We report on a polarization-maintaining narrow-linewidth high power ytterbium-doped photonic crystal fiber amplifier with an output as high as 260 W and a slope efficiency of approximately 74%. Measurements of the beam quality yielded M2 values in the range of 1.2-1.3. The linewidth was determined at two different powers using an optical heterodyne detection technique and yielded values that were less than 10 KHz. Our maximum output power was pump limited and measurements of the reflected light indicated that we operated below the stimulated Brillouin scattering (SBS) threshold. Using a pump-probe technique, we estimated the Brillouin gain bandwidth to be approximately 68 MHz. In addition, the Brillouin gain spectrum revealed secondary peaks lying at the high-frequency side. In order to study the power limitations of our amplifier, we developed a detailed model that included a distributed noise source for the SBS process and a temperature gradient obtained via quantum defect heating. Our simulations indicated that for this particular fiber amplifier configuration an output power approaching 1 KW can be achieved. We also found that for forced air cooling the SBS threshold saturates regardless of the operating temperature of the polymer coating. Finally, we show that relatively small enhancement is obtained if a continuous transverse acoustic velocity gradient was implemented in conjunction with the thermal gradient. The latter conclusions drawn from our simulations also hold true for conventional fibers.
©2009 Optical Society of America
Since the invention of the laser, there has been extensive and sustained interest in developing high average power lasers. In recent years, rare-earth doped fiber lasers have garnered considerable attention as a means of realizing this goal due mainly to their compact and robust structures, superior thermal management properties, near diffraction-limited beam quality, and high conversion efficiencies. Reliable diode pumps and innovative fiber designs have led to the development of kilowatt level single transverse mode fiber lasers . In general, rare earth-doped double clad fiber lasers require several meters of gain fibers and are characterized by broad gain bandwidths leading to linewidths in the range of 10-20 nm. While such lasers can be of considerable benefit in material processing where raw power is sought, their broad linewidths render them ineffective for a range of applications that require single frequency (narrow linewidth) operation such as coherent beam combination , nonlinear frequency conversion in single pass configurations  or in resonant cavities , inter-satellite communications , and gravitational wave detection . For example, a laser possessing a linewidth of the order of 0.1 nm will lead to a fairly appreciable drop in second harmonic conversion efficiency in a commercial periodically poled nonlinear crystal . Spectral purity can be achieved in a fiber gain medium, however, by constructing a master-oscillator-power amplifier (MOPA) whereby the final stage fiber amplifier inherits the narrow linewidth and frequency stability characteristics of the seed laser.
It is generally agreed upon that power scaling in single frequency continuous-wave (CW) fiber amplifiers is primarily impaired by the onset of stimulated Brillouin scattering (SBS). This process is a third-order nonlinear effect that couples acoustic phonons to the optical field and its associated backscattered Stokes field. SBS can be initiated from spontaneous Brillouin scattering which describes the interaction of the signal light and the thermally activated noise. The resulting Stokes light interacts with the laser light leading, through electrostriction, to variations in density and pressure in the fiber and consequently further amplification of the acoustic and Stokes waves. Over the years, several techniques have been proposed to suppress SBS in fiber amplifiers including large-mode area (LMA) fibers , thermal gradients [8,9], stress , anti-guiding acoustic fibers , fibers possessing acoustic index of refraction gradients [12,13], and multi-tone amplification [14–16]. LMA fibers which are realized by lowering the numerical aperture of the core while increasing the core diameter and by bending the fiber to achieve modal discrimination, have led to a significant increase in the output power in narrow linewidth fiber amplifiers. Further power scaling was achieved through the thermal gradient introduced via quantum defect heating  as this leads to a broadening of the effective Brillouin gain.
State of the art conventional LMA fibers are generally limited in practice to diameters that are less than 30 μm. This makes photonic crystal fibers (PCFs) attractive as a means to mitigate the SBS process. The introduction of micron-sized air holes in a fiber allows for a more precise control of the effective index of refraction of the cladding. The ultra-low numerical apertures achieved lead to larger core diameters while maintaining single mode operation. Another significant advantage of double-clad PCFs is the high numerical apertures that can be attained for pumping purposes through the utilization of a web of sub-wavelength size silica bridges .
We report here on a 260 W polarization maintaining (PM) narrow linewidth PCF amplifier with excellent beam quality. The power output obtained was pump limited and was 76% higher than the previous record reported in the literature . While the amplifier in ref . was inferred to be single-frequency based on the specifications of the seed source, we conducted linewidth measurements at two different powers levels. In addition, a pump probe technique was used to determine the Brillouin gain bandwidth. Our measurements of the reflected light as a function of signal power revealed that, at the highest output power, we operated below the SBS threshold. Furthermore, we developed an elaborate and self-consistent numerical code in order to study the power limitations of this power amplifier. This code accounted for the interplay among laser gain, SBS, and thermal effects. For the SBS process, a distributed noise term spanning multi-frequency channels was used. We also used our model to study the SBS mitigation factor when the thermal gradient is used in conjunction with an acoustic index of refraction gradient [12,13] and found relatively marginal increase in the SBS threshold. Much of the conclusions from our simulations also hold true for conventional fibers.
2. Experimental set-up
The PCF used in our experiments was an Yb-doped DC-400-35 fabricated by Crystal Fibre A/S. A microscope image of the fiber is shown in Fig. 1 .The nominal core diameter and mode field diameter (MFD) of the fiber were 35 and 28 μm, respectively with a numerical aperture of 0.03. Stress inducing rods composed of borosilicate and running along the fiber axis ensured that the fiber was PM. The inner cladding had a diameter of 400 μm with a numerical aperture of 0.55. The diameter of the air holes in the cladding were approximately 2 μm with a pitch of 10 μm and extended to approximately 55 μm from the center of the fiber. The outer cladding was 617 μm in diameter and was surrounded by a high temperature acrylate that was approximately 52 μm in thickness. The absorption was estimated to be 2.4 dB/m for a pump wavelength of 976 nm.
A counter-propagating scheme was used as shown in Fig. 2 . The rapid rise in signal power and temperature at the output end of the fiber provides an appreciable advantage over a co-propagating scheme in terms of SBS mitigation. The master oscillator was a non- planar ring oscillator (NPRO) from Lightwave and provided a narrow linewidth output of 200 mW. This power was further amplified to the 5 W level by using a 10/125 fiber amplifier pumped with 10 W extracted from a wavelength-stabilized diode stack. Two isolators appropriately situated prevented damage from backscattered light. A Nuvonyx laser operating at 976 nm with a 10 nm spectral bandwith (FWHM) was used to pump the final stage fiber. The fiber used in our experiments was 6 meters in length and was coiled at a diameter of 40 cm. In order to evade thermal damage, a small portion of the fiber at the signal output end was inserted inside a water cooled chuck. Dichroic mirrors on both ends of the fibers were used to separate the pump and signal beams. The fiber ends were sealed by thermally collapsing the air holes and then polished to an angle of 8○ to avoid parasitic oscillations.
At a maximum launch power of approximately 360 W, the signal was measured at 260 W with an amplified spontaneous emission (ASE) suppression of better than 35 dB. The output signal power with respect to the launched pump power is shown in Fig. 3 . The slope efficiency was approximately 74%. The polarization extinction ratio was measured with a half-wave plate and a polarizing beam splitter and was found to be better than 18 dB. It is worthwhile to point out here that unlike our fiber, the fiber used in ref . was not specifically designed to be PM although the high extinction ratio obtained was attributed to birefringence caused by imperfections in the air hole structure.
In order to characterize the SBS process in the fiber, we monitored the back-reflected light. An optical spectrum analyzer was used to track the increase in the Rayleigh scattering light which possesses the same frequency as the signal and the Stokes light which is down-shifted by approximately 16 GHz due to SBS. The Stokes light exhibited a linear increase as a function of the output signal throughout our measurements, which indicated that we were operating below threshold. The spectrum of the backward propagating light was also recorded at various powers. At the highest output power, the spectrum was dominated by Rayleigh scattering. The spectrum for the maximum obtained power of 260 W is shown in the inset graph of Fig. 3. The Stokes light intensity is approximately 20 dB below that of the Rayleigh light which indicates operation below the SBS threshold.
We also conducted measurements using a Spiricon M2 beam analyzer to determine the beam quality. The values of M2 were measured to be in the range of 1.2 and 1.3 depending on the measuring axis and output power. A plot of the beam profile from one set of measurements is shown in Fig. 4 .
Measurements to determine the linewidth at output power levels of 32 W and 54 W were conducted. An optical heterodyne analysis as shown in Fig. 5 was used for these measurements. In the experimental setup, an NP Photonics single frequency narrow linewidth fiber laser with a nominal linewidth of approximately 1 KHz was used as a reference or local oscillator (LO) and was tuned appropriately. The signal from our amplifier was combined with the reference beam using a 50/50 coupler that delivered the interference signals to two ports. One port was a photodetector that generated an electrical tone. The second port was an optical spectrum analyzer (OSA). Note that the frequency of the reference beam is tuned just lower than the average frequency of the signal in order to generate a beat frequency. The heterodyne mixing product is the convolution of the two lasers.
The data for our optical heterodyne measurements is shown in Fig. 6 for the 32 W output case. This data was taken in the dB scale. A Lorentzian was fit to this data as shown in the figure. It should be noted that our frequency scan range was approximately 300 MHz and thus the data presented in Fig. 6 zooms in on the most relevant region. Frequency jitter due to the random change in the frequency of the laser over time tends to increase the effective linewidth obtained through this technique. Generally, the effects of frequency jitter can be reduced by measuring further down on the displayed lineshape19. However, one consideration with this
measurement was the signal to noise ratio. Measurements below −20 dB generated a fairly appreciable increase in the noise level. As a result, we estimated the linewidth by taking the average value of the corresponding linewidths at two measured full-width points of −10 dB and −20 dB as described in ref . This provided it us with a linewidth value of 8.2 KHz. Because of the frequency jitter, this measurement was resolution limited and indicated a linewidth of <8.2 KHz. A similar analysis for the 54 W case, provided a linewidth of <6.8 KHz. Therefore, both measurements indicate single frequency operation.
We also examined the intrinsic (spontaneous) Brillouin gain spectrum (BGS) of our fiber using a pump-probe experimental set-up as shown in Fig. 7 . Two NPRO sources were used for the pump and probe beams. The pump power was further amplified by utilizing a single mode Yb-doped fiber. The polarization of both input beams was oriented along the slow axis of the fiber using half-wave plates. Frequency tuning of the probe NPRO was achieved by slowly modulating the temperature of the gain crystal.
We scanned a frequency span of approximately 1 GHz with a resolution of the order of several MHz. The output probe intensity was monitored using a photodiode. With a probe input power of approximately 100 mW, the pump power was varied from 2 W to 7.5 W and the BGS was recorded. The gain bandwidth at different pump powers was determined by fitting the spectrum to a Lorentzian and determining the FWHM. Figure 8 shows our experimental results at a pump power of approximately 7.5 W and the Lorentzian fit to the data. As shown, the Brillouin shift is approximately 16 GHz and the gain bandwidth is approximately 48.6 MHz.
The secondary (satellite) peaks appearing to the right (high-frequency side) of our maximum peak were consistently obtained in all our measurements and do not appear to be due to noise. Furthermore, using the same pump-probe experimental setup we conducted similar measurements using a 25/400 Yb-doped conventional LMA fiber fabricated by Nufern. For this set of measurements, no secondary peaks appeared at any of the pump powers and the results were in general agreement with the results obtained by Hildebrandt et al. who used a Nufern 20/400 Yb-doped fiber to conduct their experiments . The spectrum from one of our measurements of the gain bandwidth of the Nufern fiber is shown in Fig. 9 .
One possibility is that these secondary peaks are due to the Brillouin scattering interactions of higher order transverse optical modes in the PCF. However, both pump and probe beams were operating near the diffraction limit. In addition, the Brillouin shift is given by , where is the effective index of the mode, is the laser wavelength, and is the acoustic velocity. Based on the numerical aperture of the core, the separation between these peaks would be much smaller than what was obtained experimentally. Furthermore, since the higher order optical modes possess a lower effective index of refraction, one would expect these peaks to be to the left of the primary Brillouin gain peak. Another possible reason for these observations could be variations in the polarizations of the pump and probe beams. However, upon close examination, we concluded that these polarizations were oriented along the slow axis and were stable throughout our measurements.
Dainese et al. have shown that a multi-peaked BGS is obtained in subwavelength-scale PCFs . This phenomenon was attributed to the existence of several families of guided acoustic modes; each with different proportions of longitudinal and shear strain. However, the authors of that work reported that this phenomenon was not observed in a 9 μm PCF. A study by Beugnot et al. using a PCF with a diameter of 5 μm described the co-existence of two strongly coupled acoustic waves as a result of the stress applied through the winding of the fiber . While variations in the stress (or perhaps other structural variations) along the length of our 35 μm fiber is a possible explanation, another possibility is variations in the acoustic velocity in the transverse direction. To be certain, dispersion-shifted conventional fibers as well as dispersion-shifted PCFs possessing relatively small sizes exhibited secondary BGS peaks which were attributed to the structure of the cores . We note that our fiber was fabricated using a stack and draw technique with the core consisting of 7 hexagonal segements . Although the optical index of refraction is matched to an excellent degree of tolerance among the various segments through the manipulation of the dopant levels, it is conceivable that small transverse variations in the acoustic velocity are present.
Following the work in ref , a linear fit for the gain bandwidth data was obtained. As expected, the gain bandwith tended to broaden as the pump power was decreased. These results are shown in Fig. 10 . The spontaneous Brillouin scattering bandwidth corresponds to the bandwith at zero pump power. Based on our linear fit, we estimated this gain bandwidth to be approximately 68 MHz. We point out that the appearance of the secondary peaks had a small effect on our Lorentzian fits and consequently on both our line fit and estimate of the bandwith. Nevertheless, our estimate should be accurate to within a few MHz.
3.1 Coupled system with distributed noise and thermal gradient
A model to study the spatial evolution of the pump, signal, and Stokes light in a fiber amplifier was developed in order to predict the power limitations of our PCF amplifier. This model accounts for the shift in the resonance frequency of the phonons due to the optically induced thermal gradient in the fiber through a distributed noise term. Hilderbrandt et al.  have previously used a localized noise as described by Smith  to study the spatial evolution of the Stokes light in a conventional fiber amplifier with a thermal gradient. While the work of Boyd et al.  has shown that the localized and distributed noise models are generally equivalent in a passive and homogeneous medium of sufficient length, the use of a localized noise to describe amplifiers with thermal gradients suffers from the drawback that the location of the noise is determined a priori and the dependence of the noise on temperature (and thus the position) is ill-defined. This is not much of a problem in a passive fiber, but for a medium with laser gain and thermal gradient, a self-consistent treatment becomes problematic. The coupled set of equations describing the evolution of the pump, signal, and Stokes light in a fiber amplifier can be derived using coupled mode theory. In order to model the thermal gradient, a spread in Stokes frequencies needs to be considered. This can be accounted for by discretizing the Stokes frequencies into bins of sufficient number to capture the correct physics. For the signal power,, the following equation describing its evolution along the direction of propagation,z, is obtained:26].
The dependence of the SBS gain on the temperature profile is dominated by the shift in the resonance frequency. It can be incorporated intothrough:27]. Note that the variation of with temperature is neglected in our analysis. Again, the dominant temperature-related effect on the Stokes gain is due to the shift in the resonance frequency. We also note that, in the simulations presented, we did not consider the secondary peaks that were observed experimentally and described in section 2. Also, the lifetime of the phonons at room temperature used in out simulations corresponded to a BGS bandwidth of 40 MHz which is the nominal bandwidth value in most fibers. None of this should affect the general conclusions drawn from our simulations.
The noise term which is due to thermal excitations is given by:
For the Stokes light which propagates counter to the signal, the evolution is given by:
Quantum defect heating in the core provides the heat source. Assuming a negligible effect due to spontaneous emission on the amount of heat generated, the power balance equation in counter-propagating configuration takes the form:28]. At the outer layer, both convective cooling subject to Newton’s law of cooling and radiative cooling subject to Stefan’s law are taken into account:
3.2 Numerical simulations
The system of equations describing the optical waves was integrated using an implicit solver that we developed. This solver can handle a two point boundary problem and employs a technique based on a shooting method. We found that we needed approximately 50-100 channels of Stokes light, each of the order of several MHz, to achieve excellent convergence whereby minimal change in the reflectivity was obtained by refining the resolution of the channels or by expanding the range of frequencies of the Stokes light. The heat equation was solved at 200 equally spaced points along the direction of propagation. In order to speed up this process, piecewise functions were used to provide a three-dimensional temperature profile. This was made possible by utilizing the software Mathematica to provide physically viable algebraic solutions to the set of quartic equations described in Eq. (10).
The most significant limitation on power scaling of narrow linewidth fiber amplifiers that employ thermal gradients for SBS suppression is the interplay between thermal effects and the SBS process. Based on the operating temperature of the fiber coating and the heat management system, power scaling can be either thermally limited or SBS limited. For conventional fibers, polymer material is also used for the outer cladding region in order to provide guiding for the pump light. In PCFs, guiding is achieved through the silica bridge structure although polymer coatings are present for handling purposes. It has been suggested that metallic coatings can be used as an alternative mechanical protective layer in PCFs  thus allowing for higher temperatures.
We conducted a numerical study whereby we examined the amplifier limitations in an air-cooled system as a function of the operating temperature of the coating and the convective cooling coefficient, h. The value of h was allowed to vary from 10 W/m2K, which corresponds approximately to the lower end of ambient convective cooling, to 200 W/m2K which is approximately close to the upper end of forced air convective cooling. High temperature fiber coatings have typical maximum operating temperatures of 150○C-250○C. However, in order to understand the benefits obtained by developing novel materials with higher operating temperatures, we conducted our numerical simulations well past this range. For each chosen operating temperature and h value, we increased the pump power until either the temperature reached the maximum operating temperature allowed (therefore amplifier was thermally limited) or the reflectivity reached 1% (therefore amplifier was nominally SBS limited). This allowed us to generate a set of curves for the maximum achievable power as a function of maximum operating temperature and h value. The resulting graph is shown in Fig. 11 . The y-axis which provides the output power is normalized to the output power at h = 200 W/m2K. In addition, a plot of the Stokes spectrum for three different temperatures is shown in Fig. 12 indicating a broadening of the gain bandwidth and a shift of the peak value as the temperature increases.
The widely quoted SBS gain coefficient, , for silica fibers is 5 × 10−11 m/W, although this value can vary significantly depending on the dopant levels27. For example, in ref , was estimated to be 2.4 × 10−11 m/W. Using the value 5 × 10−11 m/W, we obtained an SBS threshold of approximately 210 W at h = 200 W/m2K and a threshold of approximately 145 W at constant temperature (no thermal gradient). Therefore, it can be inferred that moderate SBS suppression due to the thermal gradient was obtained in our experiment which operated close to ambient convective cooling conditions. Assuming a polymer operating temperature somewhere in the range of 200○C-250○C, one can estimate based on the plot in Fig. 11 that an output power of approximately 850 W can be expected with the current amplifier configuration. This corresponds to h slightly exceeding 100 W/m2K. Thus, without proper level of thermal management, our fiber amplifier which was pump-limited would become thermally limited as we attempt further power scaling. It should also be pointed out here that if a midpoint value for were to be used based on the two values provided above, an output power exceeding 1 KW would be calculated.
Provided that technological innovation can lead to very high temperature coating materials, it has been theorized previously that total suppression of SBS through quantum defect heating at exceedingly higher powers is possible ,. However, as can be seen in Fig. 11, the maximum amplifier output saturates regardless of the operating temperature. Two factors contribute to this effect: 1) the thermally excited SBS noise increases with temperature as described by Eq. (5) and more significantly 2) radiative cooling in a forced air cooling scheme begins to dominate at the higher temperatures over convective cooling and consequently tempers the increase in the thermal gradient. For our configuration, our simulations show that for temperatures exceeding 500○C, the output power begins to be SBS limited on the left side of the peak value as well. This area is shaded green in Fig. 11. For a fiber with a maximum operating temperature of 620○C, the signal output is SBS limited for all low and high values of h covering our range of simulations.
To illustrate the role of radiative cooling, we selected two scenarios. One corresponding to h = 21W/m2K and a maximum average core temperature that was allowed to reach approximately 600○C, and the other one corresponding to h = 81 W/m2K and average core temperature of 425○C. Based on our simulations, both of these scenarios are SBS limited and provide the same output power. However, as can be inferred from the spatial temperature profile in Fig. 13 , the maximum thermal gradient (which in a counter-pump configuration lies at the output end) is comparable. This is due to the dominance of radiative cooling with its quartic dependence on temperature over convective cooling at the higher temperatures. As the input end of the fiber is approached, it is clear the thermal gradients for the two cases are noticeably different. However, since the Stokes gain is considerably higher at the output end of the fiber, the thermal gradient developed in that region plays the main role in determining the SBS threshold. This analysis should also hold true for conventional fibers.
We also examined the benefits of utilizing an acoustic index gradient in a PCF amplifier similar to the work performed in conventional fibers where a suppression factor of approximately 7 dB was obtained at high power . Of particular interest is whether the acoustic index gradient works in conjunction with the thermal gradient. Previous work on modeling fibers with acoustic index gradients have focused on the transverse overlap between the optical and acoustic modes with little consideration for the evolution of the Stokes spectrum along the longitudinal direction of the fiber as determined by the coupled nonlinear system of equations [12,30]. These approaches would be inadequate for conducting theoretical studies of thermal effects in acoustically tailored fibers.
We investigated this problem using a different approach where the form of the overlap integral as described by Eq. (3) was kept the same. In our work, the transverse gradient was accounted for by making a function of the transverse position as it appears in Eq. (4). In the work described in ref , experimental measurements indicated that the acoustic velocity varied linearly in the transverse direction from a value of 5650 m/s to 5850 m/s in a conventional fiber with comparable dimensions to our PCF. We used these values in our simulations. In order to capture the entire spectrum of Stokes light due to both the longitudinal and transverse variations, we launched a sufficient number of Stokes such that all resonance frequencies in the fiber lie well within this range. Furthermore, the resolution of the spectrum was refined until numerical convergence was achieved.
Four cases were compared: I) PCF at constant temperature (no thermal gradient). II) PCF with thermal gradient allowing for a maximum temperature of 250○C while optimizing the h value for maximum output power (this corresponds to h~110 200 W/m2K as can be seen from Fig. 11) III) PCF with transverse acoustic gradient at constant temperature IV) PCF with both transverse acoustic gradient and thermal gradient induced through quantum defect heating with h value corresponding to case II. The results are plotted in Fig. 14 . The signal power in the plot is normalized with respect to the output power for case I.
It is worthy to note in Fig. 14 the relatively slow rise in reflectivity near the SBS threshold for the two cases with thermal gradients relative to the two constant temperature cases. This is because an increase in power leads to an increase in the thermal gradient, which in turn tends to temper the increase in reflectivity as a function of power. Nevertheless, we use 1% reflectivity as a nominal measure of the SBS threshold. As can be seen from the figure, the transverse acoustic fiber at constant temperature (case III) possesses an SBS threshold that is slightly more than five times (~7 dB) that of case I which is in general agreement with the experimental results. However, comparison of cases II and IV reveals that relatively marginal benefit (much smaller than the product of the two suppression factors) is obtained by utilizing the thermal and the transverse acoustic gradients in conjunction. This is due to the overlap of the resonant Brillouin frequencies due to the acoustic gradient with the resonant frequencies due to the thermal gradient as the Stokes light propagates along the fiber.
This problem can possibly be overcome by exploiting the draw and stack technique currently used to fabricate PCFs. As mentioned in section 2, the PCF core used in our experiments consisted of 7 segments. It is conceivable that these segments can be properly doped such that the optical indices in all segments are matched while having the Brillouin shift frequencies sufficiently separated to effectively accommodate any frequency smearing resulting from the temperature gradient.
In summary, we have demonstrated and characterized SBS-free operation of a single frequency PCF with an output power of 260 W. Measurements of the beam quality and linewidth were conducted. A pump probe technique provided an approximate value of 68 MHz for the Brillouin gain bandwidth and revealed the existence of secondary gain peaks. Our numerical results indicated that with appropriate thermal management, this single frequency amplifier can provide an output power approaching 1 KW. Furthermore, we found that the SBS threshold levels off regardless of the operating temperature of the polymer coating. We also used our model to study the SBS mitigation factor when the thermal gradient is used in conjunction with an acoustic index of refraction gradient and found relatively marginal increase in the SBS threshold. These latter conclusions also hold true for conventional fibers.
This work was partially funded by the High Energy Laser Joint Technology Office (HEL-JTO) and the Air Force Office of Scientific Research (AFOSR). We thank Tim Newell for help with the linewidth measurements and Tom Shay for fruitful discussions.
References and links
1. Y. Jeong, J. K. Sahu, D. N. Payne, and J. Nilsson, “Ytterbium-doped large-core fiber laser with 1 KW of continous-wave ouput power,” Electron. Lett. 40(8), 470–472 (2004). [CrossRef]
4. C. A. Denman, P. D. Hellman, G. T. Moore, J. M. Telle, J. D. Drummond, and A. L. Tuffli, “20 W CW 589 nm sodium beacon excitation source for adaptive optical telescope applications,” Opt. Mater. 26(4), 507–513 (2004). [CrossRef]
5. E. Rochat, K. Haroud, and R. Dändliker, “High power Nd-doped fiber amplifier for coherent intersatellite links,” J. Quantum Electron. 35(10), 1419–1423 (1999). [CrossRef]
6. D. Kracht, R. Wilhelm, M. Frede, C. Fallnich, F. Seifert, B. Willke, and K. Danzmann, “High power single- frequency laser for gravitational wave detection,” in Advanced Solid-State Photonics, Technical Digest Optical Society of America, paper WE1 (2006).
8. 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,” in Fiber Lasers IV: Technology, Systems, and Applications,” Proc. SPIE 6453, 64531F (2007). [CrossRef]
9. Y. Jeong, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, L. M. B. Hickey, and P. W. Turner, “Power scaling of single frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500 W,” IEEE J. Sel. Top. Quantum Electron. 13(3), 546–551 (2007). [CrossRef]
10. A. Wada, T. Nozawa, D. Tanaka, and R. Yamauchi, “Suppression of SBS by intentionally induced periodic residual-strain in single-mode optical fibers,” in Proc. of 17th ECOC, paper B1.1 (1991).
11. P. D. Dragic, C. H. Liu, G. C. Papen, and A. Galvanauskas, “Optical Fiber with an Acoustic Guiding Stimulated Brillouin Scattering Suppression,” in Conference on lasers and Electro-Optics (CLEO), paper CThZ3 (2005).
12. M. J. Li, X. Chen, J. Wang, S. Gray, A. Liu, J. A. 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(13), 8290–8299 (2007). [CrossRef] [PubMed]
13. 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,” in Fiber Lasers V: Technology, Systems, and Applications,” Proc. SPIE 6873, 68730N (2008). [CrossRef]
14. I. Dajani, C. Zeringue, T. J. Bronder, T. Shay, A. Gavrielides, and C. Robin, “A theoretical treatment of two approaches to SBS mitigation with two-tone amplification,” Opt. Express 16(18), 14233–14247 (2008). [CrossRef] [PubMed]
15. I. Dajani, C. Zeringue, and T. Shay, “Investigation of nonlinear effects in multitone-driven narrow linewidth high-power amplifiers,” IEEE J. Sel. Top. Quantum Electron. 15(2), 406–414 (2009). [CrossRef]
16. C. Zeringue, I. Dajani, C. Lu, A. Lobad, and C. Vergien, “Experimental verification of two-tone amplification in single frequency fiber amplifiers,” in Nonlinear Optics: Materials, Fundamentals and Applications (NLO), paper PDPA2 (2009).
18. M. Hildebrandt, M. Frede, P. Kwee, B. Willke, and D. Kracht, “Single-frequency master-oscillator photonic crystal fiber amplifier with 148 W output power,” Opt. Express 14(23), 11071–11076 (2006). [CrossRef] [PubMed]
19. D. Baney, and W. Sorin, “High Resolution Optical Frequency analysis,” in Fiber Optic Test and Measurement, edited by D. Derickson (Prentice-Hall, 1998).
20. M. Hildebrandt, S. Büsche, P. Wessels, M. Frede, and D. Kracht, “Brillouin scattering spectra in high-power single-frequency ytterbium doped fiber amplifiers,” Opt. Express 16(20), 15970–15979 (2008). [CrossRef] [PubMed]
21. P. Dainese, P. St. Russell, N. Joly, J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin Scattering from multi-GHZ-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2(6), 388–392 (2006). [CrossRef]
22. J. C. Beugnot, T. Sylvestre, D. Alasia, H. Maillotte, V. Laude, A. Monteville, L. Provino, N. Traynor, S. F. Mafang, and L. Thévenaz, “Complete experimental characterization of stimulated Brillouin scattering in photonic crystal fiber,” Opt. Express 15(23), 15517–15522 (2007). [CrossRef] [PubMed]
23. K. Furusawa, Z. Yusoff, F. Poletti, T. M. Monro, N. G. R. Broderick, and D. J. Richardson, “Brillouin characterization of holey optical fibers,” Opt. Lett. 31(17), 2541–2543 (2006). [CrossRef] [PubMed]
26. P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-doped fiber amplifiers: Fundamentals and Technology (Academic press 1999).
27. G. Agrawal, Nonlinear Fiber Optics, Third Edition (Academic Press 2001).
28. C. T. Hsu, P. Cheng, and K. W. Wong, “A lumped-parameter model for stagnant thermal conductivity of spatially periodic porous media,” J. Heat Transfer 117(2), 264–269 (1995). [CrossRef]
30. J. K. Sahu, S. Yoo, A. J. Boyland, A. S. Webb, M. Kalita, J. Maran, Y. Jeong, J. Nilsson, W. A. Clarkson, and D. N. Payne, ““Fiber design for high-power lasers,” Fiber Lasers VI: Technology, Systems, and Applications,” Proc. SPIE 7195, 71950I (2009). [CrossRef]