A novel monolithic fiber-optic chirped pulse amplification (CPA) system for high energy, femtosecond pulse generation is proposed and experimentally demonstrated. By employing a high gain amplifier comprising merely 20 cm of high efficiency media (HEM) gain fiber, an optimal balance of output pulse energy, optical efficiency, and B-integral is achieved. The HEM amplifier is fabricated from erbium-doped phosphate glass fiber and yields gain of 1.443 dB/cm with slope efficiency >45%. We experimentally demonstrate near diffraction-limited beam quality and near transform-limited femtosecond pulse quality at 1.55 µm wavelength. With pulse energy >100 µJ and pulse duration of 636 fs (FWHM), the peak power is estimated to be ~160 MW. NAVAIR Public Release Distribution Statement A-“Approved for Public release; distribution is unlimited”.
© 2013 Optical Society of America
Fiber-optic chirped pulse amplification (CPA) systems are highly attractive as femtosecond class laser pulse sources for practical applications, such as industrial micromachining, owing to the excellent laser stability, reliability and thermal management enabled by the fiber format. Nonetheless, pulse energy output increase beyond a few microjoules has been constrained by the necessarily high peak irradiance and resultant distortion of pulses during amplification in single mode fibers. We herein describe and experimentally demonstrate a novel fiber amplifier approach that can substantially increase the pulse energy generating capability of monolithic fiber CPA systems. Our approach employs a short length, highly doped gain fiber to achieve an optimal balance of output pulse energy, pulse quality, and slope efficiency.
In this first section, we review the benefits and challenges of working in the monolithic fiber-optic CPA format and describe the fiber amplifier innovations that have occurred to date—primarily by enlarging the fiber effective mode area (Aeff)—to increase pulse energy output. In the next section, we propose and analyze a novel approach to increasing pulse energy output by dramatically reducing the total length of the fiber amplifier in order to reduce the accumulated nonlinear phase. In the third section, we reveal experimental data for the first demonstration of high energy femtosecond pulse generation using an optimized, short length fiber amplifier. The analyses and demonstrations confirm the efficacy of this approach and indicate that much greater pulse energy scaling is feasible in this form factor.
Not long after the invention of the laser, optical fiber waveguides were identified as an attractive and efficient medium for the implementation of optical amplifiers in laser systems . The benefits include ease of fabrication and assembly, good environmental stability and reliability, well controlled overlap between optical power and active media, high design flexibility, superior spatial mode quality, and the availability of efficient glass hosts as well as active ions [2–5]. The continuing symbiotic advancement of optical fibers (where a smaller doped core is surrounded by a larger mode-confining cladding) and highly efficient pump sources, such as high brightness, fiber coupled laser diodes  and high power Raman fiber lasers , continues to trigger both research and commercialization of high power fiber lasers [8–12]. Meanwhile, monolithic fiber-optic femtosecond fiber laser systems now offer pulse energy up to 100 microjoules (µJ) using the CPA scheme with large mode area (LMA) erbium-doped (Er-doped) fiber amplifiers with Aeff up to 1060 µm2 [13,14].
In high value, precision manufacturing systems, increased energy in femtosecond pulses enables cutting and drilling through thicker materials at faster rates without imparting a heat-affected zone. Generating this femtosecond beam with a monolithic fiber-optic system provides the most compact and stable form factor. The energy scaling of femtosecond fiber laser systems, however, is limited by the temporal pulse distortion caused by self-phase modulation (SPM) as the pulses propagate through the system amplifiers. The magnitude of SPM is quantified by the B-Integral [15,16] and is proportional to both the beam irradiance inside the amplifier and the propagation length, as shown by Eq. (1).17–19].
The typical approach to postponing the onset of nonlinear pulse distortion in fiber amplifiers is to increase Aeff proportional to the desired output pulse energy. That is, to keep B < π, the guided mode diameter would increase to sustain a sufficiently low peak irradiance inside the fiber. However, in order to maintain a diffraction-limited spatial beam quality, these large Aeff fibers have to be designed and operated so as to ensure robust single-mode condition. Conventional step-index and other types of single-mode fibers can be adapted to provide a very large Aeff by simultaneously increasing core diameter and decreasing core numerical aperture (NA). In practice, these low-NA fibers comprise very weak waveguides that are extremely sensitive to fiber bending (coiling) or other modest mechanical disturbance. Recent progress toward larger Aeff fibers has focused on exotic fiber structures that attempt to address mode stability and other issues.
Most efforts to develop LMA waveguides have focused on approaches such as low NA photonic crystal fiber [20–26], leakage channel fiber [27,28], chirally-coupled core fiber [29–31], large-pitch fiber [32,33], and distributed mode filtering rod fiber . These established approaches all operate in the fundamental fiber mode (LP0,1) which suffers from bend-induced reductions in the mode size and increases in modal instability. These become increasingly pronounced as the mode size is increased , and for Aeff >1000 µm2 the LMA fiber must be kept straight . This may be accomplished by making the fiber into a rigid rod with typical diameter of 1.5 mm or more [37,38]. These rods are limited in length to ~1 m, however, due to practical packaging constraints.
It has been demonstrated that these traditional LMA fiber limitations may be overcome by using a higher-order mode (HOM) fiber amplifier due to its scalable mode size, resistance to bend-induced mode size reductions, and superior stability [39,40]. Nonetheless, reconversion of the mode back to LP0,1 with high energy at the amplifier output is a remaining challenge for the HOM approach in CPA systems.
Due to these limitations, progress towards practical fibers with Aeff >>1000 µm2 has stagnated in recent years, putting a ceiling on femtosecond pulse energy from practical fiber-optic, linear CPA systems at a few tens of microjoules. The slow progress here contrasts the enormous advancement made in high power, continuous wave (CW) and longer pulse fiber lasers as a whole. Since optical fibers feature small diameter waveguides to retain their single mode characteristics, there is an inherent disadvantage with respect to energy scaling when compared to the alternative bulk-optics laser rod or thin disk geometry. Nonetheless, the overwhelming size, weight, and power advantages of monolithic fiber-optic femtosecond laser systems offer compelling motivation to resolve the energy scaling challenge. In a break from conventional thinking, we propose a novel amplifier concept that better optimizes amplifier efficiency, mode area, fiber length and B-integral to achieve high energy, excellent pulse and beam quality, and adequate thermal management.
2. HEM fiber amplifiers for high energy CPA systems
As revealed by Eq. (1), the B-integral is proportional to both the peak irradiance of the pulse and the amplifier fiber length. In order to reduce the amplifier fiber length while maintaining the required signal gain, the amplifier gain per unit length must be increased by doping the fiber with higher active ion concentration. For example, Fig. 1 shows the optimal fiber length at which the amplifier reaches its highest gain, as a function of erbium doping concentration (up to 23.8 × 1025 ions/m3). The solid line shows the result of a simulation using Liekki application designer (LAD) software, and the open squares show experimental data for Er-doped silica fibers with doping concentrations of 1.22 × 1025 ions/m3, 1.74 × 1025 ions/m3, 1.94 × 1025 ions/m3, and 2.4 × 1025 ions/m3. In all cases, the signal input to the amplifier was 18.7 mW at 100 kHz pulse repetition rate and 1552.5 nm center wavelength. All fibers are core-pumped with 39 W at 1480 nm from a single mode fiber laser. Both the signal and the pump propagate in the fiber fundamental mode.
It is clear that increasing the erbium doping concentration results in decrease for the optimal fiber length. The shape of the curve does not depend significantly on the actual size or NA of the fiber core. Although, in practice, optimized amplifier performance relies upon injecting the appropriate input pump and signal fluence. In addition, varying the active ion cluster parameter does not have an obvious impact on the simulation curve shown in Fig. 1.
Historically, a ceiling on erbium doping concentration at about 4.0 × 1025 ions/m3 in silica glass LMA fibers has been imposed by strong ion clustering effects, where the close spatial proximity of erbium ions leads to cooperative energy coupling into transitions that are parasitic to the laser transition efficiency [13,14,41]. Owing to these ion-ion interactions at high erbium concentration, the upper laser level (4I13/2) lifetime decreases when pump power is increased, further degrading amplifier efficiency [42,43]. In an alternative to the situation with silica fiber, the undesirable effects of high concentration of erbium, or other rare-earth (RE) ions, can be minimized by using a high efficiency medium (HEM) as host. Phosphate glass is the presently considered HEM host due to its high solubility of RE ions and weak ion-ion interactions [44–50]. The reduction of clustering phenomena substantially improves amplifier efficiency when the optimized fiber length must balance gain vs. B-integral.
Figure 2 shows a comparison of the simulated output signal power and corresponding B-integral vs. the fiber length for an Er-doped silica fiber (a) and an Er-doped HEM fiber (b). The silica fiber has an erbium doping concentration of 4.0 × 1025 ions/m3 with 9.2% clustering and core/clad diameters of 20/125 µm (nLight LIEKKITM Er120-20/125DC). The HEM fiber has an erbium doping concentration of 2.38 × 1026 ions/m3 with 7.2% clustering and core/clad diameters of 25/125 µm. In the LAD software, the cluster concentration parameter was used to account for clustering of the Er ions, which acts as a loss mechanism for excited-state population generation [51,52]. The clustering parameter is found empirically by anchoring the simulation curve to experimental data. Although the erbium concentration of the HEM fiber is 6 × higher than that of the silica fiber, its clustering remains lower. Both cases use the same core pump source (39 W at 1480 nm) and input signal level (18.7 mW at 100 kHz and 1552.5 nm with 1.4 ns pulse duration).
In Fig. 2, the blue dashed lines show a practical ceiling for the B-integral at π radians, below which pulse distortion remains tolerable . The red dashed lines point to the output signal power at this B-integral limit. With 6 × the erbium concentration of the silica fiber, the HEM fiber is capable of providing much higher output power—14.4 W for HEM compared with 7.4 W for silica fiber with B-integral of π radians—owing to the optimized balance of gain, efficiency and B-integral. The pump-to-signal efficiency for the Er-doped HEM fiber is 38% (output signal power divided by pump power). The conventional Er-doped silica fiber retains merely 19% efficiency.
Figure 3 illustrates the pump-to-signal efficiency vs. erbium concentration for silica glass fiber amplifiers (red line and symbols) as well as HEM phosphate glass fiber amplifiers (blue line and symbols) at their optimal fiber lengths. The simulation data (solid lines) show performance for the amplification of a CW laser signal in high erbium density glass fiber with 25 μm core diameter using LAD software. These cases use the same core pump source (39 W at 1480 nm) and input signal level (18.7 mW at 1552.5 nm).
The clustering parameters for the fibers in the simulation were adjusted at each erbium concentration by anchoring the simulation curves with the experimentally measured pump-to-signal efficiency values (open symbols). Background losses of 0.04 dB/m and 3 dB/m  were assumed for the silica fibers and HEM phosphate fibers, respectively. As revealed in Fig. 3, the pump-to-signal efficiency of the silica fiber decreases rapidly with increasing erbium concentration, right up to the erbium concentration ceiling (previously identified as ~4.0 × 1025 ions/m3) where the efficiency is less than 30%. For the silica fiber, the total background loss is negligible and does not have a significant impact on the simulation results. For the HEM fibers, however, the higher background loss of 3 dB/m has a notable impact on the pump-to-signal efficiency. This is particularly true for the lower erbium concentration HEM fibers due to their longer optimal fiber length. The phosphate fiber background loss has weak erbium concentration dependence. As a consequence, the pump-to-signal efficiency of the HEM fiber increases with erbium doping concentration up to 1.2 × 1025 ions/m3, before decreasing with further concentration increase. Here, the corresponding optimal fiber length is 0.4 m. Further improvements in background loss in HEM fiber are possible and are under investigation.
Based on these analyses, the heavily RE doped HEM phosphate glass fiber has the potential for greatly reducing the length of a fiber amplifier. This is key to minimizing the B-integral while maintaining high optical efficiency. Due to its greatly reduced length, the HEM amplifier fiber will sustain equivalent B-integral at much smaller core size versus the necessarily longer silica fibers. Due to its shorter fiber length (on the order of a few tens of cm), the HEM fiber may not require coiling to achieve a compact form factor. This straightened layout introduces two benefits: (1) reduced mode area disturbance, hence a more stable mode quality, and (2) no bend-induced reduction in the effective mode size .
In the following section, we experimentally demonstrate the first Er-doped HEM fiber in a high energy, fiber CPA system. This system generates near-diffraction limited, fully compressed femtosecond pulses with 102 µJ of energy and 636 fs (FWHM) pulse duration (~160 MW peak power) at 1.55 µm. The CPA architecture implements a 20 cm long, heavily Er-doped (2.38 × 1026 ions/m3) HEM phosphate glass fiber with Aeff = 310 µm2. This novel, short length HEM fiber CPA technology opens a new direction for pulse energy maximization in industrial femtosecond laser systems. With increases in the core size, HEM fiber amplifiers may enable femtosecond fiber laser systems with millijoule level pulse energy in the near future.
3. Experimental demonstration of the HEM fiber amplifier
We have experimentally validated the HEM fiber amplifier based CPA system approach and achieved a new performance benchmark for monolithic fiber-optic femtosecond laser system output pulse energy in the linear pulse propagation regime. The HEM Er-doped phosphate fiber was fabricated using a rod-in-tube technique  with an erbium concentration in the core glass of 2.38 × 1026 ions/m3. The core and cladding diameters are 25 µm and 125 µm, respectively, and the fiber core NA = 0.13. The HEM fiber doesn’t have a polymer coating. Assuming a step-index profile, the Aeff for this fiber design is 310 µm2 (simulated by MODE Solutions).
A simplified schematic of the CPA system is displayed in Fig. 4. An all-fiber seed laser module was spliced to a fiber pre-amplifier subsequently providing 18.7 mW at 100 kHz pulse repetition rate and 1.4 ns stretched (chirped) pulse duration. A 10/90 fiber splitter was used to monitor signal input to the HEM fiber amplifier as well as any back-reflected light. The 1480 nm pump light from a Raman fiber laser and the signal were combined by a single mode, high power 1480/1553 nm wavelength division multiplexer (WDM). The WDM output port was fusion spliced and fundamental-mode-matched with the HEM gain fiber which was mounted on a water-chilled aluminum plate. The gain fiber had optimal length of 20 cm (based on its erbium doping concentration), and its output end was spliced to a short length of coreless fiber, angle-polished at 8°, to serve as an end cap. The fiber output beam was collimated, then directed through a spectral band-pass filter to deflect any residual pump light, a quarter-wave plate and half-wave plate pair to align the beam state of polarization (SoP) to the dual-grating compressor, and an optical isolator to protect the amplifier from back-reflections. The output optical spectrum, beam propagation parameter (M2), and beam profile were measured by splitting a small fraction of the output signal beam using a pellicle splitter. Finally, a free-space Treacy grating compressor with groove density of 1200 lines per millimeter was used to compress the pulses. Intensity autocorrelation and optical power were measured at the compressor output.
Figure 5 shows the HEM fiber amplifier output signal average power and corresponding pulse energy at 100 kHz vs. the coupled 1480 nm pump power. With 39 W pump power, the output signal reaches 14.4 W average power and 144 µJ pulse energy. The calculated gain for this condition is 1.443 dB/cm. It should be noted that there is no signal roll-over up to the maximum pump power. Within this range, there is no significant thermal or optical nonlinearity induced efficiency drop. The efficiency derived from the slope of the linear curve fit shown in Fig. 5 is 45%. At the maximum pump power of 39 W, the simple pump-to-signal conversion efficiency is 37%.
Figure 6 shows the measured data used to calculate M2 for the horizontal and vertical (X and Y) planes at the maximum output signal power of 14.4 W and pulse energy of 144 µJ. For a typical LMA fiber amplifier, spatial beam quality would degrade with increased pump power due to increased coupling into higher order modes. This problem is exacerbated with larger core diameter fibers or when the input signal and pump are not launched completely into the fundamental mode (LP0,1) of the gain fiber. For the HEM amplifier, however, the measured M2 values remain very low at just 1.05 and 1.18 in the X and Y directions, respectively. The inset of Fig. 6 shows the beam profile recorded with a CCD camera near focus in the measurement apparatus.
At the HEM fiber amplifier output, a quarter-wave plate and a half-wave plate were sequentially rotated to obtain maximum power (Pmax) and minimum power (Pmin) through the polarization beam splitter (PBS) cube measured by a power meter. The degree of polarization (DoP) is calculated using Eq. (2) following ISO12005 protocol.
Figure 7 shows the HEM amplifier output DoP versus pulse energy. The wave plates were optimized for each data point of Fig. 7. The DoP drops slightly with each increase in amplifier output energy due to increase in un-polarized amplified spontaneous emission (ASE) mixed with the signal pulse train along with modest nonlinear polarization rotation for the chirped pulses [55,56]. Nevertheless, 86% DoP was achieved with the Raman pump at 39 W and corresponding output signal power of 14.4 W. Since the Treacy grating compressor in this demonstration employs multi-layer dielectric diffraction gratings with strong polarization discrimination, the drop in DoP represents a signal loss equal to (1-DoP)/2. At the maximum amplifier output, this comprises a signal loss of 7%.
Figure 8 shows optical spectra of the HEM amplifier input (black line) and output signals at 24 µJ, 55 µJ, 90 µJ and 144 µJ (red, blue, green, and purple lines, respectively). It should be noted that the signal-to-background ratio is higher than 30 dB. In addition, there is only minor spectral broadening at higher energy levels, which is one indication of low nonlinear phase accumulation (or small B-integral value) seen from this high-gain HEM amplifier. The inset of Fig. 8 shows the optical spectrum taken at 144 µJ in linear scale. The estimated total B-integral from the HEM amplifier was just π radians.
Figure 9 shows the background-free, second harmonic generation (SHG) intensity autocorrelation of the 102 µJ pulses output from the system pulse compressor (blue line). Using the optical spectrum measured at 144 µJ (amplifier output), the transform limited pulse FWHM is 563 fs. The FWHM of the measured autocorrelation trace is 978 fs. We have used a sech2 pulse autocorrelation with assumed 0.65 deconvolution factor to estimate the duration of the pulse to be 636 fs, ~1.13x the transform limited pulse FWHM. The estimated peak power of these pulses is ~160 MW. The actual pulse duration may be slightly longer than 636 fs considering the difference between the actual pulse shape and the assumed sech2 shape. Similarly, the actual peak power may be lower than the estimated peak power due to its non sech2 shaped pulse and portion of the energy that lies in the pedestal. Both the transform limited pulse autocorrelation and the theoretical sech2-shaped pulse autocorrelation are included in Fig. 9 for reference (black solid line and red dashed line).
With a relatively small Aeff of only 310 µm2, we have demonstrated an Er-doped HEM fiber amplifier producing >100 µJ pulse energy in the femtosecond regime output from a linear propagation CPA fiber-optic architecture. This matches the pulse energy output capability of state-of-the-art fiber-optic CPA systems with amplifiers leveraging 4 × larger Aeff and adaptive pulse shaping to compensate for SPM-induced pulse distortion . Based on this demonstration, we expect that much higher pulse energy scaling is possible in monolithic fiber-optic CPA systems using this HEM amplifier concept. For example, with similar pump and signal configuration and HEM fiber core diameter increased to 75 µm or beyond, the maximum pulse energy would reach 1 mJ for the equivalent B-integral (π radians). In addition, when coupled with other advancements to manage nonlinear pulse distortion, such as adaptive phase tailoring and longer pulse stretch factor , the maximum pulse energy of these monolithic fiber optic femtosecond laser systems could reach several millijoules in the near future.
B-integral is the key figure of merit that must be minimized when increasing the pulse energy output from fiber CPA systems. Whereas most other energy scaling strategies have reduced B-integral by implementing LMA fiber amplifiers with larger and larger Aeff, those approaches suffer substantial beam quality degradation and practical packaging challenges. In contrast, the presently proposed HEM amplifier approach reduces B-integral by shortening the gain fiber length while maintaining high gain and high efficiency. In order to dramatically reduce fiber length, we employed heavily doped (2.38 × 1026 ions/m3) erbium in phosphate glass, which prevents the parasitic energy loss associated with ion clustering in other types of fibers, e.g. silica. We have experimentally demonstrated the first monolithic fiber-optic CPA system for high energy femtosecond pulse generation using a compact RE-doped HEM fiber amplifier. The HEM erbium phosphate gain fiber was only 20 cm in length with Aeff = 310 µm2, and this fiber was spliced to a standard single mode fiber input pigtail to form a monolithic fiber CPA circuit. The resultant 1.55 µm wavelength laser architecture produced 102 µJ pulse energy with 636 fs pulse duration at 100 kHz repetition rate (10 W average power and ~160 MW peak power). This system output performance was achieved with HEM amplifier B-integral < π radians, putting it in the linear regime of operation where no adaptive pulse shaping was required. It is anticipated that when the HEM fiber amplifier approach is combined with other pulse energy scaling techniques, such as increasing Aeff to >1000 µm2, compensating SPM via pulse shaping, or longer CPA stretch factor, the resultant system should achieve >1 mJ pulse energy in the monolithic fiber-optic format.
Elements of this work were sponsored by Navy Contract N00164-11-C-BT07. NAVAIR Public Release Distribution Statement A-“Approved for Public release; distribution is unlimited”.
References and links
1. C. J. Koester and E. Snitzer, “Amplification in a fiber laser,” Appl. Opt. 3(10), 1182–1186 (1964). [CrossRef]
2. S. B. Poole, D. N. Payne, and M. E. Fermann, “Fabrication of low loss optical fibers containing rare earth ions,” Electron. Lett. 21(17), 737–738 (1985). [CrossRef]
3. S. B. Poole, D. N. Payne, R. J. Mears, M. E. Fermann, and R. Laming, “Fabrication and characterization of low-loss optical fibers containing rare earth ions,” J. Lightwave Technol. 4(7), 870–876 (1986). [CrossRef]
4. S. Tanabe, “Rare-earth-doped glasses for fiber amplifiers in broadband telecommunication,” C. R. Chim. 5(12), 815–824 (2002). [CrossRef]
5. M. J. F. Digonnet, Rare-Earth-Doped Fiber Lasers and Amplifiers (CRC Press, 2001).
6. P. Yalamanchili, V. Rossin, J. Skidmore, K. Tai, X. Qiu, R. Duesterberg, V. Wong, S. Bajwa, K. Duncan, D. Venables, R. Verbera, Y. Dai, J. P. Feve, and E. Zucker, “High-power, high-efficiency fiber-coupled multimode laser-diode pump module (9XX nm) with high reliability,” Proc. SPIE 6876, 687612, 687612-9 (2008). [CrossRef]
7. V. R. Supradeepa, J. W. Nichsolson, C. E. Headley, M. F. Yan, B. Palsdottir, and D. Jakobsen, “A high efficiency architecture for cascaded Raman fiber lasers,” Opt. Express 21(6), 7148–7155 (2013). [CrossRef] [PubMed]
8. D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: current status and future perspective,” J. Opt. Soc. Am. B 27(11), B63–B92 (2010). [CrossRef]
10. H. Sekiguchi, K. Ito, A. Tanaka, H. Yamaura, H. Kan, and K. Ueda, “1 kW output fibre lasers,” Rev. Laser Eng. 31(8), 525–529 (2003). [CrossRef]
12. J. Limpert, A. Liem, H. Zellmer, and A. Tünnermann, “500 W continuous-wave fibre laser with excellent beam quality,” Electron. Lett. 39(8), 645–647 (2003). [CrossRef]
13. M. Mielke, X. Peng, K. Kim, T. Booth, W. Lee, G. Masor, X. Gu, R. Lu, M. Hamamoto, R. Cline, J. Nicholson, J. Fini, X. Liu, A. DeSantolo, P. Westbrook, R. Windeler, E. Monberg, F. DiMarcello, C. Headley, and D. DiGiovanni, “High energy, monolithic fiber femtosecond lasers,” in Conference on Lasers and Electro-Optics Europe/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2013), paper PD-A.3.
14. T. Yilmaz, L. Vaissie, M. Akbulut, D. M. Gaudiosi, L. Collura, T. J. Booth, J. C. Jasapara, M. J. Andrejco, A. D. Yablon, C. E. Headley III, and D. J. DiGiovanni, “Large-mode-area Er-doped fiber chirped-pulse amplification system for high-energy sub-picosecond pulses at 1.55 μm,” Proc. SPIE 6873, 68731I, 68731I-8 (2008). [CrossRef]
15. J. Limpert, F. Roser, T. Schreiber, and A. Tunnermann, “High-power ultrafast fiber laser systems,” IEEE J. Sel. Top. Quantum Electron. 12(2), 233–244 (2006). [CrossRef]
16. A. Galvanauskas, “Ultrashort-pulse fiber amplifiers”, in Ultrafast Lasers: Technology and Applications, eds. M. Fermann, A. Galvanauskas, G. Sucha (Marcel Dekker, 2002), Chapter 4, pp. 155–218.
17. J. Limpert, F. Roser, D. N. Schimpf, E. Seise, T. Eidam, S. Hadrich, J. Rothhardt, C. J. Misas, and A. Tunnermann, “High repetition rate gigawatt peak power fiber laser systems: challenges, design, and experiment,” IEEE J. Sel. Top. Quantum Electron. 15(1), 159–169 (2009). [CrossRef]
18. L. Shah, Z. Liu, I. Hartl, G. Imeshev, G. C. Cho, and M. E. Fermann, “Ultrafast high energy amplifiers beyond the B-integral limit,” Proc. SPIE 6102, 61020Z–1, 61020Z-5 (2006). [CrossRef]
19. S. Zhou, L. Kuznetsova, A. Chong, and F. Wise, “Compensation of nonlinear phase shifts with third-order dispersion in short-pulse fiber amplifiers,” Opt. Express 13(13), 4869–4877 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-13-4869. [CrossRef] [PubMed]
20. J. Limpert, N. Deguil-Robin, I. Manek-Hönninger, F. Salin, F. Röser, A. Liem, T. Schreiber, S. Nolte, H. Zellmer, A. Tünnermann, J. Broeng, A. Petersson, and C. Jakobsen, “High-power rod-type photonic crystal fiber laser,” Opt. Express 13(4), 1055–1058 (2005). [CrossRef] [PubMed]
23. J. C. Knight, R. F. Cregan, P. S. J. Russell, and J. P. de Sandro, “Large mode area photonic crystal fibre,” Electron. Lett. 34(13), 1347–1348 (1998). [CrossRef]
26. K. Hougaard and F. D. Nielsen, “Amplifiers and lasers in PCF configurations,” J. Opt. Fiber Commun. Rep. 1(1), 63–83 (2004). [CrossRef]
27. L. Dong, X. Peng, and J. Li, “Leakage channel optical fibers with large effective area,” J. Opt. Soc. Am. B 24(8), 1689–1697 (2007). [CrossRef]
28. W. S. Wong, X. Peng, J. M. McLaughlin, and L. Dong, “Breaking the limit of maximum effective area for robust single-mode propagation in optical fibers,” Opt. Lett. 30(21), 2855–2857 (2005). [CrossRef] [PubMed]
29. C. Liu, G. Chang, N. Litchinitser, A. Galvanauskas, D. Guertin, N. Jabobson, and K. Tankala, “Effectively single-mode chirally-coupled core fiber,” in Advanced Solid-State Photonics, OSA Technical Digest Series (CD), paper ME2 (2007).
30. A. Galvanauskas, M. C. Swan, and C. Liu, “Effectively single-mode large core passive and active fibers with chirally coupled-core structures,” paper CMB1 at CLEO/QELS (2008).
31. J. Želudevičius, R. Danilevičius, K. Viskontas, N. Rusteika, and K. Regelskis, “Femtosecond fiber CPA system based on picosecond master oscillator and power amplifier with CCC fiber,” Opt. Express 21(5), 5338–5345 (2013). [CrossRef] [PubMed]
32. F. Stutzki, F. Jansen, T. Eidam, A. Steinmetz, C. Jauregui, J. Limpert, and A. Tünnermann, “High average power large-pitch fiber amplifier with robust single-mode operation,” Opt. Lett. 36(5), 689–691 (2011), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-36-5-689. [CrossRef] [PubMed]
33. F. Jansen, F. Stutzki, T. Eidam, J. Rothhardt, S. Hädrich, H. Carstens, C. Jauregui, J. Limpert, and A. Tünnermann, “Yb-doped large pitch fiber with 105µm mode field diameter,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2011, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OTuC5. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2011-OTuC5
34. M. Laurila, M. M. Jørgensen, K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Distributed mode filtering rod fiber amplifier delivering 292W with improved mode stability,” Opt. Express 20(5), 5742–5753 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-5-5742. [CrossRef] [PubMed]
36. J. Li, X. Peng, and L. Dong, “Robust fundamental mode operation in a ytterbium-doped leakage channel fiber with an effective area of ~3000μm2,” in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper ME3.
37. J. Limpert, N. Deguil-Robin, I. Manek-Hönninger, F. Salin, F. Röser, A. Liem, T. Schreiber, S. Nolte, H. Zellmer, A. Tünnermann, J. Broeng, A. Petersson, and C. Jakobsen, “High-power rod-type photonic crystal fiber laser,” Opt. Express 13(4), 1055–1058 (2005). [CrossRef] [PubMed]
38. T. Eidam, J. Rothhardt, F. Stutzki, F. Jansen, S. Hädrich, H. Carstens, C. Jauregui, J. Limpert, and A. Tünnermann, “Fiber chirped-pulse amplification system emitting 3.8 GW peak power,” Opt. Express 19(1), 255–260 (2011). [CrossRef] [PubMed]
39. J. W. Nicholson, J. M. Fini, A. M. DeSantolo, X. Liu, K. Feder, P. S. Westbrook, V. R. Supradeepa, E. Monberg, F. DiMarcello, R. Ortiz, C. Headley, and D. J. DiGiovanni, “Scaling the effective area of higher-order-mode erbium-doped fiber amplifiers,” Opt. Express 20(22), 24575–24584 (2012). [CrossRef] [PubMed]
40. J. W. Nicholson, J. M. Fini, X. Liu, A. DeSantolo, P. Westbrook, R. Windeler, E. Monberg, F. DiMarcello, C. Headley, and D. DiGiovanni, “Single-frequency pulse amplification in a higher-order mode fiber amplifier with fundamental-mode output,” in CLEO: 2013, OSA Technical Digest (online) (Optical Society of America, 2013), paper CW3M.3.
41. J. L. Wagener, P. F. Wysocki, M. J. F. Digonnet, H. J. Shaw, and D. J. Digiovanni, “Effects of concentration and clusters in erbium-doped fiber lasers,” Opt. Lett. 18(23), 2014–2016 (1993). [CrossRef] [PubMed]
42. B. C. Hwang, S. Jiang, T. Luo, J. Watson, G. Sorbello, and N. Peygham-barian, “Cooperative upconversion and energy transfer of new high Er - and Yb –Er -doped phosphate glasses,” J. Opt. Soc. Am. B 17(5), 833–839 (2000). [CrossRef]
43. E. Delevaque, T. Georges, M. Monerie, P. Lamouler, and J. F. Bayon, “Modeling of pair induced quenching in erbium doped silica fibers,” IEEE Photon. Technol. Lett. 5(1), 73–75 (1993). [CrossRef]
44. S. Jiang, M. J. Myers, and N. Peyghambarian, “Er doped phosphate glasses and lasers,” J. Non-Cryst. Solids 239(1-3), 143–148 (1998). [CrossRef]
45. V. P. Gapontsev, S. M. Matitsin, A. A. Isineev, and V. B. Kravchenko, “Erbium glass lasers and their applications,” Opt. Laser Technol. 14(4), 189–196 (1982). [CrossRef]
46. A. Chavez-Pirson, “Highly doped phosphate glass fibers for fiber lasers and amplifiers with applications,” Proc. SPIE 7839, 78390K-1–1, 78390K-4 (2010). [CrossRef]
47. D. T. Nguyen, A. Chavez-Pirson, S. Jiang, and N. Peyghambarian, “A novel approach of modeling cladding-pumped highly Er/Yb co-doped fiber amplifiers,” IEEE J. Quantum Electron. 43(11), 1018–1027 (2007). [CrossRef]
48. A. Polynkin, D. Panasenko, N. Peyghambarian, and J. V. Moloney, “All-fiber picoseconds laser system at 1.5 µm based on amplification in short and heavily doped phosphate-glass fiber,” IEEE Photon. Technol. Lett. 18(21), 2194–2196 (2006). [CrossRef]
49. W. Shi, E. B. Petersen, M. Leigh, J. Zong, Z. Yao, A. Chavez-Pirson, and N. Peyghambarian, “High SBS-threshold single-mode single-frequency monolithic pulsed fiber laser in the C-band,” Opt. Express 17(10), 8237–8245 (2009). [CrossRef] [PubMed]
50. W. Shi, E. B. Petersen, Z. Yao, D. T. Nguyen, J. Zong, M. A. Stephen, A. Chavez-Pirson, and N. Peyghambarian, “Kilowatt-level stimulated-Brillouin-scattering-threshold monolithic transform-limited 100 ns pulsed fiber laser at 1530 nm,” Opt. Lett. 35(14), 2418–2420 (2010). [CrossRef] [PubMed]
51. E. Delevaque, T. Georges, M. Monerie, P. Lamouler, and J. F. Bayon, “Modeling of pair-induced quenching in erbium doped silicate fibers,” IEEE Photon. Technol. Lett. 5(1), 73–75 (1993). [CrossRef]
52. P. Myslinki, D. Nguyen, and J. Chrostowski, “Effect of concentration on the performance of erbium-doped fiber amplifiers,” J. Lightwave Technol. 15(1), 112–120 (1997). [CrossRef]
53. Y. W. Lee, M. J. F. Digonnet, S. Sinha, K. E. Urbanek, R. L. Byer, and S. Jiang, “High-power Yb3+-doped phosphate fiber amplifier,” IEEE J. Sel. Top. Quantum Electron. 15(1), 93–102 (2009). [CrossRef]
54. X. Wang, Q. Nie, T. Xu, and L. Liu, “A review of the fabrication of optic fiber,” Proc. SPIE 6034, 60341D, 60341D-9 (2006). [CrossRef]
56. F. Doutre, D. Pagnoux, V. Couderc, A. Tonello, B. Vergne, and A. Jalocha, “Large temporal narrowing of subnanosecond pulses in a low-birefringence optical fiber,” Opt. Lett. 33(16), 1789–1791 (2008). [CrossRef] [PubMed]