of second-order Stokes wave in Brillouin ring fiber laser," Opt. Express 19, 25741-25748 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-25-25741


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References

  1. M. F. Ferreira, J. F. Rocha, and J. L. Pinto, “Analysis of the gain and noise characteristics of fiber Brillouin amplifiers,” Opt. Quantum Electron.26(1), 35–44 (1994). [CrossRef]
  2. S. P. Smith, F. Zarinetchi, and S. Ezekiel, “Narrow-linewidth stimulated Brillouin fiber laser and applications,” Opt. Lett.16(6), 393–395 (1991). [CrossRef] [PubMed]
  3. K. Schneider and S. Schiller, “Narrow-linewidth, pump-enhanced singly-resonant parametric oscillator pumped at 532 nm,” Appl. Phys. (Berl.)65(6), 775–777 (1997). [CrossRef]
  4. J. Geng, S. Staines, Z. Wang, J. Zong, M. Blake, and S. Jiang, “Highly stable low-noise Brillouin fiber laser with ultranarrow spectral linewidth,” IEEE Photon. Technol. Lett.18(17), 1813–1815 (2006). [CrossRef]
  5. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2007).
  6. T. A. Haddud, M. H. Al-Mansoori, A. K. Zamzuri, S. Shaharudin, M. K. Abdullah, and M. A. Mahdi, “24-Line of Brillouin-erbium fiber laser utilizing a Fabry-Perot cavity in L-band,” Microw. Opt. Technol. Lett.45(2), 165–167 (2005). [CrossRef]
  7. M. H. Al-Mansoori, M. A. Mahdi, and M. Premaratne, “Novel multiwavelength L-band Brillouin-Erbium fiber laser utilizing double-pass Brillouin pump preamplified technique,” IEEE J. Sel. Top. Quantum Electron.15(2), 415–421 (2009). [CrossRef]
  8. M. H. Al-Mansoori and M. A. Mahdi, “Multiwavelength L-band Brillouin-erbium comb fiber laser utilizing nonlinear amplifying loop mirror,” J. Lightwave Technol.27(22), 5038–5044 (2009). [CrossRef]
  9. T. H. Russell, W. B. Roh, and J. R. Marciante, “Incoherent beam combining using stimulated Brillouin scattering in multimode fibers,” Opt. Express8(4), 246–254 (2001). [CrossRef] [PubMed]
  10. B. C. Rodgers, T. H. Russell, and W. B. Roh, “Laser beam combining and cleanup by stimulated Brillouin scattering in a multimode optical fiber,” Opt. Lett.24(16), 1124–1126 (1999). [CrossRef] [PubMed]
  11. T. H. Russell and W. B. Roh, “Threshold of the second Stokes scattering in a fiber stimulated Brillouin scattering beam combiner,” in Conference Proceedings - Lasers and Electro-Optics Society Annual Meeting-LEOS (2001), 665–666.
  12. K. D. Park, H. Ryu, W. K. Lee, S. K. Kim, H. S. Moon, and H. S. Suh, “Threshold features of a Brillouin Stokes comb generated in a distributed fiber Raman amplifier,” Opt. Lett.28(15), 1311–1313 (2003). [CrossRef] [PubMed]
  13. D. Zhang, X. Zhang, X. Li, A. Xu, Z. Wang, F. Zhang, and Z. Chen, “Stimulated Brillouin scattering and Rayleigh cooperative process in 300 Km optical transmission,” Microw. Opt. Technol. Lett.49(12), 2939–2941 (2007). [CrossRef]
  14. N. F. P. Zel'dovich and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985).
  15. N. A. M. A. Hambali, M. A. Mahdi, M. H. Al-Mansoori, M. I. Saripan, A. F. Abas, and M. Ajiya, “Effect of output coupling ratio on the performance of ring-cavity Brillouin fiber laser,” Laser Phys.20(7), 1618–1624 (2010). [CrossRef]

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