OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 18 — Sep. 1, 2008
  • pp: 14233–14247
« Show journal navigation

A theoretical treatment of two approaches to SBS mitigation with two-tone amplification

Iyad Dajani, Clint Zeringue, T. Justin Bronder, Thomas Shay, Athanasios Gavrielides, and Craig Robin  »View Author Affiliations


Optics Express, Vol. 16, Issue 18, pp. 14233-14247 (2008)
http://dx.doi.org/10.1364/OE.16.014233


View Full Text Article

Acrobat PDF (242 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A technique that employs two seed signals for the purpose of mitigating stimulated Brillouin scattering (SBS) effects in narrow-linewidth Yb-doped fiber amplifiers is investigated theoretically by constructing a self-consistent model that incorporates the laser gain, SBS, and four-wave mixing (FWM). The model reduces to solving a two-point boundary problem consisting of an 8x8 system of coupled nonlinear differential equations. Optimal operating conditions are determined by examining the interplay between the wavelength separation and power ratio of the two seeds. Two variants of this ‘two-tone’ amplification are considered. In one case the wavelength separation is precisely twice the Brillouin shift, while the other case considers a greater wavelength separation. For the former case, a two-fold increase in total output power over a broad range of seed power ratios centered about a ratio of approximately 2 is obtained, but with fairly large FWM. For the latter case, this model predicts an approximately 100% increase in output power (at SBS threshold with no signs of FWM) for a ‘two-tone’ amplifier with seed signals at 1064nm and 1068nm, compared to a conventional fiber amplifier with a single 1068nm seed. More significantly for this case, it is found that at a wavelength separation greater than 10nm, it is possible to appreciably enhance the power output of one of the laser frequencies.

© 2008 Optical Society of America

1. Introduction

Recent technological advances have made possible fiber lasers with outputs well beyond the kilowatt level. However, the highest output powers are characterized by broad spectra making them unsuitable for a range of applications including coherent beam combination for directed energy purposes, harmonic generation, lidar, and gravitational wave detection. A major limitation for high power CW narrow linewidth fiber amplifiers is the onset of stimulated Brillouin Scattering (SBS) which is the lowest threshold nonlinear process for such amplifiers. To reduce SBS, a number of approaches - such as the use of thermal gradients [1

1. D. P. Machewirth, Q. Wang, B. Samson, K. Tankala, M. O’Connor, and M. Alam, “Current developments in high-power, monolithic, polarization maintaining fiber amplifiers for coherent beam combining applications,” Fiber Lasers IV: Technology, Systems, and Applications, Proc. SPIE 6453, 64531F (2007).

], polarization effects [2

2. J. B. Spring, T. H. Russell, T. M. Shay, R. W. Berdine, A. D. Sanchez, B. G. Ward, and W. B. Roh, “Comparison of Stimulated Brillouin Scattering thresholds and spectra in non-polarization maintaining and polarization-maintaining passive fibers,” Fiber Lasers II: Technology, Systems, and Applications, Proc. SPIE 5709, 147–156 (2005).

], large flattened mode area fibers [3

3. B. G. Ward, C. Robin, and M. Culpepper, “Photonic crystal fiber designs for power scaling of single-polarization amplifiers.” Fiber Lasers IV: Technology, Systems, and Applications, Proc. SPIE 6453, 645307 (2007).

], and fibers designed to reduce the overlap between the incident light and the resulting acoustic wave or to induce a negative acoustic lens effect [4

4. M. Li, X. Chen, J. Wang, S. Gray, A. Liu, J. Demeritt, A. B. Ruffin, A. M. Crowley, D. T. Walton, and L. A. Zenteno, “ Al/Ge co-doped large mode area fiber with high SBS threshold,” Opt. Express 15, 8290–8299 (2007). [CrossRef] [PubMed]

,5

5. S. Gray, A. Liu, D. T. Walton, J. Wang, M. Li, X. Chen, A. B. Ruffin, J. A. Demeritt, and L. A. Zenteno, “502 Watt, single transverse mode, narrow linewidth, bidirectionally pumped Yb-doped fiber amplifier,” Opt. Express 15, 17044–17050 (2007). [CrossRef] [PubMed]

,6

6. M. D. Mermelstein, M. J. Andrejco, J. Fini, C. Headley, and D. J. DiGiovanni, “11.2 dB SBS Gain Suppression in a Large Mode Area Yb-Doped Optical Fiber,” Fiber Lasers V: Technology, Systems, and Applications, Proc. SPIE 6873, 68730N (2008).

] - have been either demonstrated or suggested. This paper presents theoretical verification of another technique that increases the SBS threshold in a fiber amplifier using two narrow linewidth master oscillators, or ‘tones’, oscillating at wavelengths λ1 and λ2.

2. Large wavelength separation

2.1 Derivation of the two-tone model

The two-tone method discussed here has been specifically designed to increase the SBS threshold and avoid FWM. Both effects are third-order nonlinear effects. SBS describes the interaction among the laser signal, its Stokes signal, and an acoustic signal that beats at the difference frequency of the optical fields due to electrostriction. In a fiber amplifier the Stokes photons and the acoustic phonons are initiated from noise. By assuming steady-state conditions and strong damping of the phonon field, a coupled 2x2 system of the laser and Stokes intensities is typically obtained. The effects of FWM are well-known; in the case of two input frequency components oscillating at ω 1 and ω 2 the interaction of the waves is mediated through the third-order susceptibility of the mediumχ (3). Two sidebands oscillating at ω 3=ω 1ω and ω 4=ω 1+2Δω, where Δω=ω 2-ω 1, are generated.

In order to formulate a self-consistent model laser gain, SBS, and FWM are all incorporated in our work into a set of 8x8 coupled nonlinear differential equations that describe the evolution of 7 optical fields and the population density of one of the atomic levels of a two-level laser system.

The evolution of the electric field of each frequency component can be derived from the nonlinear wave equation

2Eini2c22t2Ei=1ε0c22t2Pi(nl),
(1)

where the subscript i represents the frequency component of the electric field and Pi (nl) is the nonlinear polarization. The electric field is expressed as

Ei(r,t)=j(12)Ai,j(z)ϕi,j(x,y)exp[i(βi,jωit)]+c.c.
(2)

where j represents the mode, Ai,j (z) is the amplitude, β i,j is the propagation constant, and ϕi,j (x,y) is the transverse profile.

dA1dz=g12A1gB,1ε0cn1Sκao4A1S2A1+iω1n1(2)κpmc[(A12+2i1Ai2)A1+2A1*A2A3exp(iΔβ1z)+2A2*A3A4exp(iΔβ2z)+A22A4*exp(iΔβ3z)],
(3)

Δβ1=β2+β32β1=β(2)(Δω)2,
(4a)
Δβ3=2β2β1β4=β(2)(Δω)2,
(4b)
Δβ2=β3+β4β1β2=2β(2)(Δω)2,
(4c)

where we used a Taylor’s expansion to relate these terms to β (2) the group-velocity dispersion (GVD) parameter. The overlap integral for the SPM and XPM, κpm, and the overlap integral for the acoustic and optical wave interaction, κao, are given by:

κpm=κao=ϕ4dxdyϕ2dxdy.
(5)

Note that in obtaining κao we assumed the transverse acoustic profile is described by |ϕ|2 as can be inferred from the form of the electrostrictive force. If one were to subscribe to the notion of guided acoustic modes [4

4. M. Li, X. Chen, J. Wang, S. Gray, A. Liu, J. Demeritt, A. B. Ruffin, A. M. Crowley, D. T. Walton, and L. A. Zenteno, “ Al/Ge co-doped large mode area fiber with high SBS threshold,” Opt. Express 15, 8290–8299 (2007). [CrossRef] [PubMed]

], then ao κ will be of the form:

κao=ϕ2ψ*dxdy2ϕ2dxdy·ψ2dxdy

where ψ represents the acoustic mode.

We model the gain medium as a two-level system. The laser Yb-gain coefficient, g 1, is given by

g1=(N2σ1(e)N1σ1(a))ϕ2dxdyϕ2dxdy,
(6)

where N 2 and N 1 are the population densities of the upper and lower energy levels, respectively, and where σ (e) 1 and σ (a) 1 a represent the emission and absorption cross sections for the seed frequency ω 1, respectively. The integration in the numerator of Eq. (6) is carried out within the core.

The Stokes wave, A 1 S, is initiated from noise at the opposite end of the fiber and travels in the backward direction. The evolution of its amplitude along its direction of propagation is given by

dA1Sdz=g1S2A1SgB,1ε0cn1κao4A12A1S,
(7)

where g 1S is the laser gain coefficient at the Stokes wavelength and has a similar form to that in Eq. (6) except that the emission and absorption cross sections correspond to the Stokes wavelength. Note that the noise contribution is incorporated into Eq. (7) as we employ a localized source model as proposed by Smith [15

15. R. G. Smith, “Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and Brillouin scattering,” Appl. Opt. 11, 2489–2494 (1972). [CrossRef] [PubMed]

] or, alternatively, Zel’dovich et al. [16

16. B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer- Verlag,, Berlin, 1985).

].

Similar equations can be derived for the seed wave oscillating at the input frequency ω 2, and its associated Stokes waves. These equations are given by:

dA2dz=g22A2gB,2ε0cn2Sκao4A2S2A2+iω2n2(2)κpmc[(A22+2i2Ai2)A2+2A2*A1A4exp(iΔβ3z)+2A1*A3A4exp(iΔβ2z)+A12A3*exp(iΔβ1z)]
(8)
dA2Sdz=g2S2A2SgB,2ε0cn2κa04A22A2S,
(9)

where g 2 and g 2 S have similar expressions to Eq. (6). We neglect the SBS interaction for the FWM sidebands ω 3 and ω 4. This is justified as long as their amplitudes are much smaller than the laser signals. The evolution of their amplitudes along z is given by:

dA3dz=g32A3+iω3n3(2)κpmc[(A32+2i3Ai2)A3+A12A2*exp(iΔβ1z)+2A1A2A4*exp(iΔβ2z)],
(10)
dA4dz=g42A4+iω4n4(2)κpmc[(A42+2i4Ai2)A4+A22A1*exp(iΔβ3z)+2A2A1A3*exp(iΔβ2z)].
(11)

N0=N1(z)+N2(z),
(12)
N2(z)=i=14τσi(a)ωiIi+i=12τσiS(a)ωiSIiS+τσp(a)ωpIpi=14τ(σi(a)+σi(e))ωiIi+i=12τ(σiS(a)+σiS(e))ωiSIiS+τ(σp(a)+σp(e))ωpIp+1·N0,
(13)

where N ο represents the density of Yb ions in the fiber core, τ is the lifetime of the upper laser level, and the subscripted I’s represent the intensities of the various waves. The intensity of the pump which in our simulation is taken to propagate in the same direction evolves according to:

dIpdz=dcore2dclad2(N2σp(e)N1σp(a))Ip
(14)

where dcore and dclad are the diameters of the core and the cladding, respectively.

2.2 ‘Two-tone’ simulations and results

Fig. 1. The sensitivity of SBS to the ratio of the input signals in ‘two-tone’ amplification. The x-axis shows the ratio of power in one input signal (1068nm) to the total input power. The y-axis represents percentage of Stokes power.

The case of a single 2.0 W 1064 nm seed was also modeled for comparison. In these model runs, the power from a 977nm pump was increased for each seed method until the SBS threshold was reached. For clarity, we used a working definition of the SBS threshold as the point where the generated SBS power from a signal, that is, from a single 1064. nm seed or either of the ‘two-tone’ seeds, reached 1% of the output power for that amplified signal. The results of the model runs at this defined SBS threshold are shown in Figs. (2)-(4).

Fig. 2. The output powers of the two amplified signals in a simulated ‘two-tone’ amplifier and a typical single seed fiber amplifier versus propagation distance along fiber
Fig. 3. Power of backward travelling Stokes light signals corresponding to 1068 nm and 1064 nm.

The typical single seed amplification reached SBS threshold at 33 W of pump power for an amplified power of approximately 28 W; the two-tone case reached its SBS threshold at 62 W of pump. Here the output power of the 1064nm signal was approximately 24.5 W and 30 W for the 1068 nm signal for a total exceeding 54 W. Thus, the total amplified power from the two-tone amplifier was almost twice the single seed case with minimal FWM while maintaining the overall optical efficiency and suppressing SBS. Note from Fig. (3) and (4), FWM is an order of magnitude lower than SBS. Furthermore, it can be inferred that the coherence lengths of the two FWM sidebands are different. This is due to laser gain in the sidebands as well as SPM and XPM effects. Referring to Fig. (2), it is worthwhile to mention here that at some point along the fiber, the 1064 nm light will experience negative gain. We will elaborate on this point further below.

Fig. 4. The first two FWM-generated sidebands in the case of ‘two-tone’ amplification of a 1064nm seed and 1068nm seed as described above. Note that the power in these sidebands is one order of magnitude lower than the SBS power.

Fig. 5. The FWM behavior of SBS-suppressed two-tone amplifiers with a) 350 W (top) and b) 550 W (bottom) of pump power. The wavelength separation in this case is 4 nm. The additional pumping has altered the coherence period due to SPM and XPM.

Going back to our initial amplifier configuration (with the SBS gain suppressing factor turned off), the wavelength separation of the two input signals was increased and decreased. For these tests, the pump power was held constant at approximately 60W which was near our defined SBS threshold for Δλ=4.0 nm. For Δλ<3nm the FWM increased considerably and became comparable to the Stokes light. For Δλ>10nm, the FWM was extremely small. Most remarkably for this wavelength separation, considerable enhancement in the power output of the lower laser frequency was obtained. For example, at Δλ=14nm and input seeds with wavelengths 1064 nm and 1050 nm, 46 W of output power was obtained for the 1064 nm light. The power ratio needed to obtain this output was approximately 9:1 with the 1050 nm having the higher input power. The 46 W output power represented a 64% enhancement over a 1064 nm single tone amplifier as shown in Fig. (6). Higher power output in one of the tones is possible to the point where almost all the output power would be in a single frequency. This can be achieved through an optimal ratio of seed and wavelength separation, or by selecting a more suitable fiber configuration; the details will be discussed in a future publication.

Fig. 6. The evolution of two laser signals along the direction of propagation. For comparison, the case of single tone seeding is plotted.

Note that the 1050 nm signal reaches its maximum value at a distance shorter than the midway point of the fiber. This is due to the higher pump power, the skewed input seed power ratio, and the higher emission cross section of the 1050 nm light as compared to that of 1064 nm light. As the two laser signals propagate down the fiber, the population density of the upper level state, N 2, decreases. Immediately past the point where the maximum power for the 1050 nm light is obtained, the population inversion is such that the 1050 nm light will experience negative gain. The 1064 nm light which has an appreciably lower absorption cross section will, however, continue to experience positive laser gain. As a consequence, power transfer occurs from the 1050 nm light and into the 1064 nm light. The SBS threshold is raised because the spatially integrated Stokes light gain for the two-tone 1064 nm light will be close to the 1064 nm single tone case even though more 1064 nm output power is obtained in the former. This is made possible because, for a significant portion of the fiber, the power in the 1064 nm light for the two tone case is less than that for the single tone case as can be seen from Fig. (6). We examined the total gain for the electric field amplitude of the Stokes light as a function of position. Referring to Eq. (7) in Section 2, this total gain is due to the total of the laser and Brillouin gain. It is worthwhile to point out here that the amplitude gain is half that of the intensity or power gain. Figure (7) represents a comparison of the amplitude gain for the two tone case pumped such that the power output at 1064 nm is equal to the power output in a single tone amplifier at threshold. Note that the spatially integrated Stokes gain for two-tone is reduced significantly, thus allowing for higher pumping power and consequently higher output at 1064 nm. As mentioned in the Section 1, this power enhancement was not thought to be possible. Thus, this is a novel way to increase power in CW narrow linewidth Yb-doped amplifiers.

Fig. 7. Total Stokes gain for the 1064 nm light for the two tone and one tone cases. For the two tone case the pump power is approximately 38 W which generated an output 1064 nm power of approximately 28 W (equal to the output at threshold in the single tone case).

3. Wavelength separation of twice the Brillouin shift

We now investigate theoretically the two-tone suppressing technique implemented experimentally by Wessels et al. [7

7. P. Wessels, P. Adel, M. Auerbach, D. Wandt, and C. Fallnich, “ Novel suppression scheme for Brillouin scattering,” Opt. Express 12, 4443–4448 (2004). [CrossRef] [PubMed]

]. This technique relies on selecting the wavelength separation between the two input frequencies to be equal to twice the Brillouin shift νB, i.e. twice the frequency of the phonon field. In optical fibers, this value is approximately 34 GHz (Δλ≈0.1 nm). It is important to point out here if the frequency separation does not lie within the range defined by 2(νB±ΔνB, where ΔνB is the SBS gain linewidth, then there will be a one fold maximum increase in total amplifier output power as we described in Section 2. For Δν=2ΔνB, the equations describing the spatial evolution of A 1 and A 2 S are modified to become:

dA1dz=g12A1gB,1ε0cn1Sκa04A1S2A1+gB,1ε0cn1κao4A2S2A1
+iω1n1(2)κpmc[(A12+2i1Ai2)A1+2A1*A2A3exp(iΔβ1z)+2A2*A3A4exp(iΔβ2z)+A22A4*exp(iΔβ3z)],
(15)
dA2Sdz=g2S2A2SgB,2ε0cn2κa04A22A2S+gB,1ε0cn1κao4A12A2S.
(16)

As indicated by the equations above, The Stokes light generated by the input frequency ω 2 is SBS-scattered into the input frequency ω 1, thus effectively raising the SBS threshold for ω 2. In order to gain maximum benefit from such a system, an optimal power ratio between the two input beams should be selected. To theoretically determine this ratio, we define r=P 1/P 2 and neglect laser gain and FWM. For small SBS signal gain, we can work in the undepleted pump limit to obtain from Eq. (7) and Eq. (16)

16. B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer- Verlag,, Berlin, 1985).

:

A1S=A1S(L)exp[gBε0cnκaoA224(1r)(Lz)],
(17)
A1S=A1S(L)exp[gBε0cnκaoA224r(Lz)].
(18)

Where for simplicity we set g B1=g B2=gB, and n 1=n 2=n. In order to achieve the largest suppression of SBS, the SBS small signal gain for each of the Stokes lights has to be approximately equal. Therefore r=1/2, i.e. the input power of ω 2 is twice that of ω 1. This is the power ratio used by Wessels et al. and our analysis above is further borne out by the numerical simulations presented below.

The fiber parameters used in our simulations were the same as described in Section 2.2; the wavelengths selected were close to 1068 nm. The amplified powers are shown in Fig. (8) with the single-seed case also shown for comparison. The maximum total power out of this two-tone amplifier was greater than 80 W, an approximately two-fold increase in total power over the single seed case. Furthermore, the total power output in one of the signals was twice that of the single tone case. This is close to the improvement noted in the experimental results of Reference [7

7. P. Wessels, P. Adel, M. Auerbach, D. Wandt, and C. Fallnich, “ Novel suppression scheme for Brillouin scattering,” Opt. Express 12, 4443–4448 (2004). [CrossRef] [PubMed]

]. The nonlinear effects in this amplifier are shown in Fig. (9). The FWM effects are more pronounced than in the case of the two tone amplifier with large wavelength separation, but they are still roughly a factor of 10 less than what was previously experimentally observed [7

7. P. Wessels, P. Adel, M. Auerbach, D. Wandt, and C. Fallnich, “ Novel suppression scheme for Brillouin scattering,” Opt. Express 12, 4443–4448 (2004). [CrossRef] [PubMed]

]. This is due mainly to the much shorter length of out Yb-doped amplifier.

Fig. 8. The power output of a two tone amplifier. The two tones are separated by twice the Brillouin shift allowing Stokes light generated by seed light to transfer its energy to the second seed. λ=1068 (2νB/ν) nm.
Fig. 9. The FWM for the two tones separated by twice the Brillouin shift. Due to the small wavelength separation the FWM is the lowest threshold nonlinear process.

We also tested additional aspects of this case of two-tone amplification, such as the optimal 2:1 ratio that we theoretically investigated above. Keeping track of the total output power, we varied this input ratio from 1:1 up to 3:1. For these set of simulations, we held the total seed power constant but varied the pump power until the SBS threshold was reached.

Fig. 10. The dependence of total output power for two-tone amplifier on seed power ratio. The two frequencies are separated by twice the Brillouin shift. Here, The seed power ratio is defined as the input power of the higher frequency wave divided by that of the lower frequency.

As shown in Fig. (10), there is actually a broad range of input ratios spanning approximately 1.8 to 2.3 that effectively mitigate SBS and provide an output power that is within 5% of the maximum achievable power output.

In comparing these results with those obtained in Section 2 for Δλ=14 nm, we note that the total power for the latter is one third less, but that fairly comparable outputs are obtained at the wavelength possessing the higher power. Therefore, if certain applications require the use of single frequency, the case of large wavelength separation will have a higher efficiency.

4. Conclusion

We have rigorously formulated the problem of an Yb-doped amplifier seeded with two laser frequencies to account for stimulated Brillouin scattering and four-wave mixing. Two cases were considered and were shown to enhance the power output of one of the laser signals: 1) a large wavelength separation and 2) a wavelength separation corresponding to precisely the Brillouin shift. It was thought previously that power enhancement was not possible for the former case. Experimental implementation of this two-tone work as well as theoretical extension to multi-tone seeding is already underway.

References and links

1.

D. P. Machewirth, Q. Wang, B. Samson, K. Tankala, M. O’Connor, and M. Alam, “Current developments in high-power, monolithic, polarization maintaining fiber amplifiers for coherent beam combining applications,” Fiber Lasers IV: Technology, Systems, and Applications, Proc. SPIE 6453, 64531F (2007).

2.

J. B. Spring, T. H. Russell, T. M. Shay, R. W. Berdine, A. D. Sanchez, B. G. Ward, and W. B. Roh, “Comparison of Stimulated Brillouin Scattering thresholds and spectra in non-polarization maintaining and polarization-maintaining passive fibers,” Fiber Lasers II: Technology, Systems, and Applications, Proc. SPIE 5709, 147–156 (2005).

3.

B. G. Ward, C. Robin, and M. Culpepper, “Photonic crystal fiber designs for power scaling of single-polarization amplifiers.” Fiber Lasers IV: Technology, Systems, and Applications, Proc. SPIE 6453, 645307 (2007).

4.

M. Li, X. Chen, J. Wang, S. Gray, A. Liu, J. Demeritt, A. B. Ruffin, A. M. Crowley, D. T. Walton, and L. A. Zenteno, “ Al/Ge co-doped large mode area fiber with high SBS threshold,” Opt. Express 15, 8290–8299 (2007). [CrossRef] [PubMed]

5.

S. Gray, A. Liu, D. T. Walton, J. Wang, M. Li, X. Chen, A. B. Ruffin, J. A. Demeritt, and L. A. Zenteno, “502 Watt, single transverse mode, narrow linewidth, bidirectionally pumped Yb-doped fiber amplifier,” Opt. Express 15, 17044–17050 (2007). [CrossRef] [PubMed]

6.

M. D. Mermelstein, M. J. Andrejco, J. Fini, C. Headley, and D. J. DiGiovanni, “11.2 dB SBS Gain Suppression in a Large Mode Area Yb-Doped Optical Fiber,” Fiber Lasers V: Technology, Systems, and Applications, Proc. SPIE 6873, 68730N (2008).

7.

P. Wessels, P. Adel, M. Auerbach, D. Wandt, and C. Fallnich, “ Novel suppression scheme for Brillouin scattering,” Opt. Express 12, 4443–4448 (2004). [CrossRef] [PubMed]

8.

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently coupled high power fiber arrays,” Proc. SPIE 6102, 61020U (2006). [CrossRef]

9.

T. M. Shay, “Theory of electronically phased coherent beam combination without a reference beam,” Opt. Express 24, 12188–12195 (2006). [CrossRef]

10.

J. E. Kansky, C. X. Yu, D. V. Murphy, S. R. Shaw, R. C. Lawrence, and C. Higgs, “Beam control for a 2D polarization maintaining fiber optic phased array with a high-fiber count,” Proc. SPIE. 6306, 63060G (2006). [CrossRef]

11.

V. Daneu, A. Sanchez, T. Y. Fan, H. K. Choi, G. W. Turner, and C. C. Cook, “Spectral beam combining of a broad-stripe diode laser array in an external cavity,” Opt. Lett. 25, 405–407 (2000). [CrossRef]

12.

T. H. Loftus, A. M. Thomas, P. R. Hoffman, M. Norsen, R. Royse, A. Liu, and E. C. Honea, “ Spectrally beam-combined fiber lasers for high-average-power applications,” IEEE J. Sel. Top. Quantum Electron. 13, 487–497 (2007). [CrossRef]

13.

F. Patel, Ph. D. Dissertation, University of California, Davis (2000).

14.

L. G. Cohen, “Comparison of single-mode fiber dispersion measurement techniques,” J. Lightwave Technol. LT-3, 958 (1985). [CrossRef]

15.

R. G. Smith, “Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and Brillouin scattering,” Appl. Opt. 11, 2489–2494 (1972). [CrossRef] [PubMed]

16.

B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer- Verlag,, Berlin, 1985).

OCIS Codes
(140.3510) Lasers and laser optics : Lasers, fiber
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(290.5900) Scattering : Scattering, stimulated Brillouin

ToC Category:
Nonlinear Optics

History
Original Manuscript: July 9, 2008
Revised Manuscript: August 20, 2008
Manuscript Accepted: August 20, 2008
Published: August 27, 2008

Citation
Iyad Dajani, Clint Zeringue, T. J. Bronder, Thomas Shay, Athanasios Gavrielides, and Craig Robin, "A theoretical treatment of two approaches to SBS mitigation with two-tone amplification," Opt. Express 16, 14233-14247 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-18-14233


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. D. P. Machewirth, Q. Wang, B. Samson, K. Tankala, M. O�??Connor, and M. Alam, "Current developments in high-power, monolithic, polarization maintaining fiber amplifiers for coherent beam combining applications," Fiber Lasers IV: Technology, Systems, and Applications, Proc. SPIE 6453, 64531F (2007).
  2. J. B. Spring, T. H. Russell, T. M. Shay, R. W. Berdine, A. D. Sanchez, B. G. Ward, and W. B. Roh, "Comparison of Stimulated Brillouin Scattering thresholds and spectra in non-polarization maintaining and polarization-maintaining passive fibers," Fiber Lasers II: Technology, Systems, and Applications, Proc. SPIE 5709, 147-156 (2005).
  3. B. G. Ward, C. Robin, and M. Culpepper, "Photonic crystal fiber designs for power scaling of single-polarization amplifiers," Fiber Lasers IV: Technology, Systems, and Applications, Proc. SPIE 6453, 645307 (2007).
  4. M. Li, X. Chen, J. Wang, S. Gray, A. Liu, J. Demeritt, A. B. Ruffin, A. M. Crowley, D. T. Walton, and L. A. Zenteno, " Al/Ge co-doped large mode area fiber with high SBS threshold," Opt. Express 15, 8290-8299 (2007). [CrossRef] [PubMed]
  5. S. Gray, A. Liu, D. T. Walton, J. Wang, M. Li, X. Chen, A. B. Ruffin, J. A. Demeritt, and L. A. Zenteno, "502 Watt, single transverse mode, narrow linewidth, bidirectionally pumped Yb-doped fiber amplifier," Opt. Express 15, 17044-17050 (2007). [CrossRef] [PubMed]
  6. M. D. Mermelstein, M. J. Andrejco, J. Fini, C. Headley, and D. J. DiGiovanni, "11.2 dB SBS Gain Suppression in a Large Mode Area Yb-Doped Optical Fiber," Fiber Lasers V: Technology, Systems, and Applications, Proc. SPIE 6873,68730N (2008).
  7. P. Wessels, P. Adel, M. Auerbach, D. Wandt, and C. Fallnich, "Novel suppression scheme for Brillouin scattering," Opt. Express 12, 4443-4448 (2004). [CrossRef] [PubMed]
  8. J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, "Coherently coupled high power fiber arrays," Proc. SPIE 6102, 61020U (2006). [CrossRef]
  9. T. M. Shay, "Theory of electronically phased coherent beam combination without a reference beam," Opt. Express 24, 12188-12195 (2006). [CrossRef]
  10. J. E. Kansky, C. X. Yu, D. V. Murphy, S. R. Shaw, R. C. Lawrence, and C. Higgs, "Beam control for a 2D polarization maintaining fiber optic phased array with a high-fiber count," Proc. SPIE. 6306, 63060G (2006). [CrossRef]
  11. V. Daneu, A. Sanchez, T. Y. Fan, H. K. Choi, G. W. Turner, and C. C. Cook, "Spectral beam combining of a broad-stripe diode laser array in an external cavity," Opt. Lett. 25, 405- 407 (2000). [CrossRef]
  12. T. H. Loftus, A. M. Thomas, P. R. Hoffman, M. Norsen, R. Royse, A. Liu, and E. C. Honea, "Spectrally beam-combined fiber lasers for high-average-power applications," IEEE J. Sel. Top. Quantum Electron. 13, 487-497 (2007). [CrossRef]
  13. F. Patel, Ph.D. Dissertation, University of California, Davis (2000).
  14. L. G. Cohen, "Comparison of single-mode fiber dispersion measurement techniques," J. Lightwave Technol. LT-3, 958 (1985). [CrossRef]
  15. R. G. Smith, "Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and Brillouin scattering," Appl. Opt. 11, 2489-2494 (1972). [CrossRef] [PubMed]
  16. B. Ya. Zel�??dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited